diff --git a/.gitignore b/.gitignore --- a/.gitignore +++ b/.gitignore @@ -1,6 +1,6 @@ # gitignore for Conjure # -# Part of Conjure, Copyright 2021 Rudy Matela, +# Part of Conjure, Copyright 2021-2024 Rudy Matela, # distribued under the 3-clause BSD license. # temporary files @@ -33,6 +33,7 @@ eg/bools eg/count eg/dupos +eg/either eg/factorial eg/fibonacci eg/fib01 @@ -41,6 +42,8 @@ eg/ints eg/gcd eg/list +eg/maybe +eg/oddeven eg/pow eg/tapps eg/tree @@ -54,11 +57,11 @@ bench/longshot bench/ill-hit bench/take-drop -bench/lots bench/p12 bench/p30 bench/candidates bench/redundants +bench/erroneous bench/gps bench/gps2 bench/lowtests @@ -68,6 +71,6 @@ test/expr test/conjurable test/utils -test/cases test/defn test/derive +test/red diff --git a/LICENSE b/LICENSE --- a/LICENSE +++ b/LICENSE @@ -1,4 +1,4 @@ -Copyright (c) 2021, Rudy Matela +Copyright (c) 2021-2024, Rudy Matela All rights reserved. diff --git a/Makefile b/Makefile --- a/Makefile +++ b/Makefile @@ -14,6 +14,7 @@ eg/arith \ eg/count \ eg/dupos \ + eg/either \ eg/factorial \ eg/fibonacci \ eg/fib01 \ @@ -23,6 +24,8 @@ eg/bools \ eg/gcd \ eg/list \ + eg/maybe \ + eg/oddeven \ eg/pow \ eg/replicate \ eg/setelem \ @@ -34,6 +37,7 @@ eg/bst \ bench/candidates \ bench/redundants \ + bench/erroneous \ bench/ill-hit \ bench/longshot \ bench/lowtests \ @@ -51,21 +55,30 @@ test/expr \ test/defn \ test/conjurable \ + test/derive \ + test/red \ test/utils all: mk/toplibs all-all: all $(EG) $(TESTS) -test: $(TESTS) $(patsubst %,%.run,$(TESTS)) diff-test test-sdist +test: test-makefile $(TESTS) $(patsubst %,%.run,$(TESTS)) diff-test test-sdist +ghci: src/Conjure.ghci + +tags: src test/Test.hs + hasktags $^ + +# Disclaimer: This bench target is not intended to generate paper-grade runtime +# datapoints as it runs each benchmark just once. This target is +# meant to track large runtime changes across different git +# versions. .PHONY: bench bench: $(EG) $(patsubst %,%.bench,$(EG)) @mkdir -p bench/runtime/$$HOSTNAME ./bench/versions | tee bench/runtime/$$HOSTNAME/versions -ghci: src/Conjure.ghci - %.bench: % @mkdir -p bench/runtime/$$HOSTNAME/`dirname $<` @printf "%-18s " $< @@ -73,13 +86,17 @@ python3 -c 'print("%.1f" % float(input()))' | \ tee bench/runtime/$$HOSTNAME/$<.runtime -diff-test: $(EG) $(patsubst %,%.diff-test,$(EG)) +diff-test: $(EG) $(patsubst %,%.diff,$(EG)) -out: $(EG) $(patsubst %,%.out,$(EG)) +out: txt +txt: $(EG) $(patsubst %,%.txt,$(EG)) + test-sdist: ./test/sdist +test-makefile: test/mk.run + test-via-cabal: cabal configure --enable-tests --enable-benchmarks --ghc-options="$(GHCFLAGS) -O0" cabal build @@ -97,15 +114,15 @@ %.run: % ./$< -%.out: % - ./$< >$<.out +%.txt: % + ./$< >$<.txt -%.diff-test: % - ./$< | diff -rud $<.out - +%.diff: % + ./$< | diff -rud $<.txt - # lists files missing copyright notices list-missing-copyright: - grep -LRE '(Copyright|\(C\))' `git ls-tree -r master --name-only | grep -vE '(\.(runtime|out)|versions|toplibs|(Toplibs|All)\.hs|depend.mk)$$'` || true + grep -LRE '(Copyright|\(C\))' `git ls-tree -r master --name-only | grep -vE '(\.(runtime|txt)|versions|toplibs|(Toplibs|All)\.hs|depend.mk)$$'` || true # NOTE: (very hacky!) the following target allows parallel compilation (-jN) of # eg and test programs so long as they don't share dependencies _not_ stored @@ -133,5 +150,10 @@ gps2-each: bench/gps2 for i in {1..25}; do ./bench/time ./bench/gps2 $$i; done +ls-eg: + @for eg in $(EG); do echo $$eg; done + +ls-test: + @for test in $(TESTS); do echo $$test; done include mk/haskell.mk diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -347,7 +347,7 @@ [PushGP]: https://github.com/lspector/Clojush [G3P]: https://github.com/t-h-e/HeuristicLab.CFGGP -[PushGP] (2002) and [G3P] (2017) are genetic programming systems +[PushGP] (2002) and [G3P] (2017) are genetic programming systems that are able to synthesize programs in Push and Python respectively. Differently from Conjure or MagicHaskeller, they require around a hundred tests for traning @@ -368,7 +368,7 @@ contains more than 60 examples of use. -Conjure, Copyright 2021 Rudy Matela, +Conjure, Copyright 2021-2024 Rudy Matela, distribued under the 3-clause BSD license. diff --git a/Setup.hs b/Setup.hs --- a/Setup.hs +++ b/Setup.hs @@ -1,5 +1,5 @@ -- Setup.hs for code-conjure / Conjure --- Part of Conjure, Copyright 2021 Rudy Matela, +-- Part of Conjure, Copyright 2021-2024 Rudy Matela, -- distribued under the 3-clause BSD license. import Distribution.Simple main = defaultMain diff --git a/TODO.md b/TODO.md --- a/TODO.md +++ b/TODO.md @@ -3,29 +3,27 @@ A non-exhaustive list of things TO DO for Conjure. -* Review `bench/redundants.out` and prune redundant candidates. - See sections below for ideas. +* improve documentation of `conjureIsDeconstruction`. + Document behaviour outside of function, not inside of it. +* `bench/erroneous`: report number of errors in addition to the example error -## Prune modulo rewriting +* consider non top-level cases -The following is redundant, as only the second equation is necessary: - foo 0 = 0 - foo x = x + x - -Another example is: - - foo 0 = 1 - foo x = x + 1 +## Non top-level cases -The tricky part is when dealing with multiple arguments: +Consider allowing non top-level cases, +so that functions like the following are reachable: - x ? 0 = x - x ? y = x + y + last [] = undefined + last [x] = x + last (x:y:xs) = last (y:xs) -One possible path would be to replace 0 in the second equation -then use the Theory to discover x + 0 is equal to 0. +Perhaps the negative runtime impact would not be so great +given the delayed tiers enumeration, +and we would avoid some `prif` hacks +needed to conjure some functions. This file is part of Conjure, diff --git a/bench/avgs.hs b/bench/avgs.hs --- a/bench/avgs.hs +++ b/bench/avgs.hs @@ -1,6 +1,6 @@ -- Computes averages of several benchmarks -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Data.List import Data.Function diff --git a/bench/bench b/bench/bench --- a/bench/bench +++ b/bench/bench @@ -2,7 +2,7 @@ # # A more elaborate benchmark for p12 and p30 # -# Copyright (C) 2021 Rudy Matela +# Copyright (C) 2021-2024 Rudy Matela # Distributed under the 3-Clause BSD licence (see the file LICENSE). run1() { diff --git a/bench/candidates.hs b/bench/candidates.hs --- a/bench/candidates.hs +++ b/bench/candidates.hs @@ -1,6 +1,6 @@ -- print candidates -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure import Conjure.Engine diff --git a/bench/candidates.out b/bench/candidates.out deleted file mode 100644 --- a/bench/candidates.out +++ /dev/null @@ -1,6739 +0,0 @@ -Candidates for: foo :: Int -> Int - pruning with 15/35 rules - [3,0,7,0,19,0,90,0,454] direct candidates, 0 duplicates - [3,3,8,13,29,52,139,212,629] pattern candidates, 0 duplicates - -rules: -x * y == x + y -x * y == y + x -x - x == 0 -x + 0 == x -0 + x == x -x - 0 == x -(x + y) + z == x + (y + z) -(x + y) + z == y + (x + z) -x - (y - z) == z + (x - y) -(x - y) - z == x - (y + z) -(x - y) - z == x - (z + y) -(x + y) - z == x + (y - z) -(x + y) - z == y + (x - z) -x + (y - x) == y -(x - y) + y == x -equations: -y + x == x + y -y + (x + z) == x + (y + z) -z + (x + y) == x + (y + z) -z + (y + x) == x + (y + z) -y + (x - z) == x + (y - z) -(x - z) + y == x + (y - z) -(z - y) + x == (x - y) + z -y - (x + y) == 0 - x -y - (y + x) == 0 - x -z - (y + z) == x - (x + y) -z - (y + z) == x - (y + x) -z - (z + y) == x - (x + y) -z - (z + y) == x - (y + x) -x + (0 - y) == x - y -(0 - y) + x == x - y -x - (x + 1) == 0 - 1 -x - (1 + x) == 0 - 1 -y - (y + 1) == x - (x + 1) -y - (y + 1) == x - (1 + x) -y - (1 + y) == x - (1 + x) - -direct candidates: - -foo x = x - -foo x = 0 - -foo x = 1 - -foo x = x + x - -foo x = x + 1 - -foo x = 1 + 1 - -foo x = x - 1 - -foo x = 0 - x - -foo x = 0 - 1 - -foo x = 1 - x - -foo x = x + (x + x) - -foo x = x + (x + 1) - -foo x = x + (1 + 1) - -foo x = x + (x - 1) - -foo x = x + (0 - 1) - -foo x = 1 + (x + x) - -foo x = 1 + (x + 1) - -foo x = 1 + (1 + 1) - -foo x = 1 + (0 - x) - -foo x = 1 + (1 - x) - -foo x = x - (x + x) - -foo x = x - (x + 1) - -foo x = x - (1 + 1) - -foo x = 0 - (x + x) - -foo x = 0 - (x + 1) - -foo x = 0 - (1 + 1) - -foo x = 1 - (x + x) - -foo x = 1 - (x + 1) - -foo x = 1 - (1 + 1) - - -pattern candidates: - -foo x = x - -foo x = 0 - -foo x = 1 - -foo 0 = 0 -foo x = 1 - -foo 0 = 1 -foo x = x - -foo 0 = 1 -foo x = 0 - -foo x = x + x - -foo x = x + 1 - -foo x = x - 1 - -foo x = 0 - x - -foo x = 1 - x - -foo 1 = 0 -foo x = x - -foo 1 = 0 -foo x = 1 - -foo 1 = 1 -foo x = 0 - -foo 0 = 0 -foo x = x + x - -foo 0 = 0 -foo x = x + 1 - -foo 0 = 0 -foo x = x - 1 - -foo 0 = 0 -foo x = 0 - x - -foo 0 = 0 -foo x = 1 - x - -foo 0 = 1 -foo x = x + x - -foo 0 = 1 -foo x = x + 1 - -foo 0 = 1 -foo x = x - 1 - -foo 0 = 1 -foo x = 0 - x - -foo 0 = 1 -foo x = 1 - x - -foo 0 = 0 -foo 1 = 0 -foo x = 1 - -foo 0 = 1 -foo 1 = 0 -foo x = x - -foo 0 = 1 -foo 1 = 1 -foo x = 0 - -foo 0 = 0 -foo x = foo (x - 1) - -foo 0 = 0 -foo x = foo (0 - x) - -foo 0 = 0 -foo x = foo (1 - x) - -foo 0 = 1 -foo x = foo (x - 1) - -foo 0 = 1 -foo x = foo (0 - x) - -foo 0 = 1 -foo x = foo (1 - x) - -foo x = x + (x + x) - -foo x = x + (x + 1) - -foo x = x + (x - 1) - -foo x = 1 + (x + x) - -foo x = 1 + (x + 1) - -foo x = 1 + (0 - x) - -foo x = 1 + (1 - x) - -foo x = x - (x + x) - -foo x = x - (x + 1) - -foo x = 0 - (x + x) - -foo x = 0 - (x + 1) - -foo x = 1 - (x + x) - -foo x = 1 - (x + 1) - -foo 1 = 0 -foo x = x + x - -foo 1 = 0 -foo x = x + 1 - -foo 1 = 0 -foo x = x - 1 - -foo 1 = 0 -foo x = 0 - x - -foo 1 = 0 -foo x = 1 - x - -foo 1 = 1 -foo x = x + x - -foo 1 = 1 -foo x = x + 1 - -foo 1 = 1 -foo x = x - 1 - -foo 1 = 1 -foo x = 0 - x - -foo 1 = 1 -foo x = 1 - x - -foo 1 = 0 -foo x = foo (x - 1) - -foo 1 = 0 -foo x = foo (0 - x) - -foo 1 = 0 -foo x = foo (1 - x) - -foo 1 = 1 -foo x = foo (x - 1) - -foo 1 = 1 -foo x = foo (0 - x) - -foo 1 = 1 -foo x = foo (1 - x) - -foo 0 = 0 -foo x = x + (x + x) - -foo 0 = 0 -foo x = x + (x + 1) - -foo 0 = 0 -foo x = x + (x - 1) - -foo 0 = 0 -foo x = 1 + (x + x) - -foo 0 = 0 -foo x = 1 + (x + 1) - -foo 0 = 0 -foo x = 1 + (0 - x) - -foo 0 = 0 -foo x = 1 + (1 - x) - -foo 0 = 0 -foo x = x - (x + x) - -foo 0 = 0 -foo x = x - (x + 1) - -foo 0 = 0 -foo x = 0 - (x + x) - -foo 0 = 0 -foo x = 0 - (x + 1) - -foo 0 = 0 -foo x = 1 - (x + x) - -foo 0 = 0 -foo x = 1 - (x + 1) - -foo 0 = 1 -foo x = x + (x + x) - -foo 0 = 1 -foo x = x + (x + 1) - -foo 0 = 1 -foo x = x + (x - 1) - -foo 0 = 1 -foo x = 1 + (x + x) - -foo 0 = 1 -foo x = 1 + (x + 1) - -foo 0 = 1 -foo x = 1 + (0 - x) - -foo 0 = 1 -foo x = 1 + (1 - x) - -foo 0 = 1 -foo x = x - (x + x) - -foo 0 = 1 -foo x = x - (x + 1) - -foo 0 = 1 -foo x = 0 - (x + x) - -foo 0 = 1 -foo x = 0 - (x + 1) - -foo 0 = 1 -foo x = 1 - (x + x) - -foo 0 = 1 -foo x = 1 - (x + 1) - -foo 0 = 0 -foo 1 = 0 -foo x = x + x - -foo 0 = 0 -foo 1 = 0 -foo x = x + 1 - -foo 0 = 0 -foo 1 = 0 -foo x = x - 1 - -foo 0 = 0 -foo 1 = 0 -foo x = 0 - x - -foo 0 = 0 -foo 1 = 0 -foo x = 1 - x - -foo 0 = 0 -foo 1 = 1 -foo x = x + x - -foo 0 = 0 -foo 1 = 1 -foo x = x + 1 - -foo 0 = 0 -foo 1 = 1 -foo x = x - 1 - -foo 0 = 0 -foo 1 = 1 -foo x = 0 - x - -foo 0 = 0 -foo 1 = 1 -foo x = 1 - x - -foo 0 = 1 -foo 1 = 0 -foo x = x + x - -foo 0 = 1 -foo 1 = 0 -foo x = x + 1 - -foo 0 = 1 -foo 1 = 0 -foo x = x - 1 - -foo 0 = 1 -foo 1 = 0 -foo x = 0 - x - -foo 0 = 1 -foo 1 = 0 -foo x = 1 - x - -foo 0 = 1 -foo 1 = 1 -foo x = x + x - -foo 0 = 1 -foo 1 = 1 -foo x = x + 1 - -foo 0 = 1 -foo 1 = 1 -foo x = x - 1 - -foo 0 = 1 -foo 1 = 1 -foo x = 0 - x - -foo 0 = 1 -foo 1 = 1 -foo x = 1 - x - - -Candidates for: ? :: Int -> Int -> Int - pruning with 10/23 rules - [3,3,6,9,21,39,87,180,390] direct candidates, 0 duplicates - [3,7,22,53,129,313,747,1743,4077] pattern candidates, 0 duplicates - -rules: -x * y == x + y -x * y == y + x -x + 0 == x -0 + x == x -dec (x + y) == x + dec y -dec (x + y) == y + dec x -dec (x + y) == dec x + y -dec (x + y) == dec y + x -(x + y) + z == x + (y + z) -(x + y) + z == y + (x + z) -equations: -y + x == x + y -y + dec x == x + dec y -dec x + y == x + dec y -dec y + x == dec x + y -x + dec 0 == dec x -dec 0 + x == dec x -y + (x + z) == x + (y + z) -z + (x + y) == x + (y + z) -z + (y + x) == x + (y + z) -y + dec (dec x) == x + dec (dec y) -dec (dec x) + y == x + dec (dec y) -x + dec (dec 0) == dec (dec x) -dec (dec 0) + x == dec (dec x) - -direct candidates: - -x ? y = x - -x ? y = y - -x ? y = 0 - -x ? y = dec x - -x ? y = dec y - -x ? y = dec 0 - -x ? y = x + x - -x ? y = x + y - -x ? y = y + y - -x ? y = dec (dec x) - -x ? y = dec (dec y) - -x ? y = dec (dec 0) - -x ? y = dec (dec (dec x)) - -x ? y = dec (dec (dec y)) - -x ? y = dec (dec (dec 0)) - -x ? y = x + dec x - -x ? y = x + dec y - -x ? y = x + dec 0 - -x ? y = y + dec x - -x ? y = y + dec y - -x ? y = y + dec 0 - -x ? y = dec (dec (dec (dec x))) - -x ? y = dec (dec (dec (dec y))) - -x ? y = dec (dec (dec (dec 0))) - -x ? y = x + (x + x) - -x ? y = x + (x + y) - -x ? y = x + (y + y) - -x ? y = x + dec (dec x) - -x ? y = x + dec (dec y) - -x ? y = x + dec (dec 0) - -x ? y = y + (x + x) - -x ? y = y + (x + y) - -x ? y = y + (y + y) - -x ? y = y + dec (dec x) - -x ? y = y + dec (dec y) - -x ? y = y + dec (dec 0) - -x ? y = dec x + dec x - -x ? y = dec x + dec y - -x ? y = dec x + dec 0 - -x ? y = dec y + dec y - -x ? y = dec y + dec 0 - -x ? y = dec 0 + dec 0 - -x ? y = dec (dec (dec (dec (dec x)))) - -x ? y = dec (dec (dec (dec (dec y)))) - -x ? y = dec (dec (dec (dec (dec 0)))) - -x ? y = x + dec (dec (dec x)) - -x ? y = x + dec (dec (dec y)) - -x ? y = x + dec (dec (dec 0)) - -x ? y = x + (x + dec x) - -x ? y = x + (x + dec y) - -x ? y = x + (x + dec 0) - -x ? y = x + (y + dec x) - -x ? y = x + (y + dec y) - -x ? y = x + (y + dec 0) - -x ? y = y + dec (dec (dec x)) - -x ? y = y + dec (dec (dec y)) - -x ? y = y + dec (dec (dec 0)) - -x ? y = y + (x + dec x) - -x ? y = y + (x + dec y) - -x ? y = y + (x + dec 0) - -x ? y = y + (y + dec x) - -x ? y = y + (y + dec y) - -x ? y = y + (y + dec 0) - -x ? y = dec x + (x + x) - -x ? y = dec x + (x + y) - -x ? y = dec x + (y + y) - -x ? y = dec x + dec (dec x) - -x ? y = dec x + dec (dec y) - -x ? y = dec x + dec (dec 0) - -x ? y = dec y + (x + x) - -x ? y = dec y + (x + y) - -x ? y = dec y + (y + y) - -x ? y = dec y + dec (dec x) - -x ? y = dec y + dec (dec y) - -x ? y = dec y + dec (dec 0) - -x ? y = dec 0 + (x + x) - -x ? y = dec 0 + (x + y) - -x ? y = dec 0 + (y + y) - -x ? y = dec 0 + dec (dec x) - -x ? y = dec 0 + dec (dec y) - -x ? y = dec 0 + dec (dec 0) - - -pattern candidates: - -x ? y = x - -x ? y = y - -x ? y = 0 - -x ? y = dec x - -x ? y = dec y - -x ? 0 = x -x ? y = y - -x ? 0 = x -x ? y = 0 - -x ? 0 = 0 -x ? y = x - -0 ? x = x -x ? y = 0 - -0 ? x = 0 -x ? y = y - -x ? y = x + x - -x ? y = x + y - -x ? y = y + y - -x ? y = dec (dec x) - -x ? y = dec (dec y) - -x ? 0 = x -x ? y = dec x - -x ? 0 = x -x ? y = dec y - -x ? 0 = 0 -x ? y = dec x - -x ? 0 = 0 -x ? y = dec y - -x ? 0 = dec x -x ? y = x - -x ? 0 = dec x -x ? y = y - -x ? 0 = dec x -x ? y = 0 - -0 ? x = x -x ? y = dec x - -0 ? x = x -x ? y = dec y - -0 ? x = 0 -x ? y = dec x - -0 ? x = 0 -x ? y = dec y - -0 ? x = dec x -x ? y = x - -0 ? x = dec x -x ? y = y - -0 ? x = dec x -x ? y = 0 - -0 ? x = x -x ? 0 = x -x ? y = 0 - -0 ? x = x -x ? 0 = 0 -x ? y = x - -0 ? x = 0 -x ? 0 = x -x ? y = y - -x ? y = dec (dec (dec x)) - -x ? y = dec (dec (dec y)) - -x ? y = x + dec x - -x ? y = x + dec y - -x ? y = y + dec x - -x ? y = y + dec y - -x ? 0 = x -x ? y = x + x - -x ? 0 = x -x ? y = x + y - -x ? 0 = x -x ? y = y + y - -x ? 0 = x -x ? y = dec (dec x) - -x ? 0 = x -x ? y = dec (dec y) - -x ? 0 = 0 -x ? y = x + x - -x ? 0 = 0 -x ? y = x + y - -x ? 0 = 0 -x ? y = y + y - -x ? 0 = 0 -x ? y = dec (dec x) - -x ? 0 = 0 -x ? y = dec (dec y) - -x ? 0 = dec x -x ? y = dec y - -x ? 0 = x + x -x ? y = x - -x ? 0 = x + x -x ? y = y - -x ? 0 = x + x -x ? y = 0 - -x ? 0 = dec (dec x) -x ? y = x - -x ? 0 = dec (dec x) -x ? y = y - -x ? 0 = dec (dec x) -x ? y = 0 - -0 ? x = x -x ? y = x + x - -0 ? x = x -x ? y = x + y - -0 ? x = x -x ? y = y + y - -0 ? x = x -x ? y = dec (dec x) - -0 ? x = x -x ? y = dec (dec y) - -0 ? x = 0 -x ? y = x + x - -0 ? x = 0 -x ? y = x + y - -0 ? x = 0 -x ? y = y + y - -0 ? x = 0 -x ? y = dec (dec x) - -0 ? x = 0 -x ? y = dec (dec y) - -0 ? x = x + x -x ? y = x - -0 ? x = x + x -x ? y = y - -0 ? x = x + x -x ? y = 0 - -0 ? x = dec (dec x) -x ? y = x - -0 ? x = dec (dec x) -x ? y = y - -0 ? x = dec (dec x) -x ? y = 0 - -0 ? x = x -x ? 0 = x -x ? y = dec x - -0 ? x = x -x ? 0 = x -x ? y = dec y - -0 ? x = x -x ? 0 = 0 -x ? y = dec x - -0 ? x = x -x ? 0 = 0 -x ? y = dec y - -0 ? x = x -x ? 0 = dec x -x ? y = x - -0 ? x = x -x ? 0 = dec x -x ? y = 0 - -0 ? x = 0 -x ? 0 = x -x ? y = dec x - -0 ? x = 0 -x ? 0 = x -x ? y = dec y - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec x - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec y - -0 ? x = 0 -x ? 0 = dec x -x ? y = y - -0 ? x = dec x -x ? 0 = x -x ? y = y - -0 ? x = dec x -x ? 0 = x -x ? y = 0 - -0 ? x = dec x -x ? 0 = 0 -x ? y = x - -x ? 0 = x -x ? y = x ? dec y - -x ? 0 = x -x ? y = y ? dec y - -x ? 0 = x -x ? y = 0 ? dec y - -x ? 0 = x -x ? y = dec x ? x - -x ? 0 = x -x ? y = dec x ? y - -x ? 0 = 0 -x ? y = x ? dec y - -x ? 0 = 0 -x ? y = y ? dec y - -x ? 0 = 0 -x ? y = 0 ? dec y - -x ? 0 = 0 -x ? y = dec x ? x - -x ? 0 = 0 -x ? y = dec x ? y - -0 ? x = x -x ? y = x ? dec y - -0 ? x = x -x ? y = y ? dec y - -0 ? x = x -x ? y = dec x ? x - -0 ? x = x -x ? y = dec x ? y - -0 ? x = x -x ? y = dec x ? 0 - -0 ? x = 0 -x ? y = x ? dec y - -0 ? x = 0 -x ? y = y ? dec y - -0 ? x = 0 -x ? y = dec x ? x - -0 ? x = 0 -x ? y = dec x ? y - -0 ? x = 0 -x ? y = dec x ? 0 - -x ? y = dec (dec (dec (dec x))) - -x ? y = dec (dec (dec (dec y))) - -x ? y = x + (x + x) - -x ? y = x + (x + y) - -x ? y = x + (y + y) - -x ? y = x + dec (dec x) - -x ? y = x + dec (dec y) - -x ? y = y + (x + x) - -x ? y = y + (x + y) - -x ? y = y + (y + y) - -x ? y = y + dec (dec x) - -x ? y = y + dec (dec y) - -x ? y = dec x + dec x - -x ? y = dec x + dec y - -x ? y = dec y + dec y - -x ? 0 = x -x ? y = dec (dec (dec x)) - -x ? 0 = x -x ? y = dec (dec (dec y)) - -x ? 0 = x -x ? y = x + dec x - -x ? 0 = x -x ? y = x + dec y - -x ? 0 = x -x ? y = y + dec x - -x ? 0 = x -x ? y = y + dec y - -x ? 0 = 0 -x ? y = dec (dec (dec x)) - -x ? 0 = 0 -x ? y = dec (dec (dec y)) - -x ? 0 = 0 -x ? y = x + dec x - -x ? 0 = 0 -x ? y = x + dec y - -x ? 0 = 0 -x ? y = y + dec x - -x ? 0 = 0 -x ? y = y + dec y - -x ? 0 = dec x -x ? y = x + x - -x ? 0 = dec x -x ? y = x + y - -x ? 0 = dec x -x ? y = y + y - -x ? 0 = dec x -x ? y = dec (dec x) - -x ? 0 = dec x -x ? y = dec (dec y) - -x ? 0 = x + x -x ? y = dec x - -x ? 0 = x + x -x ? y = dec y - -x ? 0 = dec (dec x) -x ? y = dec x - -x ? 0 = dec (dec x) -x ? y = dec y - -x ? 0 = dec (dec (dec x)) -x ? y = x - -x ? 0 = dec (dec (dec x)) -x ? y = y - -x ? 0 = dec (dec (dec x)) -x ? y = 0 - -x ? 0 = x + dec x -x ? y = x - -x ? 0 = x + dec x -x ? y = y - -x ? 0 = x + dec x -x ? y = 0 - -0 ? x = x -x ? y = dec (dec (dec x)) - -0 ? x = x -x ? y = dec (dec (dec y)) - -0 ? x = x -x ? y = x + dec x - -0 ? x = x -x ? y = x + dec y - -0 ? x = x -x ? y = y + dec x - -0 ? x = x -x ? y = y + dec y - -0 ? x = 0 -x ? y = dec (dec (dec x)) - -0 ? x = 0 -x ? y = dec (dec (dec y)) - -0 ? x = 0 -x ? y = x + dec x - -0 ? x = 0 -x ? y = x + dec y - -0 ? x = 0 -x ? y = y + dec x - -0 ? x = 0 -x ? y = y + dec y - -0 ? x = dec x -x ? y = x + x - -0 ? x = dec x -x ? y = x + y - -0 ? x = dec x -x ? y = y + y - -0 ? x = dec x -x ? y = dec (dec x) - -0 ? x = dec x -x ? y = dec (dec y) - -0 ? x = x + x -x ? y = dec x - -0 ? x = x + x -x ? y = dec y - -0 ? x = dec (dec x) -x ? y = dec x - -0 ? x = dec (dec x) -x ? y = dec y - -0 ? x = dec (dec (dec x)) -x ? y = x - -0 ? x = dec (dec (dec x)) -x ? y = y - -0 ? x = dec (dec (dec x)) -x ? y = 0 - -0 ? x = x + dec x -x ? y = x - -0 ? x = x + dec x -x ? y = y - -0 ? x = x + dec x -x ? y = 0 - -0 ? x = x -x ? 0 = x -x ? y = x + x - -0 ? x = x -x ? 0 = x -x ? y = x + y - -0 ? x = x -x ? 0 = x -x ? y = y + y - -0 ? x = x -x ? 0 = x -x ? y = dec (dec x) - -0 ? x = x -x ? 0 = x -x ? y = dec (dec y) - -0 ? x = x -x ? 0 = 0 -x ? y = x + x - -0 ? x = x -x ? 0 = 0 -x ? y = x + y - -0 ? x = x -x ? 0 = 0 -x ? y = y + y - -0 ? x = x -x ? 0 = 0 -x ? y = dec (dec x) - -0 ? x = x -x ? 0 = 0 -x ? y = dec (dec y) - -0 ? x = x -x ? 0 = dec x -x ? y = dec y - -0 ? x = x -x ? 0 = x + x -x ? y = x - -0 ? x = x -x ? 0 = x + x -x ? y = 0 - -0 ? x = x -x ? 0 = dec (dec x) -x ? y = x - -0 ? x = x -x ? 0 = dec (dec x) -x ? y = 0 - -0 ? x = 0 -x ? 0 = x -x ? y = x + x - -0 ? x = 0 -x ? 0 = x -x ? y = x + y - -0 ? x = 0 -x ? 0 = x -x ? y = y + y - -0 ? x = 0 -x ? 0 = x -x ? y = dec (dec x) - -0 ? x = 0 -x ? 0 = x -x ? y = dec (dec y) - -0 ? x = 0 -x ? 0 = 0 -x ? y = x + x - -0 ? x = 0 -x ? 0 = 0 -x ? y = x + y - -0 ? x = 0 -x ? 0 = 0 -x ? y = y + y - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec (dec x) - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec (dec y) - -0 ? x = 0 -x ? 0 = dec x -x ? y = dec y - -0 ? x = 0 -x ? 0 = x + x -x ? y = y - -0 ? x = 0 -x ? 0 = dec (dec x) -x ? y = y - -0 ? x = dec x -x ? 0 = x -x ? y = dec x - -0 ? x = dec x -x ? 0 = 0 -x ? y = dec x - -0 ? x = dec x -x ? 0 = dec x -x ? y = x - -0 ? x = dec x -x ? 0 = dec x -x ? y = y - -0 ? x = dec x -x ? 0 = dec x -x ? y = 0 - -0 ? x = x + x -x ? 0 = x -x ? y = y - -0 ? x = x + x -x ? 0 = x -x ? y = 0 - -0 ? x = x + x -x ? 0 = 0 -x ? y = x - -0 ? x = dec (dec x) -x ? 0 = x -x ? y = y - -0 ? x = dec (dec x) -x ? 0 = x -x ? y = 0 - -0 ? x = dec (dec x) -x ? 0 = 0 -x ? y = x - -0 ? 0 = 0 -0 ? x = dec x -x ? y = dec x - -x ? 0 = x -x ? y = x ? dec (dec y) - -x ? 0 = x -x ? y = y ? dec (dec y) - -x ? 0 = x -x ? y = 0 ? dec (dec y) - -x ? 0 = x -x ? y = dec x ? dec x - -x ? 0 = x -x ? y = dec x ? dec y - -x ? 0 = x -x ? y = dec y ? dec y - -x ? 0 = x -x ? y = dec (dec x) ? x - -x ? 0 = x -x ? y = dec (dec x) ? y - -x ? 0 = 0 -x ? y = x ? dec (dec y) - -x ? 0 = 0 -x ? y = y ? dec (dec y) - -x ? 0 = 0 -x ? y = 0 ? dec (dec y) - -x ? 0 = 0 -x ? y = dec x ? dec x - -x ? 0 = 0 -x ? y = dec x ? dec y - -x ? 0 = 0 -x ? y = dec y ? dec y - -x ? 0 = 0 -x ? y = dec (dec x) ? x - -x ? 0 = 0 -x ? y = dec (dec x) ? y - -0 ? x = x -x ? y = x ? dec (dec y) - -0 ? x = x -x ? y = y ? dec (dec y) - -0 ? x = x -x ? y = dec x ? dec x - -0 ? x = x -x ? y = dec x ? dec y - -0 ? x = x -x ? y = dec y ? dec y - -0 ? x = x -x ? y = dec (dec x) ? x - -0 ? x = x -x ? y = dec (dec x) ? y - -0 ? x = x -x ? y = dec (dec x) ? 0 - -0 ? x = 0 -x ? y = x ? dec (dec y) - -0 ? x = 0 -x ? y = y ? dec (dec y) - -0 ? x = 0 -x ? y = dec x ? dec x - -0 ? x = 0 -x ? y = dec x ? dec y - -0 ? x = 0 -x ? y = dec y ? dec y - -0 ? x = 0 -x ? y = dec (dec x) ? x - -0 ? x = 0 -x ? y = dec (dec x) ? y - -0 ? x = 0 -x ? y = dec (dec x) ? 0 - -x ? 0 = x -x ? y = dec (x ? dec y) - -x ? 0 = x -x ? y = dec (y ? dec y) - -x ? 0 = x -x ? y = dec (0 ? dec y) - -x ? 0 = x -x ? y = dec (dec x ? x) - -x ? 0 = x -x ? y = dec (dec x ? y) - -x ? 0 = 0 -x ? y = dec (x ? dec y) - -x ? 0 = 0 -x ? y = dec (y ? dec y) - -x ? 0 = 0 -x ? y = dec (0 ? dec y) - -x ? 0 = 0 -x ? y = dec (dec x ? x) - -x ? 0 = 0 -x ? y = dec (dec x ? y) - -x ? 0 = dec x -x ? y = x ? dec y - -x ? 0 = dec x -x ? y = y ? dec y - -x ? 0 = dec x -x ? y = 0 ? dec y - -x ? 0 = dec x -x ? y = dec x ? x - -x ? 0 = dec x -x ? y = dec x ? y - -0 ? x = x -x ? y = dec (x ? dec y) - -0 ? x = x -x ? y = dec (y ? dec y) - -0 ? x = x -x ? y = dec (dec x ? x) - -0 ? x = x -x ? y = dec (dec x ? y) - -0 ? x = x -x ? y = dec (dec x ? 0) - -0 ? x = 0 -x ? y = dec (x ? dec y) - -0 ? x = 0 -x ? y = dec (y ? dec y) - -0 ? x = 0 -x ? y = dec (dec x ? x) - -0 ? x = 0 -x ? y = dec (dec x ? y) - -0 ? x = 0 -x ? y = dec (dec x ? 0) - -0 ? x = dec x -x ? y = x ? dec y - -0 ? x = dec x -x ? y = y ? dec y - -0 ? x = dec x -x ? y = dec x ? x - -0 ? x = dec x -x ? y = dec x ? y - -0 ? x = dec x -x ? y = dec x ? 0 - -0 ? x = x -x ? 0 = x -x ? y = x ? dec y - -0 ? x = x -x ? 0 = x -x ? y = y ? dec y - -0 ? x = x -x ? 0 = x -x ? y = dec x ? x - -0 ? x = x -x ? 0 = x -x ? y = dec x ? y - -0 ? x = x -x ? 0 = 0 -x ? y = x ? dec y - -0 ? x = x -x ? 0 = 0 -x ? y = y ? dec y - -0 ? x = x -x ? 0 = 0 -x ? y = dec x ? x - -0 ? x = x -x ? 0 = 0 -x ? y = dec x ? y - -0 ? x = 0 -x ? 0 = x -x ? y = x ? dec y - -0 ? x = 0 -x ? 0 = x -x ? y = y ? dec y - -0 ? x = 0 -x ? 0 = x -x ? y = dec x ? x - -0 ? x = 0 -x ? 0 = x -x ? y = dec x ? y - -0 ? x = 0 -x ? 0 = 0 -x ? y = x ? dec y - -0 ? x = 0 -x ? 0 = 0 -x ? y = y ? dec y - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec x ? x - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec x ? y - -x ? y = dec (dec (dec (dec (dec x)))) - -x ? y = dec (dec (dec (dec (dec y)))) - -x ? y = x + dec (dec (dec x)) - -x ? y = x + dec (dec (dec y)) - -x ? y = x + (x + dec x) - -x ? y = x + (x + dec y) - -x ? y = x + (y + dec x) - -x ? y = x + (y + dec y) - -x ? y = y + dec (dec (dec x)) - -x ? y = y + dec (dec (dec y)) - -x ? y = y + (x + dec x) - -x ? y = y + (x + dec y) - -x ? y = y + (y + dec x) - -x ? y = y + (y + dec y) - -x ? y = dec x + (x + x) - -x ? y = dec x + (x + y) - -x ? y = dec x + (y + y) - -x ? y = dec x + dec (dec x) - -x ? y = dec x + dec (dec y) - -x ? y = dec y + (x + x) - -x ? y = dec y + (x + y) - -x ? y = dec y + (y + y) - -x ? y = dec y + dec (dec x) - -x ? y = dec y + dec (dec y) - -x ? 0 = x -x ? y = dec (dec (dec (dec x))) - -x ? 0 = x -x ? y = dec (dec (dec (dec y))) - -x ? 0 = x -x ? y = x + (x + x) - -x ? 0 = x -x ? y = x + (x + y) - -x ? 0 = x -x ? y = x + (y + y) - -x ? 0 = x -x ? y = x + dec (dec x) - -x ? 0 = x -x ? y = x + dec (dec y) - -x ? 0 = x -x ? y = y + (x + x) - -x ? 0 = x -x ? y = y + (x + y) - -x ? 0 = x -x ? y = y + (y + y) - -x ? 0 = x -x ? y = y + dec (dec x) - -x ? 0 = x -x ? y = y + dec (dec y) - -x ? 0 = x -x ? y = dec x + dec x - -x ? 0 = x -x ? y = dec x + dec y - -x ? 0 = x -x ? y = dec y + dec y - -x ? 0 = 0 -x ? y = dec (dec (dec (dec x))) - -x ? 0 = 0 -x ? y = dec (dec (dec (dec y))) - -x ? 0 = 0 -x ? y = x + (x + x) - -x ? 0 = 0 -x ? y = x + (x + y) - -x ? 0 = 0 -x ? y = x + (y + y) - -x ? 0 = 0 -x ? y = x + dec (dec x) - -x ? 0 = 0 -x ? y = x + dec (dec y) - -x ? 0 = 0 -x ? y = y + (x + x) - -x ? 0 = 0 -x ? y = y + (x + y) - -x ? 0 = 0 -x ? y = y + (y + y) - -x ? 0 = 0 -x ? y = y + dec (dec x) - -x ? 0 = 0 -x ? y = y + dec (dec y) - -x ? 0 = 0 -x ? y = dec x + dec x - -x ? 0 = 0 -x ? y = dec x + dec y - -x ? 0 = 0 -x ? y = dec y + dec y - -x ? 0 = dec x -x ? y = dec (dec (dec x)) - -x ? 0 = dec x -x ? y = dec (dec (dec y)) - -x ? 0 = dec x -x ? y = x + dec x - -x ? 0 = dec x -x ? y = x + dec y - -x ? 0 = dec x -x ? y = y + dec x - -x ? 0 = dec x -x ? y = y + dec y - -x ? 0 = x + x -x ? y = x + y - -x ? 0 = x + x -x ? y = y + y - -x ? 0 = x + x -x ? y = dec (dec x) - -x ? 0 = x + x -x ? y = dec (dec y) - -x ? 0 = dec (dec x) -x ? y = x + x - -x ? 0 = dec (dec x) -x ? y = x + y - -x ? 0 = dec (dec x) -x ? y = y + y - -x ? 0 = dec (dec x) -x ? y = dec (dec y) - -x ? 0 = dec (dec (dec x)) -x ? y = dec x - -x ? 0 = dec (dec (dec x)) -x ? y = dec y - -x ? 0 = x + dec x -x ? y = dec x - -x ? 0 = x + dec x -x ? y = dec y - -x ? 0 = dec (dec (dec (dec x))) -x ? y = x - -x ? 0 = dec (dec (dec (dec x))) -x ? y = y - -x ? 0 = dec (dec (dec (dec x))) -x ? y = 0 - -x ? 0 = x + (x + x) -x ? y = x - -x ? 0 = x + (x + x) -x ? y = y - -x ? 0 = x + (x + x) -x ? y = 0 - -x ? 0 = x + dec (dec x) -x ? y = x - -x ? 0 = x + dec (dec x) -x ? y = y - -x ? 0 = x + dec (dec x) -x ? y = 0 - -x ? 0 = dec x + dec x -x ? y = x - -x ? 0 = dec x + dec x -x ? y = y - -x ? 0 = dec x + dec x -x ? y = 0 - -0 ? x = x -x ? y = dec (dec (dec (dec x))) - -0 ? x = x -x ? y = dec (dec (dec (dec y))) - -0 ? x = x -x ? y = x + (x + x) - -0 ? x = x -x ? y = x + (x + y) - -0 ? x = x -x ? y = x + (y + y) - -0 ? x = x -x ? y = x + dec (dec x) - -0 ? x = x -x ? y = x + dec (dec y) - -0 ? x = x -x ? y = y + (x + x) - -0 ? x = x -x ? y = y + (x + y) - -0 ? x = x -x ? y = y + (y + y) - -0 ? x = x -x ? y = y + dec (dec x) - -0 ? x = x -x ? y = y + dec (dec y) - -0 ? x = x -x ? y = dec x + dec x - -0 ? x = x -x ? y = dec x + dec y - -0 ? x = x -x ? y = dec y + dec y - -0 ? x = 0 -x ? y = dec (dec (dec (dec x))) - -0 ? x = 0 -x ? y = dec (dec (dec (dec y))) - -0 ? x = 0 -x ? y = x + (x + x) - -0 ? x = 0 -x ? y = x + (x + y) - -0 ? x = 0 -x ? y = x + (y + y) - -0 ? x = 0 -x ? y = x + dec (dec x) - -0 ? x = 0 -x ? y = x + dec (dec y) - -0 ? x = 0 -x ? y = y + (x + x) - -0 ? x = 0 -x ? y = y + (x + y) - -0 ? x = 0 -x ? y = y + (y + y) - -0 ? x = 0 -x ? y = y + dec (dec x) - -0 ? x = 0 -x ? y = y + dec (dec y) - -0 ? x = 0 -x ? y = dec x + dec x - -0 ? x = 0 -x ? y = dec x + dec y - -0 ? x = 0 -x ? y = dec y + dec y - -0 ? x = dec x -x ? y = dec (dec (dec x)) - -0 ? x = dec x -x ? y = dec (dec (dec y)) - -0 ? x = dec x -x ? y = x + dec x - -0 ? x = dec x -x ? y = x + dec y - -0 ? x = dec x -x ? y = y + dec x - -0 ? x = dec x -x ? y = y + dec y - -0 ? x = x + x -x ? y = x + y - -0 ? x = x + x -x ? y = dec (dec x) - -0 ? x = x + x -x ? y = dec (dec y) - -0 ? x = dec (dec x) -x ? y = x + x - -0 ? x = dec (dec x) -x ? y = x + y - -0 ? x = dec (dec x) -x ? y = y + y - -0 ? x = dec (dec (dec x)) -x ? y = dec x - -0 ? x = dec (dec (dec x)) -x ? y = dec y - -0 ? x = x + dec x -x ? y = dec x - -0 ? x = x + dec x -x ? y = dec y - -0 ? x = dec (dec (dec (dec x))) -x ? y = x - -0 ? x = dec (dec (dec (dec x))) -x ? y = y - -0 ? x = dec (dec (dec (dec x))) -x ? y = 0 - -0 ? x = x + (x + x) -x ? y = x - -0 ? x = x + (x + x) -x ? y = y - -0 ? x = x + (x + x) -x ? y = 0 - -0 ? x = x + dec (dec x) -x ? y = x - -0 ? x = x + dec (dec x) -x ? y = y - -0 ? x = x + dec (dec x) -x ? y = 0 - -0 ? x = dec x + dec x -x ? y = x - -0 ? x = dec x + dec x -x ? y = y - -0 ? x = dec x + dec x -x ? y = 0 - -0 ? x = x -x ? 0 = x -x ? y = dec (dec (dec x)) - -0 ? x = x -x ? 0 = x -x ? y = dec (dec (dec y)) - -0 ? x = x -x ? 0 = x -x ? y = x + dec x - -0 ? x = x -x ? 0 = x -x ? y = x + dec y - -0 ? x = x -x ? 0 = x -x ? y = y + dec x - -0 ? x = x -x ? 0 = x -x ? y = y + dec y - -0 ? x = x -x ? 0 = 0 -x ? y = dec (dec (dec x)) - -0 ? x = x -x ? 0 = 0 -x ? y = dec (dec (dec y)) - -0 ? x = x -x ? 0 = 0 -x ? y = x + dec x - -0 ? x = x -x ? 0 = 0 -x ? y = x + dec y - -0 ? x = x -x ? 0 = 0 -x ? y = y + dec x - -0 ? x = x -x ? 0 = 0 -x ? y = y + dec y - -0 ? x = x -x ? 0 = dec x -x ? y = x + x - -0 ? x = x -x ? 0 = dec x -x ? y = x + y - -0 ? x = x -x ? 0 = dec x -x ? y = y + y - -0 ? x = x -x ? 0 = dec x -x ? y = dec (dec x) - -0 ? x = x -x ? 0 = dec x -x ? y = dec (dec y) - -0 ? x = x -x ? 0 = x + x -x ? y = dec x - -0 ? x = x -x ? 0 = x + x -x ? y = dec y - -0 ? x = x -x ? 0 = dec (dec x) -x ? y = dec x - -0 ? x = x -x ? 0 = dec (dec x) -x ? y = dec y - -0 ? x = x -x ? 0 = dec (dec (dec x)) -x ? y = x - -0 ? x = x -x ? 0 = dec (dec (dec x)) -x ? y = 0 - -0 ? x = x -x ? 0 = x + dec x -x ? y = x - -0 ? x = x -x ? 0 = x + dec x -x ? y = 0 - -0 ? x = 0 -x ? 0 = x -x ? y = dec (dec (dec x)) - -0 ? x = 0 -x ? 0 = x -x ? y = dec (dec (dec y)) - -0 ? x = 0 -x ? 0 = x -x ? y = x + dec x - -0 ? x = 0 -x ? 0 = x -x ? y = x + dec y - -0 ? x = 0 -x ? 0 = x -x ? y = y + dec x - -0 ? x = 0 -x ? 0 = x -x ? y = y + dec y - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec (dec (dec x)) - -0 ? x = 0 -x ? 0 = 0 -x ? y = dec (dec (dec y)) - -0 ? x = 0 -x ? 0 = 0 -x ? y = x + dec x - -0 ? x = 0 -x ? 0 = 0 -x ? y = x + dec y - -0 ? x = 0 -x ? 0 = 0 -x ? y = y + dec x - -0 ? x = 0 -x ? 0 = 0 -x ? y = y + dec y - -0 ? x = 0 -x ? 0 = dec x -x ? y = x + x - -0 ? x = 0 -x ? 0 = dec x -x ? y = x + y - -0 ? x = 0 -x ? 0 = dec x -x ? y = y + y - -0 ? x = 0 -x ? 0 = dec x -x ? y = dec (dec x) - -0 ? x = 0 -x ? 0 = dec x -x ? y = dec (dec y) - -0 ? x = 0 -x ? 0 = x + x -x ? y = dec x - -0 ? x = 0 -x ? 0 = x + x -x ? y = dec y - -0 ? x = 0 -x ? 0 = dec (dec x) -x ? y = dec x - -0 ? x = 0 -x ? 0 = dec (dec x) -x ? y = dec y - -0 ? x = 0 -x ? 0 = dec (dec (dec x)) -x ? y = y - -0 ? x = 0 -x ? 0 = x + dec x -x ? y = y - -0 ? x = dec x -x ? 0 = x -x ? y = x + x - -0 ? x = dec x -x ? 0 = x -x ? y = x + y - -0 ? x = dec x -x ? 0 = x -x ? y = y + y - -0 ? x = dec x -x ? 0 = x -x ? y = dec (dec x) - -0 ? x = dec x -x ? 0 = x -x ? y = dec (dec y) - -0 ? x = dec x -x ? 0 = 0 -x ? y = x + x - -0 ? x = dec x -x ? 0 = 0 -x ? y = x + y - -0 ? x = dec x -x ? 0 = 0 -x ? y = y + y - -0 ? x = dec x -x ? 0 = 0 -x ? y = dec (dec x) - -0 ? x = dec x -x ? 0 = 0 -x ? y = dec (dec y) - -0 ? x = dec x -x ? 0 = x + x -x ? y = x - -0 ? x = dec x -x ? 0 = x + x -x ? y = y - -0 ? x = dec x -x ? 0 = x + x -x ? y = 0 - -0 ? x = dec x -x ? 0 = dec (dec x) -x ? y = x - -0 ? x = dec x -x ? 0 = dec (dec x) -x ? y = y - -0 ? x = dec x -x ? 0 = dec (dec x) -x ? y = 0 - -0 ? x = x + x -x ? 0 = x -x ? y = dec x - -0 ? x = x + x -x ? 0 = x -x ? y = dec y - -0 ? x = x + x -x ? 0 = 0 -x ? y = dec x - -0 ? x = x + x -x ? 0 = 0 -x ? y = dec y - -0 ? x = x + x -x ? 0 = dec x -x ? y = x - -0 ? x = x + x -x ? 0 = dec x -x ? y = y - -0 ? x = x + x -x ? 0 = dec x -x ? y = 0 - -0 ? x = dec (dec x) -x ? 0 = x -x ? y = dec x - -0 ? x = dec (dec x) -x ? 0 = x -x ? y = dec y - -0 ? x = dec (dec x) -x ? 0 = 0 -x ? y = dec x - -0 ? x = dec (dec x) -x ? 0 = 0 -x ? y = dec y - -0 ? x = dec (dec x) -x ? 0 = dec x -x ? y = x - -0 ? x = dec (dec x) -x ? 0 = dec x -x ? y = y - -0 ? x = dec (dec x) -x ? 0 = dec x -x ? y = 0 - -0 ? x = dec (dec (dec x)) -x ? 0 = x -x ? y = y - -0 ? x = dec (dec (dec x)) -x ? 0 = x -x ? y = 0 - -0 ? x = dec (dec (dec x)) -x ? 0 = 0 -x ? y = x - -0 ? x = x + dec x -x ? 0 = x -x ? y = y - -0 ? x = x + dec x -x ? 0 = x -x ? y = 0 - -0 ? x = x + dec x -x ? 0 = 0 -x ? y = x - -0 ? 0 = 0 -0 ? x = dec x -x ? y = x + x - -0 ? 0 = 0 -0 ? x = dec x -x ? y = x + y - -0 ? 0 = 0 -0 ? x = dec x -x ? y = y + y - -0 ? 0 = 0 -0 ? x = dec x -x ? y = dec (dec x) - -0 ? 0 = 0 -0 ? x = dec x -x ? y = dec (dec y) - -0 ? 0 = 0 -0 ? x = x + x -x ? y = dec x - -0 ? 0 = 0 -0 ? x = x + x -x ? y = dec y - -0 ? 0 = 0 -0 ? x = dec (dec x) -x ? y = dec x - -0 ? 0 = 0 -0 ? x = dec (dec x) -x ? y = dec y - - -Candidates for: goo :: [Int] -> [Int] - pruning with 4/4 rules - [2,0,1,0,1,0,1,0,1] direct candidates, 0 duplicates - [2,1,2,3,4,7,10,17,26] pattern candidates, 0 duplicates - -rules: -xs ++ [] == xs -[] ++ xs == xs -(xs ++ ys) ++ zs == xs ++ (ys ++ zs) -(x:xs) ++ ys == x:(xs ++ ys) - -direct candidates: - -goo xs = xs - -goo xs = [] - -goo xs = xs ++ xs - -goo xs = xs ++ (xs ++ xs) - - -pattern candidates: - -goo xs = xs - -goo xs = [] - -goo [] = [] -goo (x:xs) = xs - -goo [] = [] -goo (x:xs) = goo xs - -goo xs = xs ++ xs - -goo [] = [] -goo (x:xs) = x:xs - -goo [] = [] -goo (x:xs) = [x] - -goo [] = [] -goo (x:xs) = xs ++ xs - -goo [] = [] -goo (x:xs) = x:goo xs - -goo [] = [] -goo (x:xs) = xs ++ goo xs - -goo [] = [] -goo (x:xs) = goo xs ++ xs - -goo xs = xs ++ (xs ++ xs) - -goo [] = [] -goo (x:xs) = goo xs ++ goo xs - -goo [] = [] -goo (x:xs) = x:x:xs - -goo [] = [] -goo (x:xs) = [x,x] - -goo [] = [] -goo (x:xs) = x:(xs ++ xs) - -goo [] = [] -goo (x:xs) = xs ++ (x:xs) - -goo [] = [] -goo (x:xs) = xs ++ [x] - -goo [] = [] -goo (x:xs) = xs ++ (xs ++ xs) - - -Candidates for: ?? :: [Int] -> [Int] -> [Int] - pruning with 4/4 rules - [3,0,4,0,8,0,16,0,32] direct candidates, 0 duplicates - [3,7,15,59,139,331,987,2016,6970] pattern candidates, 0 duplicates - -rules: -xs ++ [] == xs -[] ++ xs == xs -(xs ++ ys) ++ zs == xs ++ (ys ++ zs) -(x:xs) ++ ys == x:(xs ++ ys) - -direct candidates: - -xs ?? ys = xs - -xs ?? ys = ys - -xs ?? ys = [] - -xs ?? ys = xs ++ xs - -xs ?? ys = xs ++ ys - -xs ?? ys = ys ++ xs - -xs ?? ys = ys ++ ys - -xs ?? ys = xs ++ (xs ++ xs) - -xs ?? ys = xs ++ (xs ++ ys) - -xs ?? ys = xs ++ (ys ++ xs) - -xs ?? ys = xs ++ (ys ++ ys) - -xs ?? ys = ys ++ (xs ++ xs) - -xs ?? ys = ys ++ (xs ++ ys) - -xs ?? ys = ys ++ (ys ++ xs) - -xs ?? ys = ys ++ (ys ++ ys) - - -pattern candidates: - -xs ?? ys = xs - -xs ?? ys = ys - -xs ?? ys = [] - -xs ?? [] = xs -xs ?? (x:ys) = ys - -xs ?? [] = xs -xs ?? (x:ys) = [] - -xs ?? [] = [] -xs ?? (x:ys) = xs - -xs ?? [] = [] -xs ?? (x:ys) = ys - -[] ?? xs = xs -(x:xs) ?? ys = [] - -[] ?? xs = [] -(x:xs) ?? ys = xs - -[] ?? xs = [] -(x:xs) ?? ys = ys - -xs ?? ys = xs ++ xs - -xs ?? ys = xs ++ ys - -xs ?? ys = ys ++ xs - -xs ?? ys = ys ++ ys - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = [] - -xs ?? [] = xs -xs ?? (x:ys) = xs ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = xs ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = ys ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = ys ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = [] ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = [] ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = xs ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = xs ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = ys ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = ys ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = [] ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = [] ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? [] - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? [] - -xs ?? [] = xs -xs ?? (x:ys) = x:xs - -xs ?? [] = xs -xs ?? (x:ys) = x:ys - -xs ?? [] = xs -xs ?? (x:ys) = [x] - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ ys - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = x:xs - -xs ?? [] = [] -xs ?? (x:ys) = x:ys - -xs ?? [] = [] -xs ?? (x:ys) = [x] - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ ys - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = xs - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = ys - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = [] - -[] ?? xs = xs -(x:xs) ?? ys = x:xs - -[] ?? xs = xs -(x:xs) ?? ys = x:ys - -[] ?? xs = xs -(x:xs) ?? ys = [x] - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ ys - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = x:xs - -[] ?? xs = [] -(x:xs) ?? ys = x:ys - -[] ?? xs = [] -(x:xs) ?? ys = [x] - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ ys - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = xs - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = ys - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? xs - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? ys - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? [] - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? xs - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? ys - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? [] - -[] ?? xs = xs -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = xs - -[] ?? xs = xs -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = xs - -[] ?? xs = xs -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = xs -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = ys - -[] ?? xs = xs -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ?? xs - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ?? ys - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ?? [] - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ?? xs - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ?? ys - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ?? [] - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? xs - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? ys - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? [] - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? xs - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? ys - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? [] - -[] ?? xs = [] -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = xs - -[] ?? xs = [] -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = xs - -[] ?? xs = [] -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = [] -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = ys - -[] ?? xs = [] -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = [] -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = [] - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ?? xs - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ?? ys - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ?? [] - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ?? xs - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ?? ys - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ?? [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = xs ?? xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = xs ?? ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = xs ?? [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = ys ?? xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = ys ?? ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = ys ?? [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = [] ?? xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = [] ?? ys - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? xs -(x:xs) ?? ys = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? [] -(x:xs) ?? ys = xs - -[] ?? [] = [] -[] ?? (x:xs) = [] ?? xs -(x:xs) ?? ys = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? xs -(x:xs) ?? ys = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? [] -(x:xs) ?? ys = ys - -[] ?? [] = [] -[] ?? (x:xs) = [] ?? xs -(x:xs) ?? ys = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? xs -(x:xs) ?? ys = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? [] -(x:xs) ?? ys = [] - -[] ?? [] = [] -[] ?? (x:xs) = [] ?? xs -(x:xs) ?? ys = [] - -xs ?? ys = xs ++ (xs ++ xs) - -xs ?? ys = xs ++ (xs ++ ys) - -xs ?? ys = xs ++ (ys ++ xs) - -xs ?? ys = xs ++ (ys ++ ys) - -xs ?? ys = ys ++ (xs ++ xs) - -xs ?? ys = ys ++ (xs ++ ys) - -xs ?? ys = ys ++ (ys ++ xs) - -xs ?? ys = ys ++ (ys ++ ys) - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = x:xs - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = x:ys - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [x] - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = y:xs - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = y:ys - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [y] - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ++ xs - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ++ ys - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ++ xs - -[] ?? xs = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ++ ys - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = x:xs - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = x:ys - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = [x] - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = y:xs - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = y:ys - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = [y] - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ++ xs - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ++ ys - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ++ xs - -[] ?? xs = xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ++ ys - -[] ?? xs = xs -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = xs - -[] ?? xs = xs -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = xs -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = xs - -[] ?? xs = xs -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = ys - -[] ?? xs = xs -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = xs - -[] ?? xs = xs -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = xs -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = x:xs - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = x:ys - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [x] - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = y:xs - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = y:ys - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [y] - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ++ xs - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ++ ys - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ++ xs - -[] ?? xs = [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ++ ys - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = x:xs - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = x:ys - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = [x] - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = y:xs - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = y:ys - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = [y] - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ++ xs - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs ++ ys - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ++ xs - -[] ?? xs = [] -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys ++ ys - -[] ?? xs = [] -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = xs - -[] ?? xs = [] -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = [] -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = [] -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = xs - -[] ?? xs = [] -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = ys - -[] ?? xs = [] -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = [] - -[] ?? xs = [] -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = xs - -[] ?? xs = [] -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = [] -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs ++ xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? xs = xs ++ xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? xs = xs ++ xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = xs - -[] ?? xs = xs ++ xs -(x:xs) ?? [] = [] -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = x:xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = x:ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = [x] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = xs ++ xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = xs ++ ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = ys ++ xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? ys = ys ++ ys - -[] ?? [] = [] -[] ?? (x:xs) = x:xs -(x:xs) ?? ys = xs - -[] ?? [] = [] -[] ?? (x:xs) = x:xs -(x:xs) ?? ys = ys - -[] ?? [] = [] -[] ?? (x:xs) = x:xs -(x:xs) ?? ys = [] - -[] ?? [] = [] -[] ?? (x:xs) = [x] -(x:xs) ?? ys = xs - -[] ?? [] = [] -[] ?? (x:xs) = [x] -(x:xs) ?? ys = ys - -[] ?? [] = [] -[] ?? (x:xs) = [x] -(x:xs) ?? ys = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs ++ xs -(x:xs) ?? ys = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs ++ xs -(x:xs) ?? ys = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs ++ xs -(x:xs) ?? ys = [] - -xs ?? [] = xs -xs ?? (x:ys) = (x:xs) ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = (x:xs) ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = (x:ys) ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = (x:ys) ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = [x] ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = [x] ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = (xs ++ xs) ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = (xs ++ xs) ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = (xs ++ ys) ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = (xs ++ ys) ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = (ys ++ xs) ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = (ys ++ xs) ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = (ys ++ ys) ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = (ys ++ ys) ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = (x:xs) ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = (x:xs) ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = (x:ys) ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = (x:ys) ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = [x] ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = [x] ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = (xs ++ xs) ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = (xs ++ xs) ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = (xs ++ ys) ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = (xs ++ ys) ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = (ys ++ xs) ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = (ys ++ xs) ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = (ys ++ ys) ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = (ys ++ ys) ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? (x:xs) - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? (x:ys) - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? [x] - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? (xs ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? (xs ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? (ys ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? (ys ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? (x:xs) - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? (x:ys) - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? [x] - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? (xs ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? (xs ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? (ys ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? (ys ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? (x:xs) - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? (x:ys) - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? [x] - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? (xs ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? (xs ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? (ys ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? (ys ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? (x:xs) - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? (x:ys) - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? [x] - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? (xs ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? (xs ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? (ys ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? (ys ++ ys) - -xs ?? [] = xs -xs ?? (x:ys) = x:xs ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = x:xs ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = x:ys ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = x:ys ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = x:[] ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = x:[] ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ xs ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ xs ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ ys ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ ys ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ [] ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ [] ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ xs ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ xs ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ ys ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ ys ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ [] ?? xs - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ [] ?? ys - -xs ?? [] = xs -xs ?? (x:ys) = xs ?? xs ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = xs ?? ys ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = ys ?? xs ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = ys ?? ys ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = [] ?? xs ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = [] ?? ys ++ xs - -xs ?? [] = xs -xs ?? (x:ys) = xs ?? xs ++ ys - -xs ?? [] = xs -xs ?? (x:ys) = xs ?? ys ++ ys - -xs ?? [] = xs -xs ?? (x:ys) = ys ?? xs ++ ys - -xs ?? [] = xs -xs ?? (x:ys) = ys ?? ys ++ ys - -xs ?? [] = xs -xs ?? (x:ys) = [] ?? xs ++ ys - -xs ?? [] = xs -xs ?? (x:ys) = [] ?? ys ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = x:xs ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = x:xs ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = x:ys ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = x:ys ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = x:[] ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = x:[] ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ xs ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ xs ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ ys ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ ys ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ [] ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ [] ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ xs ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ xs ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ ys ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ ys ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ [] ?? xs - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ [] ?? ys - -xs ?? [] = [] -xs ?? (x:ys) = xs ?? xs ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = xs ?? ys ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = ys ?? xs ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = ys ?? ys ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = [] ?? xs ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = [] ?? ys ++ xs - -xs ?? [] = [] -xs ?? (x:ys) = xs ?? xs ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = xs ?? ys ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = ys ?? xs ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = ys ?? ys ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = [] ?? xs ++ ys - -xs ?? [] = [] -xs ?? (x:ys) = [] ?? ys ++ ys - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = xs ?? xs - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = xs ?? ys - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = ys ?? xs - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = ys ?? ys - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = [] ?? xs - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = [] ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = x:xs ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = x:xs ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = x:xs ?? [] - -[] ?? xs = xs -(x:xs) ?? ys = x:ys ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = x:ys ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = x:ys ?? [] - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ xs ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ xs ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ xs ?? [] - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ ys ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ ys ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ ys ?? [] - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ xs ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ xs ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ xs ?? [] - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ ys ?? xs - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ ys ?? ys - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ ys ?? [] - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? xs ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? ys ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? [] ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? xs ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? ys ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? [] ++ xs - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? xs ++ ys - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? ys ++ ys - -[] ?? xs = xs -(x:xs) ?? ys = xs ?? [] ++ ys - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? xs ++ ys - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? ys ++ ys - -[] ?? xs = xs -(x:xs) ?? ys = ys ?? [] ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = x:xs ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = x:xs ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = x:xs ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = x:ys ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = x:ys ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = x:ys ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ xs ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ xs ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ xs ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ ys ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ ys ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ ys ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ xs ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ xs ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ xs ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ ys ?? xs - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ ys ?? ys - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ ys ?? [] - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? xs ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? ys ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? [] ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? xs ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? ys ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? [] ++ xs - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? xs ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? ys ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = xs ?? [] ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? xs ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? ys ++ ys - -[] ?? xs = [] -(x:xs) ?? ys = ys ?? [] ++ ys - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = xs ?? xs - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = xs ?? ys - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = xs ?? [] - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = ys ?? xs - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = ys ?? ys - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = ys ?? [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ?? [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ?? [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] ?? xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] ?? ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = [] ?? xs -(x:xs) ?? (y:ys) = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs ?? xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs ?? [] -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = [] ?? xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = [] ?? xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs ?? [] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = [] ?? xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -xs ?? [] = xs -xs ?? (x:ys) = x:x:xs - -xs ?? [] = xs -xs ?? (x:ys) = x:x:ys - -xs ?? [] = xs -xs ?? (x:ys) = [x,x] - -xs ?? [] = xs -xs ?? (x:ys) = x:(xs ++ xs) - -xs ?? [] = xs -xs ?? (x:ys) = x:(xs ++ ys) - -xs ?? [] = xs -xs ?? (x:ys) = x:(ys ++ xs) - -xs ?? [] = xs -xs ?? (x:ys) = x:(ys ++ ys) - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ (x:xs) - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ (x:ys) - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ [x] - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ (xs ++ xs) - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ (xs ++ ys) - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ (ys ++ xs) - -xs ?? [] = xs -xs ?? (x:ys) = xs ++ (ys ++ ys) - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ (x:xs) - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ (x:ys) - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ [x] - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ (xs ++ xs) - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ (xs ++ ys) - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ (ys ++ xs) - -xs ?? [] = xs -xs ?? (x:ys) = ys ++ (ys ++ ys) - -xs ?? [] = [] -xs ?? (x:ys) = x:x:xs - -xs ?? [] = [] -xs ?? (x:ys) = x:x:ys - -xs ?? [] = [] -xs ?? (x:ys) = [x,x] - -xs ?? [] = [] -xs ?? (x:ys) = x:(xs ++ xs) - -xs ?? [] = [] -xs ?? (x:ys) = x:(xs ++ ys) - -xs ?? [] = [] -xs ?? (x:ys) = x:(ys ++ xs) - -xs ?? [] = [] -xs ?? (x:ys) = x:(ys ++ ys) - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ (x:xs) - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ (x:ys) - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ [x] - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ (xs ++ xs) - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ (xs ++ ys) - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ (ys ++ xs) - -xs ?? [] = [] -xs ?? (x:ys) = xs ++ (ys ++ ys) - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ (x:xs) - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ (x:ys) - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ [x] - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ (xs ++ xs) - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ (xs ++ ys) - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ (ys ++ xs) - -xs ?? [] = [] -xs ?? (x:ys) = ys ++ (ys ++ ys) - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = x:xs - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = x:ys - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = [x] - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = xs ++ ys - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = ys ++ xs - -xs ?? [] = xs ++ xs -xs ?? (x:ys) = ys ++ ys - -xs ?? [] = xs ++ (xs ++ xs) -xs ?? (x:ys) = xs - -xs ?? [] = xs ++ (xs ++ xs) -xs ?? (x:ys) = ys - -xs ?? [] = xs ++ (xs ++ xs) -xs ?? (x:ys) = [] - -[] ?? xs = xs -(x:xs) ?? ys = x:x:xs - -[] ?? xs = xs -(x:xs) ?? ys = x:x:ys - -[] ?? xs = xs -(x:xs) ?? ys = [x,x] - -[] ?? xs = xs -(x:xs) ?? ys = x:(xs ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = x:(xs ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = x:(ys ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = x:(ys ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ (x:xs) - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ (x:ys) - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ [x] - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ (xs ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ (xs ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ (ys ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = xs ++ (ys ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ (x:xs) - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ (x:ys) - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ [x] - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ (xs ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ (xs ++ ys) - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ (ys ++ xs) - -[] ?? xs = xs -(x:xs) ?? ys = ys ++ (ys ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = x:x:xs - -[] ?? xs = [] -(x:xs) ?? ys = x:x:ys - -[] ?? xs = [] -(x:xs) ?? ys = [x,x] - -[] ?? xs = [] -(x:xs) ?? ys = x:(xs ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = x:(xs ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = x:(ys ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = x:(ys ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ (x:xs) - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ (x:ys) - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ [x] - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ (xs ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ (xs ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ (ys ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = xs ++ (ys ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ (x:xs) - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ (x:ys) - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ [x] - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ (xs ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ (xs ++ ys) - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ (ys ++ xs) - -[] ?? xs = [] -(x:xs) ?? ys = ys ++ (ys ++ ys) - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = x:xs - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = x:ys - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = [x] - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = xs ++ ys - -[] ?? xs = xs ++ xs -(x:xs) ?? ys = ys ++ xs - -[] ?? xs = xs ++ (xs ++ xs) -(x:xs) ?? ys = xs - -[] ?? xs = xs ++ (xs ++ xs) -(x:xs) ?? ys = ys - -[] ?? xs = xs ++ (xs ++ xs) -(x:xs) ?? ys = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = x:xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = x:ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [x] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = y:xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = y:ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [y] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ++ xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = xs ++ ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ++ xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys ++ ys - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = x:xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = [x] -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = xs - -[] ?? [] = [] -[] ?? (x:xs) = xs -(x:xs) ?? [] = xs ++ xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = x:xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = x:xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = [x] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = [x] -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - -[] ?? [] = [] -[] ?? (x:xs) = xs ++ xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = ys - -[] ?? [] = [] -[] ?? (x:xs) = xs ++ xs -(x:xs) ?? [] = xs -(x:xs) ?? (y:ys) = [] - - -Candidates for: ton :: Bool -> Bool - pruning with 39/49 rules - [3,1,0,2,6,10,22,40,76] direct candidates, 0 duplicates - [3,3,0,0,0,0,0,0,0] pattern candidates, 0 duplicates - -rules: -not False == True -not True == False -p && p == p -p || p == p -not (not p) == p -p && False == False -p && True == p -False && p == False -True && p == p -p || False == p -p || True == True -False || p == p -True || p == True -not (p && q) == not p || not q -not (p && q) == not q || not p -not (p || q) == not p && not q -not (p || q) == not q && not p -p && not p == False -not p && p == False -p || not p == True -not p || p == True -(p && q) && r == p && (q && r) -(p && q) && r == q && (p && r) -(p || q) || r == p || (q || r) -(p || q) || r == q || (p || r) -p && (p && q) == p && q -p && (q && p) == p && q -p && (q && p) == q && p -p || (p || q) == p || q -p || (q || p) == p || q -p || (q || p) == q || p -p && (p || q) == p -p && (q || p) == p -(p || q) && p == p -(p || q) && q == q -p || p && q == p -p || q && p == p -p && q || p == p -p && q || q == q -equations: -q && p == p && q -q || p == p || q -q && (p && r) == p && (q && r) -r && (p && q) == p && (q && r) -r && (q && p) == p && (q && r) -q || (p || r) == p || (q || r) -r || (p || q) == p || (q || r) -r || (q || p) == p || (q || r) -(r || q) && p == p && (q || r) -r && q || p == p || q && r - -direct candidates: - -ton p = p - -ton p = False - -ton p = True - -ton p = not p - -ton p = p && ton p - -ton p = p || ton p - -ton p = p && ton (not p) - -ton p = p || ton (not p) - -ton p = p && not (ton p) - -ton p = not p && ton p - -ton p = p || not (ton p) - -ton p = not p || ton p - -ton p = p && not (ton (not p)) - -ton p = not p && ton (not p) - -ton p = p || not (ton (not p)) - -ton p = not p || ton (not p) - -ton p = p && (p && ton p) - -ton p = p && (p || ton p) - -ton p = not p && not (ton p) - -ton p = p || p && ton p - -ton p = p || (p || ton p) - -ton p = not p || not (ton p) - - -pattern candidates: - -ton p = p - -ton p = False - -ton p = True - -ton p = not p - -ton False = False -ton True = True - -ton False = True -ton True = False - - -Candidates for: &| :: Bool -> Bool -> Bool - pruning with 39/49 rules - [4,2,2,4,30,112,342,1032,2852] direct candidates, 0 duplicates - [4,14,26,10,2,16,18,60,120] pattern candidates, 0 duplicates - -rules: -not False == True -not True == False -p && p == p -p || p == p -not (not p) == p -p && False == False -p && True == p -False && p == False -True && p == p -p || False == p -p || True == True -False || p == p -True || p == True -not (p && q) == not p || not q -not (p && q) == not q || not p -not (p || q) == not p && not q -not (p || q) == not q && not p -p && not p == False -not p && p == False -p || not p == True -not p || p == True -(p && q) && r == p && (q && r) -(p && q) && r == q && (p && r) -(p || q) || r == p || (q || r) -(p || q) || r == q || (p || r) -p && (p && q) == p && q -p && (q && p) == p && q -p && (q && p) == q && p -p || (p || q) == p || q -p || (q || p) == p || q -p || (q || p) == q || p -p && (p || q) == p -p && (q || p) == p -(p || q) && p == p -(p || q) && q == q -p || p && q == p -p || q && p == p -p && q || p == p -p && q || q == q -equations: -q && p == p && q -q || p == p || q -q && (p && r) == p && (q && r) -r && (p && q) == p && (q && r) -r && (q && p) == p && (q && r) -q || (p || r) == p || (q || r) -r || (p || q) == p || (q || r) -r || (q || p) == p || (q || r) -(r || q) && p == p && (q || r) -r && q || p == p || q && r - -direct candidates: - -p &| q = p - -p &| q = q - -p &| q = False - -p &| q = True - -p &| q = not p - -p &| q = not q - -p &| q = p && q - -p &| q = p || q - -p &| q = p && not q - -p &| q = q && not p - -p &| q = p || not q - -p &| q = q || not p - -p &| q = not p && not q - -p &| q = not p || not q - -p &| q = p && p &| p - -p &| q = p && p &| q - -p &| q = p && p &| False - -p &| q = p && p &| True - -p &| q = p && q &| q - -p &| q = p && False &| q - -p &| q = p && True &| q - -p &| q = q && p &| p - -p &| q = q && p &| q - -p &| q = q && p &| False - -p &| q = q && p &| True - -p &| q = q && q &| q - -p &| q = q && False &| q - -p &| q = q && True &| q - -p &| q = p || p &| p - -p &| q = p || p &| q - -p &| q = p || p &| False - -p &| q = p || p &| True - -p &| q = p || q &| q - -p &| q = p || False &| q - -p &| q = p || True &| q - -p &| q = q || p &| p - -p &| q = q || p &| q - -p &| q = q || p &| False - -p &| q = q || p &| True - -p &| q = q || q &| q - -p &| q = q || False &| q - -p &| q = q || True &| q - -p &| q = p && (q && not p) - -p &| q = p && (q || not p) - -p &| q = q && (p && not q) - -p &| q = q && (p || not q) - -p &| q = p || q && not p - -p &| q = p || (q || not p) - -p &| q = q || p && not q - -p &| q = q || (p || not q) - -p &| q = not p && (p && q) - -p &| q = not p && (p || q) - -p &| q = not q && (p && q) - -p &| q = not q && (p || q) - -p &| q = not p || p && q - -p &| q = not p || (p || q) - -p &| q = not q || p && q - -p &| q = not q || (p || q) - -p &| q = p && p &| not p - -p &| q = p && p &| not q - -p &| q = p && q &| not q - -p &| q = p && False &| not q - -p &| q = p && True &| not q - -p &| q = p && not p &| p - -p &| q = p && not p &| q - -p &| q = p && not p &| False - -p &| q = p && not p &| True - -p &| q = p && not q &| q - -p &| q = q && p &| not p - -p &| q = q && p &| not q - -p &| q = q && q &| not q - -p &| q = q && False &| not q - -p &| q = q && True &| not q - -p &| q = q && not p &| p - -p &| q = q && not p &| q - -p &| q = q && not p &| False - -p &| q = q && not p &| True - -p &| q = q && not q &| q - -p &| q = p || p &| not p - -p &| q = p || p &| not q - -p &| q = p || q &| not q - -p &| q = p || False &| not q - -p &| q = p || True &| not q - -p &| q = p || not p &| p - -p &| q = p || not p &| q - -p &| q = p || not p &| False - -p &| q = p || not p &| True - -p &| q = p || not q &| q - -p &| q = q || p &| not p - -p &| q = q || p &| not q - -p &| q = q || q &| not q - -p &| q = q || False &| not q - -p &| q = q || True &| not q - -p &| q = q || not p &| p - -p &| q = q || not p &| q - -p &| q = q || not p &| False - -p &| q = q || not p &| True - -p &| q = q || not q &| q - -p &| q = p && not (p &| p) - -p &| q = p && not (p &| q) - -p &| q = p && not (p &| False) - -p &| q = p && not (p &| True) - -p &| q = p && not (q &| q) - -p &| q = p && not (False &| q) - -p &| q = p && not (True &| q) - -p &| q = q && not (p &| p) - -p &| q = q && not (p &| q) - -p &| q = q && not (p &| False) - -p &| q = q && not (p &| True) - -p &| q = q && not (q &| q) - -p &| q = q && not (False &| q) - -p &| q = q && not (True &| q) - -p &| q = not p && p &| p - -p &| q = not p && p &| q - -p &| q = not p && p &| False - -p &| q = not p && p &| True - -p &| q = not p && q &| q - -p &| q = not p && False &| q - -p &| q = not p && True &| q - -p &| q = not q && p &| p - -p &| q = not q && p &| q - -p &| q = not q && p &| False - -p &| q = not q && p &| True - -p &| q = not q && q &| q - -p &| q = not q && False &| q - -p &| q = not q && True &| q - -p &| q = p || not (p &| p) - -p &| q = p || not (p &| q) - -p &| q = p || not (p &| False) - -p &| q = p || not (p &| True) - -p &| q = p || not (q &| q) - -p &| q = p || not (False &| q) - -p &| q = p || not (True &| q) - -p &| q = q || not (p &| p) - -p &| q = q || not (p &| q) - -p &| q = q || not (p &| False) - -p &| q = q || not (p &| True) - -p &| q = q || not (q &| q) - -p &| q = q || not (False &| q) - -p &| q = q || not (True &| q) - -p &| q = not p || p &| p - -p &| q = not p || p &| q - -p &| q = not p || p &| False - -p &| q = not p || p &| True - -p &| q = not p || q &| q - -p &| q = not p || False &| q - -p &| q = not p || True &| q - -p &| q = not q || p &| p - -p &| q = not q || p &| q - -p &| q = not q || p &| False - -p &| q = not q || p &| True - -p &| q = not q || q &| q - -p &| q = not q || False &| q - -p &| q = not q || True &| q - - -pattern candidates: - -p &| q = p - -p &| q = q - -p &| q = False - -p &| q = True - -p &| q = not p - -p &| q = not q - -p &| False = p -p &| True = False - -p &| False = p -p &| True = True - -p &| False = False -p &| True = p - -p &| False = False -p &| True = True - -p &| False = True -p &| True = p - -p &| False = True -p &| True = False - -False &| p = p -True &| p = False - -False &| p = p -True &| p = True - -False &| p = False -True &| p = p - -False &| p = False -True &| p = True - -False &| p = True -True &| p = p - -False &| p = True -True &| p = False - -p &| q = p && q - -p &| q = p || q - -p &| False = p -p &| True = not p - -p &| False = False -p &| True = not p - -p &| False = True -p &| True = not p - -p &| False = not p -p &| True = p - -p &| False = not p -p &| True = False - -p &| False = not p -p &| True = True - -False &| p = p -True &| p = not p - -False &| p = False -True &| p = not p - -False &| p = True -True &| p = not p - -False &| p = not p -True &| p = p - -False &| p = not p -True &| p = False - -False &| p = not p -True &| p = True - -False &| p = p -True &| False = False -True &| True = True - -False &| p = p -True &| False = True -True &| True = False - -False &| p = False -True &| False = False -True &| True = True - -False &| p = False -True &| False = True -True &| True = False - -False &| p = True -True &| False = False -True &| True = True - -False &| p = True -True &| False = True -True &| True = False - -False &| False = False -False &| True = True -True &| p = p - -False &| False = False -False &| True = True -True &| p = False - -False &| False = False -False &| True = True -True &| p = True - -False &| False = True -False &| True = False -True &| p = p - -False &| False = True -False &| True = False -True &| p = False - -False &| False = True -False &| True = False -True &| p = True - -p &| q = p && not q - -p &| q = q && not p - -p &| q = p || not q - -p &| q = q || not p - -False &| p = not p -True &| False = False -True &| True = True - -False &| p = not p -True &| False = True -True &| True = False - -False &| False = False -False &| True = True -True &| p = not p - -False &| False = True -False &| True = False -True &| p = not p - -False &| False = False -False &| True = True -True &| False = True -True &| True = False - -False &| False = True -False &| True = False -True &| False = False -True &| True = True - -p &| q = not p && not q - -p &| q = not p || not q - -p &| q = p && (q && not p) - -p &| q = p && (q || not p) - -p &| q = q && (p && not q) - -p &| q = q && (p || not q) - -p &| q = p || q && not p - -p &| q = p || (q || not p) - -p &| q = q || p && not q - -p &| q = q || (p || not q) - -p &| q = not p && (p && q) - -p &| q = not p && (p || q) - -p &| q = not q && (p && q) - -p &| q = not q && (p || q) - -p &| q = not p || p && q - -p &| q = not p || (p || q) - -p &| q = not q || p && q - -p &| q = not q || (p || q) - - -Candidates for: gcd :: Int -> Int -> Int - pruning with 0/0 rules - [3,0,9,0,54,0,405,0,3402] direct candidates, 0 duplicates - [3,5,11,50,98,359,786,2836,6723] pattern candidates, 0 duplicates - -no rules. - -direct candidates: - -gcd x y = x - -gcd x y = y - -gcd x y = 0 - -gcd x y = x `mod` x - -gcd x y = x `mod` y - -gcd x y = x `mod` 0 - -gcd x y = y `mod` x - -gcd x y = y `mod` y - -gcd x y = y `mod` 0 - -gcd x y = 0 `mod` x - -gcd x y = 0 `mod` y - -gcd x y = 0 `mod` 0 - -gcd x y = (x `mod` x) `mod` x - -gcd x y = (x `mod` x) `mod` y - -gcd x y = (x `mod` x) `mod` 0 - -gcd x y = (x `mod` y) `mod` x - -gcd x y = (x `mod` y) `mod` y - -gcd x y = (x `mod` y) `mod` 0 - -gcd x y = (x `mod` 0) `mod` x - -gcd x y = (x `mod` 0) `mod` y - -gcd x y = (x `mod` 0) `mod` 0 - -gcd x y = (y `mod` x) `mod` x - -gcd x y = (y `mod` x) `mod` y - -gcd x y = (y `mod` x) `mod` 0 - -gcd x y = (y `mod` y) `mod` x - -gcd x y = (y `mod` y) `mod` y - -gcd x y = (y `mod` y) `mod` 0 - -gcd x y = (y `mod` 0) `mod` x - -gcd x y = (y `mod` 0) `mod` y - -gcd x y = (y `mod` 0) `mod` 0 - -gcd x y = (0 `mod` x) `mod` x - -gcd x y = (0 `mod` x) `mod` y - -gcd x y = (0 `mod` x) `mod` 0 - -gcd x y = (0 `mod` y) `mod` x - -gcd x y = (0 `mod` y) `mod` y - -gcd x y = (0 `mod` y) `mod` 0 - -gcd x y = (0 `mod` 0) `mod` x - -gcd x y = (0 `mod` 0) `mod` y - -gcd x y = (0 `mod` 0) `mod` 0 - -gcd x y = x `mod` (x `mod` x) - -gcd x y = x `mod` (x `mod` y) - -gcd x y = x `mod` (x `mod` 0) - -gcd x y = x `mod` (y `mod` x) - -gcd x y = x `mod` (y `mod` y) - -gcd x y = x `mod` (y `mod` 0) - -gcd x y = x `mod` (0 `mod` x) - -gcd x y = x `mod` (0 `mod` y) - -gcd x y = x `mod` (0 `mod` 0) - -gcd x y = y `mod` (x `mod` x) - -gcd x y = y `mod` (x `mod` y) - -gcd x y = y `mod` (x `mod` 0) - -gcd x y = y `mod` (y `mod` x) - -gcd x y = y `mod` (y `mod` y) - -gcd x y = y `mod` (y `mod` 0) - -gcd x y = y `mod` (0 `mod` x) - -gcd x y = y `mod` (0 `mod` y) - -gcd x y = y `mod` (0 `mod` 0) - -gcd x y = 0 `mod` (x `mod` x) - -gcd x y = 0 `mod` (x `mod` y) - -gcd x y = 0 `mod` (x `mod` 0) - -gcd x y = 0 `mod` (y `mod` x) - -gcd x y = 0 `mod` (y `mod` y) - -gcd x y = 0 `mod` (y `mod` 0) - -gcd x y = 0 `mod` (0 `mod` x) - -gcd x y = 0 `mod` (0 `mod` y) - -gcd x y = 0 `mod` (0 `mod` 0) - - -pattern candidates: - -gcd x y = x - -gcd x y = y - -gcd x y = 0 - -gcd x 0 = x -gcd x y = y - -gcd x 0 = x -gcd x y = 0 - -gcd x 0 = 0 -gcd x y = x - -gcd 0 x = x -gcd x y = 0 - -gcd 0 x = 0 -gcd x y = y - -gcd x y = x `mod` x - -gcd x y = x `mod` y - -gcd x y = x `mod` 0 - -gcd x y = y `mod` x - -gcd x y = y `mod` y - -gcd x y = y `mod` 0 - -gcd x y = 0 `mod` x - -gcd x y = 0 `mod` y - -gcd 0 x = x -gcd x 0 = x -gcd x y = 0 - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = x - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = y - -gcd x 0 = x -gcd x y = x `mod` x - -gcd x 0 = x -gcd x y = x `mod` y - -gcd x 0 = x -gcd x y = x `mod` 0 - -gcd x 0 = x -gcd x y = y `mod` x - -gcd x 0 = x -gcd x y = y `mod` y - -gcd x 0 = x -gcd x y = y `mod` 0 - -gcd x 0 = x -gcd x y = 0 `mod` x - -gcd x 0 = x -gcd x y = 0 `mod` y - -gcd x 0 = 0 -gcd x y = x `mod` x - -gcd x 0 = 0 -gcd x y = x `mod` y - -gcd x 0 = 0 -gcd x y = x `mod` 0 - -gcd x 0 = 0 -gcd x y = y `mod` x - -gcd x 0 = 0 -gcd x y = y `mod` y - -gcd x 0 = 0 -gcd x y = y `mod` 0 - -gcd x 0 = 0 -gcd x y = 0 `mod` x - -gcd x 0 = 0 -gcd x y = 0 `mod` y - -gcd x 0 = x `mod` x -gcd x y = x - -gcd x 0 = x `mod` x -gcd x y = y - -gcd x 0 = x `mod` x -gcd x y = 0 - -gcd x 0 = x `mod` 0 -gcd x y = x - -gcd x 0 = x `mod` 0 -gcd x y = y - -gcd x 0 = x `mod` 0 -gcd x y = 0 - -gcd x 0 = 0 `mod` x -gcd x y = x - -gcd x 0 = 0 `mod` x -gcd x y = y - -gcd x 0 = 0 `mod` x -gcd x y = 0 - -gcd 0 x = x -gcd x y = x `mod` x - -gcd 0 x = x -gcd x y = x `mod` y - -gcd 0 x = x -gcd x y = x `mod` 0 - -gcd 0 x = x -gcd x y = y `mod` x - -gcd 0 x = x -gcd x y = y `mod` y - -gcd 0 x = x -gcd x y = y `mod` 0 - -gcd 0 x = x -gcd x y = 0 `mod` x - -gcd 0 x = x -gcd x y = 0 `mod` y - -gcd 0 x = 0 -gcd x y = x `mod` x - -gcd 0 x = 0 -gcd x y = x `mod` y - -gcd 0 x = 0 -gcd x y = x `mod` 0 - -gcd 0 x = 0 -gcd x y = y `mod` x - -gcd 0 x = 0 -gcd x y = y `mod` y - -gcd 0 x = 0 -gcd x y = y `mod` 0 - -gcd 0 x = 0 -gcd x y = 0 `mod` x - -gcd 0 x = 0 -gcd x y = 0 `mod` y - -gcd 0 x = x `mod` x -gcd x y = x - -gcd 0 x = x `mod` x -gcd x y = y - -gcd 0 x = x `mod` x -gcd x y = 0 - -gcd 0 x = x `mod` 0 -gcd x y = x - -gcd 0 x = x `mod` 0 -gcd x y = y - -gcd 0 x = x `mod` 0 -gcd x y = 0 - -gcd 0 x = 0 `mod` x -gcd x y = x - -gcd 0 x = 0 `mod` x -gcd x y = y - -gcd 0 x = 0 `mod` x -gcd x y = 0 - -gcd x y = (x `mod` x) `mod` x - -gcd x y = (x `mod` x) `mod` y - -gcd x y = (x `mod` x) `mod` 0 - -gcd x y = (x `mod` y) `mod` x - -gcd x y = (x `mod` y) `mod` y - -gcd x y = (x `mod` y) `mod` 0 - -gcd x y = (x `mod` 0) `mod` x - -gcd x y = (x `mod` 0) `mod` y - -gcd x y = (x `mod` 0) `mod` 0 - -gcd x y = (y `mod` x) `mod` x - -gcd x y = (y `mod` x) `mod` y - -gcd x y = (y `mod` x) `mod` 0 - -gcd x y = (y `mod` y) `mod` x - -gcd x y = (y `mod` y) `mod` y - -gcd x y = (y `mod` y) `mod` 0 - -gcd x y = (y `mod` 0) `mod` x - -gcd x y = (y `mod` 0) `mod` y - -gcd x y = (y `mod` 0) `mod` 0 - -gcd x y = (0 `mod` x) `mod` x - -gcd x y = (0 `mod` x) `mod` y - -gcd x y = (0 `mod` x) `mod` 0 - -gcd x y = (0 `mod` y) `mod` x - -gcd x y = (0 `mod` y) `mod` y - -gcd x y = (0 `mod` y) `mod` 0 - -gcd x y = x `mod` (x `mod` x) - -gcd x y = x `mod` (x `mod` y) - -gcd x y = x `mod` (x `mod` 0) - -gcd x y = x `mod` (y `mod` x) - -gcd x y = x `mod` (y `mod` y) - -gcd x y = x `mod` (y `mod` 0) - -gcd x y = x `mod` (0 `mod` x) - -gcd x y = x `mod` (0 `mod` y) - -gcd x y = y `mod` (x `mod` x) - -gcd x y = y `mod` (x `mod` y) - -gcd x y = y `mod` (x `mod` 0) - -gcd x y = y `mod` (y `mod` x) - -gcd x y = y `mod` (y `mod` y) - -gcd x y = y `mod` (y `mod` 0) - -gcd x y = y `mod` (0 `mod` x) - -gcd x y = y `mod` (0 `mod` y) - -gcd x y = 0 `mod` (x `mod` x) - -gcd x y = 0 `mod` (x `mod` y) - -gcd x y = 0 `mod` (x `mod` 0) - -gcd x y = 0 `mod` (y `mod` x) - -gcd x y = 0 `mod` (y `mod` y) - -gcd x y = 0 `mod` (y `mod` 0) - -gcd x y = 0 `mod` (0 `mod` x) - -gcd x y = 0 `mod` (0 `mod` y) - -gcd 0 x = x -gcd x 0 = x -gcd x y = x `mod` x - -gcd 0 x = x -gcd x 0 = x -gcd x y = x `mod` y - -gcd 0 x = x -gcd x 0 = x -gcd x y = x `mod` 0 - -gcd 0 x = x -gcd x 0 = x -gcd x y = y `mod` x - -gcd 0 x = x -gcd x 0 = x -gcd x y = y `mod` y - -gcd 0 x = x -gcd x 0 = x -gcd x y = y `mod` 0 - -gcd 0 x = x -gcd x 0 = x -gcd x y = 0 `mod` x - -gcd 0 x = x -gcd x 0 = x -gcd x y = 0 `mod` y - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = x `mod` x - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = x `mod` y - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = x `mod` 0 - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = y `mod` x - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = y `mod` y - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = y `mod` 0 - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = 0 `mod` x - -gcd 0 x = x -gcd x 0 = 0 -gcd x y = 0 `mod` y - -gcd 0 x = x -gcd x 0 = x `mod` x -gcd x y = x - -gcd 0 x = x -gcd x 0 = x `mod` x -gcd x y = 0 - -gcd 0 x = x -gcd x 0 = x `mod` 0 -gcd x y = x - -gcd 0 x = x -gcd x 0 = x `mod` 0 -gcd x y = 0 - -gcd 0 x = x -gcd x 0 = 0 `mod` x -gcd x y = x - -gcd 0 x = x -gcd x 0 = 0 `mod` x -gcd x y = 0 - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = x `mod` x - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = x `mod` y - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = x `mod` 0 - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = y `mod` x - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = y `mod` y - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = y `mod` 0 - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = 0 `mod` x - -gcd 0 x = 0 -gcd x 0 = x -gcd x y = 0 `mod` y - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = x `mod` x - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = x `mod` y - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = x `mod` 0 - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = y `mod` x - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = y `mod` y - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = y `mod` 0 - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = 0 `mod` x - -gcd 0 x = 0 -gcd x 0 = 0 -gcd x y = 0 `mod` y - -gcd 0 x = 0 -gcd x 0 = x `mod` x -gcd x y = y - -gcd 0 x = 0 -gcd x 0 = x `mod` 0 -gcd x y = y - -gcd 0 x = 0 -gcd x 0 = 0 `mod` x -gcd x y = y - -gcd 0 x = x `mod` x -gcd x 0 = x -gcd x y = y - -gcd 0 x = x `mod` x -gcd x 0 = x -gcd x y = 0 - -gcd 0 x = x `mod` x -gcd x 0 = 0 -gcd x y = x - -gcd 0 x = x `mod` 0 -gcd x 0 = x -gcd x y = y - -gcd 0 x = x `mod` 0 -gcd x 0 = x -gcd x y = 0 - -gcd 0 x = x `mod` 0 -gcd x 0 = 0 -gcd x y = x - -gcd 0 x = 0 `mod` x -gcd x 0 = x -gcd x y = y - -gcd 0 x = 0 `mod` x -gcd x 0 = x -gcd x y = 0 - -gcd 0 x = 0 `mod` x -gcd x 0 = 0 -gcd x y = x - -gcd x 0 = x -gcd x y = gcd x (x `mod` y) - -gcd x 0 = x -gcd x y = gcd x (y `mod` y) - -gcd x 0 = x -gcd x y = gcd x (0 `mod` y) - -gcd x 0 = x -gcd x y = gcd y (x `mod` y) - -gcd x 0 = x -gcd x y = gcd y (y `mod` y) - -gcd x 0 = x -gcd x y = gcd y (0 `mod` y) - -gcd x 0 = x -gcd x y = gcd 0 (x `mod` y) - -gcd x 0 = x -gcd x y = gcd 0 (y `mod` y) - -gcd x 0 = x -gcd x y = gcd 0 (0 `mod` y) - -gcd x 0 = x -gcd x y = gcd (x `mod` x) x - -gcd x 0 = x -gcd x y = gcd (x `mod` x) y - -gcd x 0 = x -gcd x y = gcd (y `mod` x) x - -gcd x 0 = x -gcd x y = gcd (y `mod` x) y - -gcd x 0 = x -gcd x y = gcd (0 `mod` x) x - -gcd x 0 = x -gcd x y = gcd (0 `mod` x) y - -gcd x 0 = 0 -gcd x y = gcd x (x `mod` y) - -gcd x 0 = 0 -gcd x y = gcd x (y `mod` y) - -gcd x 0 = 0 -gcd x y = gcd x (0 `mod` y) - -gcd x 0 = 0 -gcd x y = gcd y (x `mod` y) - -gcd x 0 = 0 -gcd x y = gcd y (y `mod` y) - -gcd x 0 = 0 -gcd x y = gcd y (0 `mod` y) - -gcd x 0 = 0 -gcd x y = gcd 0 (x `mod` y) - -gcd x 0 = 0 -gcd x y = gcd 0 (y `mod` y) - -gcd x 0 = 0 -gcd x y = gcd 0 (0 `mod` y) - -gcd x 0 = 0 -gcd x y = gcd (x `mod` x) x - -gcd x 0 = 0 -gcd x y = gcd (x `mod` x) y - -gcd x 0 = 0 -gcd x y = gcd (y `mod` x) x - -gcd x 0 = 0 -gcd x y = gcd (y `mod` x) y - -gcd x 0 = 0 -gcd x y = gcd (0 `mod` x) x - -gcd x 0 = 0 -gcd x y = gcd (0 `mod` x) y - -gcd 0 x = x -gcd x y = gcd x (x `mod` y) - -gcd 0 x = x -gcd x y = gcd x (y `mod` y) - -gcd 0 x = x -gcd x y = gcd x (0 `mod` y) - -gcd 0 x = x -gcd x y = gcd y (x `mod` y) - -gcd 0 x = x -gcd x y = gcd y (y `mod` y) - -gcd 0 x = x -gcd x y = gcd y (0 `mod` y) - -gcd 0 x = x -gcd x y = gcd (x `mod` x) x - -gcd 0 x = x -gcd x y = gcd (x `mod` x) y - -gcd 0 x = x -gcd x y = gcd (x `mod` x) 0 - -gcd 0 x = x -gcd x y = gcd (y `mod` x) x - -gcd 0 x = x -gcd x y = gcd (y `mod` x) y - -gcd 0 x = x -gcd x y = gcd (y `mod` x) 0 - -gcd 0 x = x -gcd x y = gcd (0 `mod` x) x - -gcd 0 x = x -gcd x y = gcd (0 `mod` x) y - -gcd 0 x = x -gcd x y = gcd (0 `mod` x) 0 - -gcd 0 x = 0 -gcd x y = gcd x (x `mod` y) - -gcd 0 x = 0 -gcd x y = gcd x (y `mod` y) - -gcd 0 x = 0 -gcd x y = gcd x (0 `mod` y) - -gcd 0 x = 0 -gcd x y = gcd y (x `mod` y) - -gcd 0 x = 0 -gcd x y = gcd y (y `mod` y) - -gcd 0 x = 0 -gcd x y = gcd y (0 `mod` y) - -gcd 0 x = 0 -gcd x y = gcd (x `mod` x) x - -gcd 0 x = 0 -gcd x y = gcd (x `mod` x) y - -gcd 0 x = 0 -gcd x y = gcd (x `mod` x) 0 - -gcd 0 x = 0 -gcd x y = gcd (y `mod` x) x - -gcd 0 x = 0 -gcd x y = gcd (y `mod` x) y - -gcd 0 x = 0 -gcd x y = gcd (y `mod` x) 0 - -gcd 0 x = 0 -gcd x y = gcd (0 `mod` x) x - -gcd 0 x = 0 -gcd x y = gcd (0 `mod` x) y - -gcd 0 x = 0 -gcd x y = gcd (0 `mod` x) 0 - -gcd x 0 = x -gcd x y = (x `mod` x) `mod` x - -gcd x 0 = x -gcd x y = (x `mod` x) `mod` y - -gcd x 0 = x -gcd x y = (x `mod` x) `mod` 0 - -gcd x 0 = x -gcd x y = (x `mod` y) `mod` x - -gcd x 0 = x -gcd x y = (x `mod` y) `mod` y - -gcd x 0 = x -gcd x y = (x `mod` y) `mod` 0 - -gcd x 0 = x -gcd x y = (x `mod` 0) `mod` x - -gcd x 0 = x -gcd x y = (x `mod` 0) `mod` y - -gcd x 0 = x -gcd x y = (x `mod` 0) `mod` 0 - -gcd x 0 = x -gcd x y = (y `mod` x) `mod` x - -gcd x 0 = x -gcd x y = (y `mod` x) `mod` y - -gcd x 0 = x -gcd x y = (y `mod` x) `mod` 0 - -gcd x 0 = x -gcd x y = (y `mod` y) `mod` x - -gcd x 0 = x -gcd x y = (y `mod` y) `mod` y - -gcd x 0 = x -gcd x y = (y `mod` y) `mod` 0 - -gcd x 0 = x -gcd x y = (y `mod` 0) `mod` x - -gcd x 0 = x -gcd x y = (y `mod` 0) `mod` y - -gcd x 0 = x -gcd x y = (y `mod` 0) `mod` 0 - -gcd x 0 = x -gcd x y = (0 `mod` x) `mod` x - -gcd x 0 = x -gcd x y = (0 `mod` x) `mod` y - -gcd x 0 = x -gcd x y = (0 `mod` x) `mod` 0 - -gcd x 0 = x -gcd x y = (0 `mod` y) `mod` x - -gcd x 0 = x -gcd x y = (0 `mod` y) `mod` y - -gcd x 0 = x -gcd x y = (0 `mod` y) `mod` 0 - -gcd x 0 = x -gcd x y = x `mod` (x `mod` x) - -gcd x 0 = x -gcd x y = x `mod` (x `mod` y) - -gcd x 0 = x -gcd x y = x `mod` (x `mod` 0) - -gcd x 0 = x -gcd x y = x `mod` (y `mod` x) - -gcd x 0 = x -gcd x y = x `mod` (y `mod` y) - -gcd x 0 = x -gcd x y = x `mod` (y `mod` 0) - -gcd x 0 = x -gcd x y = x `mod` (0 `mod` x) - -gcd x 0 = x -gcd x y = x `mod` (0 `mod` y) - -gcd x 0 = x -gcd x y = y `mod` (x `mod` x) - -gcd x 0 = x -gcd x y = y `mod` (x `mod` y) - -gcd x 0 = x -gcd x y = y `mod` (x `mod` 0) - -gcd x 0 = x -gcd x y = y `mod` (y `mod` x) - -gcd x 0 = x -gcd x y = y `mod` (y `mod` y) - -gcd x 0 = x -gcd x y = y `mod` (y `mod` 0) - -gcd x 0 = x -gcd x y = y `mod` (0 `mod` x) - -gcd x 0 = x -gcd x y = y `mod` (0 `mod` y) - -gcd x 0 = x -gcd x y = 0 `mod` (x `mod` x) - -gcd x 0 = x -gcd x y = 0 `mod` (x `mod` y) - -gcd x 0 = x -gcd x y = 0 `mod` (x `mod` 0) - -gcd x 0 = x -gcd x y = 0 `mod` (y `mod` x) - -gcd x 0 = x -gcd x y = 0 `mod` (y `mod` y) - -gcd x 0 = x -gcd x y = 0 `mod` (y `mod` 0) - -gcd x 0 = x -gcd x y = 0 `mod` (0 `mod` x) - -gcd x 0 = x -gcd x y = 0 `mod` (0 `mod` y) - -gcd x 0 = 0 -gcd x y = (x `mod` x) `mod` x - -gcd x 0 = 0 -gcd x y = (x `mod` x) `mod` y - -gcd x 0 = 0 -gcd x y = (x `mod` x) `mod` 0 - -gcd x 0 = 0 -gcd x y = (x `mod` y) `mod` x - -gcd x 0 = 0 -gcd x y = (x `mod` y) `mod` y - -gcd x 0 = 0 -gcd x y = (x `mod` y) `mod` 0 - -gcd x 0 = 0 -gcd x y = (x `mod` 0) `mod` x - -gcd x 0 = 0 -gcd x y = (x `mod` 0) `mod` y - -gcd x 0 = 0 -gcd x y = (x `mod` 0) `mod` 0 - -gcd x 0 = 0 -gcd x y = (y `mod` x) `mod` x - -gcd x 0 = 0 -gcd x y = (y `mod` x) `mod` y - -gcd x 0 = 0 -gcd x y = (y `mod` x) `mod` 0 - -gcd x 0 = 0 -gcd x y = (y `mod` y) `mod` x - -gcd x 0 = 0 -gcd x y = (y `mod` y) `mod` y - -gcd x 0 = 0 -gcd x y = (y `mod` y) `mod` 0 - -gcd x 0 = 0 -gcd x y = (y `mod` 0) `mod` x - -gcd x 0 = 0 -gcd x y = (y `mod` 0) `mod` y - -gcd x 0 = 0 -gcd x y = (y `mod` 0) `mod` 0 - -gcd x 0 = 0 -gcd x y = (0 `mod` x) `mod` x - -gcd x 0 = 0 -gcd x y = (0 `mod` x) `mod` y - -gcd x 0 = 0 -gcd x y = (0 `mod` x) `mod` 0 - -gcd x 0 = 0 -gcd x y = (0 `mod` y) `mod` x - -gcd x 0 = 0 -gcd x y = (0 `mod` y) `mod` y - -gcd x 0 = 0 -gcd x y = (0 `mod` y) `mod` 0 - -gcd x 0 = 0 -gcd x y = x `mod` (x `mod` x) - -gcd x 0 = 0 -gcd x y = x `mod` (x `mod` y) - -gcd x 0 = 0 -gcd x y = x `mod` (x `mod` 0) - -gcd x 0 = 0 -gcd x y = x `mod` (y `mod` x) - -gcd x 0 = 0 -gcd x y = x `mod` (y `mod` y) - -gcd x 0 = 0 -gcd x y = x `mod` (y `mod` 0) - -gcd x 0 = 0 -gcd x y = x `mod` (0 `mod` x) - -gcd x 0 = 0 -gcd x y = x `mod` (0 `mod` y) - -gcd x 0 = 0 -gcd x y = y `mod` (x `mod` x) - -gcd x 0 = 0 -gcd x y = y `mod` (x `mod` y) - -gcd x 0 = 0 -gcd x y = y `mod` (x `mod` 0) - -gcd x 0 = 0 -gcd x y = y `mod` (y `mod` x) - -gcd x 0 = 0 -gcd x y = y `mod` (y `mod` y) - -gcd x 0 = 0 -gcd x y = y `mod` (y `mod` 0) - -gcd x 0 = 0 -gcd x y = y `mod` (0 `mod` x) - -gcd x 0 = 0 -gcd x y = y `mod` (0 `mod` y) - -gcd x 0 = 0 -gcd x y = 0 `mod` (x `mod` x) - -gcd x 0 = 0 -gcd x y = 0 `mod` (x `mod` y) - -gcd x 0 = 0 -gcd x y = 0 `mod` (x `mod` 0) - -gcd x 0 = 0 -gcd x y = 0 `mod` (y `mod` x) - -gcd x 0 = 0 -gcd x y = 0 `mod` (y `mod` y) - -gcd x 0 = 0 -gcd x y = 0 `mod` (y `mod` 0) - -gcd x 0 = 0 -gcd x y = 0 `mod` (0 `mod` x) - -gcd x 0 = 0 -gcd x y = 0 `mod` (0 `mod` y) - -gcd x 0 = x `mod` x -gcd x y = x `mod` y - -gcd x 0 = x `mod` x -gcd x y = x `mod` 0 - -gcd x 0 = x `mod` x -gcd x y = y `mod` x - -gcd x 0 = x `mod` x -gcd x y = y `mod` y - -gcd x 0 = x `mod` x -gcd x y = y `mod` 0 - -gcd x 0 = x `mod` x -gcd x y = 0 `mod` x - -gcd x 0 = x `mod` x -gcd x y = 0 `mod` y - -gcd x 0 = x `mod` 0 -gcd x y = x `mod` x - -gcd x 0 = x `mod` 0 -gcd x y = y `mod` x - -gcd x 0 = x `mod` 0 -gcd x y = y `mod` y - -gcd x 0 = x `mod` 0 -gcd x y = y `mod` 0 - -gcd x 0 = x `mod` 0 -gcd x y = 0 `mod` x - -gcd x 0 = x `mod` 0 -gcd x y = 0 `mod` y - -gcd x 0 = 0 `mod` x -gcd x y = x `mod` x - -gcd x 0 = 0 `mod` x -gcd x y = x `mod` y - -gcd x 0 = 0 `mod` x -gcd x y = x `mod` 0 - -gcd x 0 = 0 `mod` x -gcd x y = y `mod` y - -gcd x 0 = 0 `mod` x -gcd x y = y `mod` 0 - -gcd x 0 = 0 `mod` x -gcd x y = 0 `mod` y - -gcd x 0 = (x `mod` x) `mod` x -gcd x y = x - -gcd x 0 = (x `mod` x) `mod` x -gcd x y = y - -gcd x 0 = (x `mod` x) `mod` x -gcd x y = 0 - -gcd x 0 = (x `mod` x) `mod` 0 -gcd x y = x - -gcd x 0 = (x `mod` x) `mod` 0 -gcd x y = y - -gcd x 0 = (x `mod` x) `mod` 0 -gcd x y = 0 - -gcd x 0 = (x `mod` 0) `mod` x -gcd x y = x - -gcd x 0 = (x `mod` 0) `mod` x -gcd x y = y - -gcd x 0 = (x `mod` 0) `mod` x -gcd x y = 0 - -gcd x 0 = (x `mod` 0) `mod` 0 -gcd x y = x - -gcd x 0 = (x `mod` 0) `mod` 0 -gcd x y = y - -gcd x 0 = (x `mod` 0) `mod` 0 -gcd x y = 0 - -gcd x 0 = (0 `mod` x) `mod` x -gcd x y = x - -gcd x 0 = (0 `mod` x) `mod` x -gcd x y = y - -gcd x 0 = (0 `mod` x) `mod` x -gcd x y = 0 - -gcd x 0 = (0 `mod` x) `mod` 0 -gcd x y = x - -gcd x 0 = (0 `mod` x) `mod` 0 -gcd x y = y - -gcd x 0 = (0 `mod` x) `mod` 0 -gcd x y = 0 - -gcd x 0 = x `mod` (x `mod` x) -gcd x y = x - -gcd x 0 = x `mod` (x `mod` x) -gcd x y = y - -gcd x 0 = x `mod` (x `mod` x) -gcd x y = 0 - -gcd x 0 = x `mod` (x `mod` 0) -gcd x y = x - -gcd x 0 = x `mod` (x `mod` 0) -gcd x y = y - -gcd x 0 = x `mod` (x `mod` 0) -gcd x y = 0 - -gcd x 0 = x `mod` (0 `mod` x) -gcd x y = x - -gcd x 0 = x `mod` (0 `mod` x) -gcd x y = y - -gcd x 0 = x `mod` (0 `mod` x) -gcd x y = 0 - -gcd x 0 = 0 `mod` (x `mod` x) -gcd x y = x - -gcd x 0 = 0 `mod` (x `mod` x) -gcd x y = y - -gcd x 0 = 0 `mod` (x `mod` x) -gcd x y = 0 - -gcd x 0 = 0 `mod` (x `mod` 0) -gcd x y = x - -gcd x 0 = 0 `mod` (x `mod` 0) -gcd x y = y - -gcd x 0 = 0 `mod` (x `mod` 0) -gcd x y = 0 - -gcd x 0 = 0 `mod` (0 `mod` x) -gcd x y = x - -gcd x 0 = 0 `mod` (0 `mod` x) -gcd x y = y - -gcd x 0 = 0 `mod` (0 `mod` x) -gcd x y = 0 - -gcd 0 x = x -gcd x y = (x `mod` x) `mod` x - -gcd 0 x = x -gcd x y = (x `mod` x) `mod` y - -gcd 0 x = x -gcd x y = (x `mod` x) `mod` 0 - -gcd 0 x = x -gcd x y = (x `mod` y) `mod` x - -gcd 0 x = x -gcd x y = (x `mod` y) `mod` y - -gcd 0 x = x -gcd x y = (x `mod` y) `mod` 0 - -gcd 0 x = x -gcd x y = (x `mod` 0) `mod` x - -gcd 0 x = x -gcd x y = (x `mod` 0) `mod` y - -gcd 0 x = x -gcd x y = (x `mod` 0) `mod` 0 - -gcd 0 x = x -gcd x y = (y `mod` x) `mod` x - -gcd 0 x = x -gcd x y = (y `mod` x) `mod` y - -gcd 0 x = x -gcd x y = (y `mod` x) `mod` 0 - -gcd 0 x = x -gcd x y = (y `mod` y) `mod` x - -gcd 0 x = x -gcd x y = (y `mod` y) `mod` y - -gcd 0 x = x -gcd x y = (y `mod` y) `mod` 0 - -gcd 0 x = x -gcd x y = (y `mod` 0) `mod` x - -gcd 0 x = x -gcd x y = (y `mod` 0) `mod` y - -gcd 0 x = x -gcd x y = (y `mod` 0) `mod` 0 - -gcd 0 x = x -gcd x y = (0 `mod` x) `mod` x - -gcd 0 x = x -gcd x y = (0 `mod` x) `mod` y - -gcd 0 x = x -gcd x y = (0 `mod` x) `mod` 0 - -gcd 0 x = x -gcd x y = (0 `mod` y) `mod` x - -gcd 0 x = x -gcd x y = (0 `mod` y) `mod` y - -gcd 0 x = x -gcd x y = (0 `mod` y) `mod` 0 - -gcd 0 x = x -gcd x y = x `mod` (x `mod` x) - -gcd 0 x = x -gcd x y = x `mod` (x `mod` y) - -gcd 0 x = x -gcd x y = x `mod` (x `mod` 0) - -gcd 0 x = x -gcd x y = x `mod` (y `mod` x) - -gcd 0 x = x -gcd x y = x `mod` (y `mod` y) - -gcd 0 x = x -gcd x y = x `mod` (y `mod` 0) - -gcd 0 x = x -gcd x y = x `mod` (0 `mod` x) - -gcd 0 x = x -gcd x y = x `mod` (0 `mod` y) - -gcd 0 x = x -gcd x y = y `mod` (x `mod` x) - -gcd 0 x = x -gcd x y = y `mod` (x `mod` y) - -gcd 0 x = x -gcd x y = y `mod` (x `mod` 0) - -gcd 0 x = x -gcd x y = y `mod` (y `mod` x) - -gcd 0 x = x -gcd x y = y `mod` (y `mod` y) - -gcd 0 x = x -gcd x y = y `mod` (y `mod` 0) - -gcd 0 x = x -gcd x y = y `mod` (0 `mod` x) - -gcd 0 x = x -gcd x y = y `mod` (0 `mod` y) - -gcd 0 x = x -gcd x y = 0 `mod` (x `mod` x) - -gcd 0 x = x -gcd x y = 0 `mod` (x `mod` y) - -gcd 0 x = x -gcd x y = 0 `mod` (x `mod` 0) - -gcd 0 x = x -gcd x y = 0 `mod` (y `mod` x) - -gcd 0 x = x -gcd x y = 0 `mod` (y `mod` y) - -gcd 0 x = x -gcd x y = 0 `mod` (y `mod` 0) - -gcd 0 x = x -gcd x y = 0 `mod` (0 `mod` x) - -gcd 0 x = x -gcd x y = 0 `mod` (0 `mod` y) - -gcd 0 x = 0 -gcd x y = (x `mod` x) `mod` x - -gcd 0 x = 0 -gcd x y = (x `mod` x) `mod` y - -gcd 0 x = 0 -gcd x y = (x `mod` x) `mod` 0 - -gcd 0 x = 0 -gcd x y = (x `mod` y) `mod` x - -gcd 0 x = 0 -gcd x y = (x `mod` y) `mod` y - -gcd 0 x = 0 -gcd x y = (x `mod` y) `mod` 0 - -gcd 0 x = 0 -gcd x y = (x `mod` 0) `mod` x - -gcd 0 x = 0 -gcd x y = (x `mod` 0) `mod` y - -gcd 0 x = 0 -gcd x y = (x `mod` 0) `mod` 0 - -gcd 0 x = 0 -gcd x y = (y `mod` x) `mod` x - -gcd 0 x = 0 -gcd x y = (y `mod` x) `mod` y - -gcd 0 x = 0 -gcd x y = (y `mod` x) `mod` 0 - -gcd 0 x = 0 -gcd x y = (y `mod` y) `mod` x - -gcd 0 x = 0 -gcd x y = (y `mod` y) `mod` y - -gcd 0 x = 0 -gcd x y = (y `mod` y) `mod` 0 - -gcd 0 x = 0 -gcd x y = (y `mod` 0) `mod` x - -gcd 0 x = 0 -gcd x y = (y `mod` 0) `mod` y - -gcd 0 x = 0 -gcd x y = (y `mod` 0) `mod` 0 - -gcd 0 x = 0 -gcd x y = (0 `mod` x) `mod` x - -gcd 0 x = 0 -gcd x y = (0 `mod` x) `mod` y - -gcd 0 x = 0 -gcd x y = (0 `mod` x) `mod` 0 - -gcd 0 x = 0 -gcd x y = (0 `mod` y) `mod` x - -gcd 0 x = 0 -gcd x y = (0 `mod` y) `mod` y - -gcd 0 x = 0 -gcd x y = (0 `mod` y) `mod` 0 - -gcd 0 x = 0 -gcd x y = x `mod` (x `mod` x) - -gcd 0 x = 0 -gcd x y = x `mod` (x `mod` y) - -gcd 0 x = 0 -gcd x y = x `mod` (x `mod` 0) - -gcd 0 x = 0 -gcd x y = x `mod` (y `mod` x) - -gcd 0 x = 0 -gcd x y = x `mod` (y `mod` y) - -gcd 0 x = 0 -gcd x y = x `mod` (y `mod` 0) - -gcd 0 x = 0 -gcd x y = x `mod` (0 `mod` x) - -gcd 0 x = 0 -gcd x y = x `mod` (0 `mod` y) - -gcd 0 x = 0 -gcd x y = y `mod` (x `mod` x) - -gcd 0 x = 0 -gcd x y = y `mod` (x `mod` y) - -gcd 0 x = 0 -gcd x y = y `mod` (x `mod` 0) - -gcd 0 x = 0 -gcd x y = y `mod` (y `mod` x) - -gcd 0 x = 0 -gcd x y = y `mod` (y `mod` y) - -gcd 0 x = 0 -gcd x y = y `mod` (y `mod` 0) - -gcd 0 x = 0 -gcd x y = y `mod` (0 `mod` x) - -gcd 0 x = 0 -gcd x y = y `mod` (0 `mod` y) - -gcd 0 x = 0 -gcd x y = 0 `mod` (x `mod` x) - -gcd 0 x = 0 -gcd x y = 0 `mod` (x `mod` y) - -gcd 0 x = 0 -gcd x y = 0 `mod` (x `mod` 0) - -gcd 0 x = 0 -gcd x y = 0 `mod` (y `mod` x) - -gcd 0 x = 0 -gcd x y = 0 `mod` (y `mod` y) - -gcd 0 x = 0 -gcd x y = 0 `mod` (y `mod` 0) - -gcd 0 x = 0 -gcd x y = 0 `mod` (0 `mod` x) - -gcd 0 x = 0 -gcd x y = 0 `mod` (0 `mod` y) - -gcd 0 x = x `mod` x -gcd x y = x `mod` y - -gcd 0 x = x `mod` x -gcd x y = x `mod` 0 - -gcd 0 x = x `mod` x -gcd x y = y `mod` x - -gcd 0 x = x `mod` x -gcd x y = y `mod` 0 - -gcd 0 x = x `mod` x -gcd x y = 0 `mod` x - -gcd 0 x = x `mod` x -gcd x y = 0 `mod` y - -gcd 0 x = x `mod` 0 -gcd x y = x `mod` x - -gcd 0 x = x `mod` 0 -gcd x y = x `mod` y - -gcd 0 x = x `mod` 0 -gcd x y = y `mod` y - -gcd 0 x = x `mod` 0 -gcd x y = 0 `mod` x - -gcd 0 x = x `mod` 0 -gcd x y = 0 `mod` y - -gcd 0 x = 0 `mod` x -gcd x y = x `mod` x - -gcd 0 x = 0 `mod` x -gcd x y = x `mod` 0 - -gcd 0 x = 0 `mod` x -gcd x y = y `mod` x - -gcd 0 x = 0 `mod` x -gcd x y = y `mod` y - -gcd 0 x = 0 `mod` x -gcd x y = y `mod` 0 - -gcd 0 x = (x `mod` x) `mod` x -gcd x y = x - -gcd 0 x = (x `mod` x) `mod` x -gcd x y = y - -gcd 0 x = (x `mod` x) `mod` x -gcd x y = 0 - -gcd 0 x = (x `mod` x) `mod` 0 -gcd x y = x - -gcd 0 x = (x `mod` x) `mod` 0 -gcd x y = y - -gcd 0 x = (x `mod` x) `mod` 0 -gcd x y = 0 - -gcd 0 x = (x `mod` 0) `mod` x -gcd x y = x - -gcd 0 x = (x `mod` 0) `mod` x -gcd x y = y - -gcd 0 x = (x `mod` 0) `mod` x -gcd x y = 0 - -gcd 0 x = (x `mod` 0) `mod` 0 -gcd x y = x - -gcd 0 x = (x `mod` 0) `mod` 0 -gcd x y = y - -gcd 0 x = (x `mod` 0) `mod` 0 -gcd x y = 0 - -gcd 0 x = (0 `mod` x) `mod` x -gcd x y = x - -gcd 0 x = (0 `mod` x) `mod` x -gcd x y = y - -gcd 0 x = (0 `mod` x) `mod` x -gcd x y = 0 - -gcd 0 x = (0 `mod` x) `mod` 0 -gcd x y = x - -gcd 0 x = (0 `mod` x) `mod` 0 -gcd x y = y - -gcd 0 x = (0 `mod` x) `mod` 0 -gcd x y = 0 - -gcd 0 x = x `mod` (x `mod` x) -gcd x y = x - -gcd 0 x = x `mod` (x `mod` x) -gcd x y = y - -gcd 0 x = x `mod` (x `mod` x) -gcd x y = 0 - -gcd 0 x = x `mod` (x `mod` 0) -gcd x y = x - -gcd 0 x = x `mod` (x `mod` 0) -gcd x y = y - -gcd 0 x = x `mod` (x `mod` 0) -gcd x y = 0 - -gcd 0 x = x `mod` (0 `mod` x) -gcd x y = x - -gcd 0 x = x `mod` (0 `mod` x) -gcd x y = y - -gcd 0 x = x `mod` (0 `mod` x) -gcd x y = 0 - -gcd 0 x = 0 `mod` (x `mod` x) -gcd x y = x - -gcd 0 x = 0 `mod` (x `mod` x) -gcd x y = y - -gcd 0 x = 0 `mod` (x `mod` x) -gcd x y = 0 - -gcd 0 x = 0 `mod` (x `mod` 0) -gcd x y = x - -gcd 0 x = 0 `mod` (x `mod` 0) -gcd x y = y - -gcd 0 x = 0 `mod` (x `mod` 0) -gcd x y = 0 - -gcd 0 x = 0 `mod` (0 `mod` x) -gcd x y = x - -gcd 0 x = 0 `mod` (0 `mod` x) -gcd x y = y - -gcd 0 x = 0 `mod` (0 `mod` x) -gcd x y = 0 - - diff --git a/bench/candidates.txt b/bench/candidates.txt new file mode 100644 --- /dev/null +++ b/bench/candidates.txt @@ -0,0 +1,5920 @@ +Candidates for: foo :: Int -> Int + pruning with 15/35 rules + [3,0,7,0,19,0,90,0,454] direct candidates, 0 duplicates + [3,3,8,9,21,27,98,133,461] pattern candidates, 0 duplicates + +rules: +x * y == x + y +x * y == y + x +x - x == 0 +x + 0 == x +0 + x == x +x - 0 == x +(x + y) + z == x + (y + z) +(x + y) + z == y + (x + z) +x - (y - z) == z + (x - y) +(x - y) - z == x - (y + z) +(x - y) - z == x - (z + y) +(x + y) - z == x + (y - z) +(x + y) - z == y + (x - z) +x + (y - x) == y +(x - y) + y == x +equations: +y + x == x + y +y + (x + z) == x + (y + z) +z + (x + y) == x + (y + z) +z + (y + x) == x + (y + z) +y + (x - z) == x + (y - z) +(x - z) + y == x + (y - z) +(z - y) + x == (x - y) + z +y - (x + y) == 0 - x +y - (y + x) == 0 - x +z - (y + z) == x - (x + y) +z - (y + z) == x - (y + x) +z - (z + y) == x - (x + y) +z - (z + y) == x - (y + x) +x + (0 - y) == x - y +(0 - y) + x == x - y +x - (x + 1) == 0 - 1 +x - (1 + x) == 0 - 1 +y - (y + 1) == x - (x + 1) +y - (y + 1) == x - (1 + x) +y - (1 + y) == x - (1 + x) + +direct candidates: + +foo x = x + +foo x = 0 + +foo x = 1 + +foo x = x + x + +foo x = x + 1 + +foo x = 1 + 1 + +foo x = x - 1 + +foo x = 0 - x + +foo x = 0 - 1 + +foo x = 1 - x + +foo x = x + (x + x) + +foo x = x + (x + 1) + +foo x = x + (1 + 1) + +foo x = x + (x - 1) + +foo x = x + (0 - 1) + +foo x = 1 + (x + x) + +foo x = 1 + (x + 1) + +foo x = 1 + (1 + 1) + +foo x = 1 + (0 - x) + +foo x = 1 + (1 - x) + +foo x = x - (x + x) + +foo x = x - (x + 1) + +foo x = x - (1 + 1) + +foo x = 0 - (x + x) + +foo x = 0 - (x + 1) + +foo x = 0 - (1 + 1) + +foo x = 1 - (x + x) + +foo x = 1 - (x + 1) + +foo x = 1 - (1 + 1) + + +pattern candidates: + +foo x = x + +foo x = 0 + +foo x = 1 + +foo 0 = 0 +foo x = 1 + +foo 0 = 1 +foo x = x + +foo 0 = 1 +foo x = 0 + +foo x = x + x + +foo x = x + 1 + +foo x = x - 1 + +foo x = 0 - x + +foo x = 1 - x + +foo 1 = 0 +foo x = x + +foo 1 = 0 +foo x = 1 + +foo 1 = 1 +foo x = 0 + +foo 0 = 0 +foo x = x + 1 + +foo 0 = 0 +foo x = x - 1 + +foo 0 = 0 +foo x = 1 - x + +foo 0 = 1 +foo x = x + x + +foo 0 = 1 +foo x = x - 1 + +foo 0 = 1 +foo x = 0 - x + +foo 0 = 0 +foo 1 = 0 +foo x = 1 + +foo 0 = 1 +foo 1 = 0 +foo x = x + +foo 0 = 1 +foo 1 = 1 +foo x = 0 + +foo x = x + (x + x) + +foo x = x + (x + 1) + +foo x = x + (x - 1) + +foo x = 1 + (x + x) + +foo x = 1 + (x + 1) + +foo x = 1 + (0 - x) + +foo x = 1 + (1 - x) + +foo x = x - (x + x) + +foo x = x - (x + 1) + +foo x = 0 - (x + x) + +foo x = 0 - (x + 1) + +foo x = 1 - (x + x) + +foo x = 1 - (x + 1) + +foo 1 = 0 +foo x = x + x + +foo 1 = 0 +foo x = x + 1 + +foo 1 = 0 +foo x = 0 - x + +foo 1 = 1 +foo x = x + x + +foo 1 = 1 +foo x = x + 1 + +foo 1 = 1 +foo x = x - 1 + +foo 1 = 1 +foo x = 0 - x + +foo 1 = 1 +foo x = 1 - x + +foo 0 = 0 +foo x = x + (x + 1) + +foo 0 = 0 +foo x = x + (x - 1) + +foo 0 = 0 +foo x = 1 + (x + x) + +foo 0 = 0 +foo x = 1 + (x + 1) + +foo 0 = 0 +foo x = 1 + (0 - x) + +foo 0 = 0 +foo x = 1 + (1 - x) + +foo 0 = 0 +foo x = x - (x + 1) + +foo 0 = 0 +foo x = 0 - (x + 1) + +foo 0 = 0 +foo x = 1 - (x + x) + +foo 0 = 1 +foo x = x + (x + x) + +foo 0 = 1 +foo x = x + (x - 1) + +foo 0 = 1 +foo x = 1 + (x + 1) + +foo 0 = 1 +foo x = 1 + (1 - x) + +foo 0 = 1 +foo x = x - (x + x) + +foo 0 = 1 +foo x = x - (x + 1) + +foo 0 = 1 +foo x = 0 - (x + x) + +foo 0 = 1 +foo x = 0 - (x + 1) + +foo 0 = 1 +foo x = 1 - (x + 1) + +foo 0 = 0 +foo 1 = 0 +foo x = x + 1 + +foo 0 = 0 +foo 1 = 1 +foo x = x + 1 + +foo 0 = 0 +foo 1 = 1 +foo x = x - 1 + +foo 0 = 0 +foo 1 = 1 +foo x = 1 - x + +foo 0 = 1 +foo 1 = 0 +foo x = x + x + +foo 0 = 1 +foo 1 = 0 +foo x = 0 - x + +foo 0 = 1 +foo 1 = 1 +foo x = x + x + +foo 0 = 1 +foo 1 = 1 +foo x = x - 1 + +foo 0 = 1 +foo 1 = 1 +foo x = 0 - x + + +Candidates for: ? :: Int -> Int -> Int + pruning with 10/23 rules + [3,3,6,9,21,39,87,180,390] direct candidates, 0 duplicates + [3,8,22,50,116,302,765,1864,4439] pattern candidates, 0 duplicates + +rules: +x * y == x + y +x * y == y + x +x + 0 == x +0 + x == x +dec (x + y) == x + dec y +dec (x + y) == y + dec x +dec (x + y) == dec x + y +dec (x + y) == dec y + x +(x + y) + z == x + (y + z) +(x + y) + z == y + (x + z) +equations: +y + x == x + y +y + dec x == x + dec y +dec x + y == x + dec y +dec y + x == dec x + y +x + dec 0 == dec x +dec 0 + x == dec x +y + (x + z) == x + (y + z) +z + (x + y) == x + (y + z) +z + (y + x) == x + (y + z) +y + dec (dec x) == x + dec (dec y) +dec (dec x) + y == x + dec (dec y) +x + dec (dec 0) == dec (dec x) +dec (dec 0) + x == dec (dec x) + +direct candidates: + +x ? y = x + +x ? y = y + +x ? y = 0 + +x ? y = dec x + +x ? y = dec y + +x ? y = dec 0 + +x ? y = x + x + +x ? y = x + y + +x ? y = y + y + +x ? y = dec (dec x) + +x ? y = dec (dec y) + +x ? y = dec (dec 0) + +x ? y = dec (dec (dec x)) + +x ? y = dec (dec (dec y)) + +x ? y = dec (dec (dec 0)) + +x ? y = x + dec x + +x ? y = x + dec y + +x ? y = x + dec 0 + +x ? y = y + dec x + +x ? y = y + dec y + +x ? y = y + dec 0 + +x ? y = dec (dec (dec (dec x))) + +x ? y = dec (dec (dec (dec y))) + +x ? y = dec (dec (dec (dec 0))) + +x ? y = x + (x + x) + +x ? y = x + (x + y) + +x ? y = x + (y + y) + +x ? y = x + dec (dec x) + +x ? y = x + dec (dec y) + +x ? y = x + dec (dec 0) + +x ? y = y + (x + x) + +x ? y = y + (x + y) + +x ? y = y + (y + y) + +x ? y = y + dec (dec x) + +x ? y = y + dec (dec y) + +x ? y = y + dec (dec 0) + +x ? y = dec x + dec x + +x ? y = dec x + dec y + +x ? y = dec x + dec 0 + +x ? y = dec y + dec y + +x ? y = dec y + dec 0 + +x ? y = dec 0 + dec 0 + +x ? y = dec (dec (dec (dec (dec x)))) + +x ? y = dec (dec (dec (dec (dec y)))) + +x ? y = dec (dec (dec (dec (dec 0)))) + +x ? y = x + dec (dec (dec x)) + +x ? y = x + dec (dec (dec y)) + +x ? y = x + dec (dec (dec 0)) + +x ? y = x + (x + dec x) + +x ? y = x + (x + dec y) + +x ? y = x + (x + dec 0) + +x ? y = x + (y + dec x) + +x ? y = x + (y + dec y) + +x ? y = x + (y + dec 0) + +x ? y = y + dec (dec (dec x)) + +x ? y = y + dec (dec (dec y)) + +x ? y = y + dec (dec (dec 0)) + +x ? y = y + (x + dec x) + +x ? y = y + (x + dec y) + +x ? y = y + (x + dec 0) + +x ? y = y + (y + dec x) + +x ? y = y + (y + dec y) + +x ? y = y + (y + dec 0) + +x ? y = dec x + (x + x) + +x ? y = dec x + (x + y) + +x ? y = dec x + (y + y) + +x ? y = dec x + dec (dec x) + +x ? y = dec x + dec (dec y) + +x ? y = dec x + dec (dec 0) + +x ? y = dec y + (x + x) + +x ? y = dec y + (x + y) + +x ? y = dec y + (y + y) + +x ? y = dec y + dec (dec x) + +x ? y = dec y + dec (dec y) + +x ? y = dec y + dec (dec 0) + +x ? y = dec 0 + (x + x) + +x ? y = dec 0 + (x + y) + +x ? y = dec 0 + (y + y) + +x ? y = dec 0 + dec (dec x) + +x ? y = dec 0 + dec (dec y) + +x ? y = dec 0 + dec (dec 0) + + +pattern candidates: + +x ? y = x + +x ? y = y + +x ? y = 0 + +x ? y = dec x + +x ? y = dec y + +x ? 0 = x +x ? y = y + +x ? 0 = x +x ? y = 0 + +x ? 0 = 0 +x ? y = x + +0 ? x = x +x ? y = x + +0 ? x = x +x ? y = 0 + +0 ? x = 0 +x ? y = y + +x ? y = x + x + +x ? y = x + y + +x ? y = y + y + +x ? y = dec (dec x) + +x ? y = dec (dec y) + +x ? 0 = x +x ? y = dec x + +x ? 0 = x +x ? y = dec y + +x ? 0 = 0 +x ? y = dec x + +x ? 0 = 0 +x ? y = dec y + +x ? 0 = dec x +x ? y = x + +x ? 0 = dec x +x ? y = y + +x ? 0 = dec x +x ? y = 0 + +0 ? x = x +x ? y = dec x + +0 ? x = x +x ? y = dec y + +0 ? x = 0 +x ? y = dec x + +0 ? x = 0 +x ? y = dec y + +0 ? x = dec x +x ? y = x + +0 ? x = dec x +x ? y = y + +0 ? x = dec x +x ? y = 0 + +0 ? x = x +x ? 0 = x +x ? y = 0 + +0 ? x = x +x ? 0 = 0 +x ? y = x + +0 ? x = 0 +x ? 0 = x +x ? y = y + +x ? y = dec (dec (dec x)) + +x ? y = dec (dec (dec y)) + +x ? y = x + dec x + +x ? y = x + dec y + +x ? y = y + dec x + +x ? y = y + dec y + +x ? 0 = x +x ? y = x + x + +x ? 0 = x +x ? y = y + y + +x ? 0 = x +x ? y = dec (dec x) + +x ? 0 = x +x ? y = dec (dec y) + +x ? 0 = 0 +x ? y = x + x + +x ? 0 = 0 +x ? y = x + y + +x ? 0 = 0 +x ? y = dec (dec x) + +x ? 0 = 0 +x ? y = dec (dec y) + +x ? 0 = dec x +x ? y = dec y + +x ? 0 = x + x +x ? y = x + +x ? 0 = x + x +x ? y = y + +x ? 0 = x + x +x ? y = 0 + +x ? 0 = dec (dec x) +x ? y = x + +x ? 0 = dec (dec x) +x ? y = y + +x ? 0 = dec (dec x) +x ? y = 0 + +0 ? x = x +x ? y = x + x + +0 ? x = x +x ? y = y + y + +0 ? x = x +x ? y = dec (dec x) + +0 ? x = x +x ? y = dec (dec y) + +0 ? x = 0 +x ? y = x + y + +0 ? x = 0 +x ? y = y + y + +0 ? x = 0 +x ? y = dec (dec x) + +0 ? x = 0 +x ? y = dec (dec y) + +0 ? x = dec x +x ? y = dec x + +0 ? x = x + x +x ? y = x + +0 ? x = x + x +x ? y = y + +0 ? x = x + x +x ? y = 0 + +0 ? x = dec (dec x) +x ? y = x + +0 ? x = dec (dec x) +x ? y = y + +0 ? x = dec (dec x) +x ? y = 0 + +0 ? x = x +x ? 0 = x +x ? y = dec x + +0 ? x = x +x ? 0 = x +x ? y = dec y + +0 ? x = x +x ? 0 = 0 +x ? y = dec x + +0 ? x = x +x ? 0 = 0 +x ? y = dec y + +0 ? x = x +x ? 0 = dec x +x ? y = x + +0 ? x = x +x ? 0 = dec x +x ? y = 0 + +0 ? x = 0 +x ? 0 = x +x ? y = dec x + +0 ? x = 0 +x ? 0 = x +x ? y = dec y + +0 ? x = 0 +x ? 0 = 0 +x ? y = dec x + +0 ? x = 0 +x ? 0 = 0 +x ? y = dec y + +0 ? x = 0 +x ? 0 = dec x +x ? y = y + +0 ? x = dec x +x ? 0 = x +x ? y = y + +0 ? x = dec x +x ? 0 = x +x ? y = 0 + +0 ? x = dec x +x ? 0 = 0 +x ? y = x + +x ? 0 = x +x ? y = x ? dec y + +x ? 0 = x +x ? y = y ? dec x + +x ? 0 = x +x ? y = y ? dec y + +x ? 0 = x +x ? y = 0 ? dec y + +x ? 0 = x +x ? y = dec x ? x + +x ? 0 = x +x ? y = dec x ? y + +x ? 0 = x +x ? y = dec y ? x + +0 ? x = x +x ? y = x ? dec y + +0 ? x = x +x ? y = y ? dec x + +0 ? x = x +x ? y = y ? dec y + +0 ? x = x +x ? y = dec x ? x + +0 ? x = x +x ? y = dec x ? y + +0 ? x = x +x ? y = dec x ? 0 + +0 ? x = x +x ? y = dec y ? x + +x ? y = dec (dec (dec (dec x))) + +x ? y = dec (dec (dec (dec y))) + +x ? y = x + (x + x) + +x ? y = x + (x + y) + +x ? y = x + (y + y) + +x ? y = x + dec (dec x) + +x ? y = x + dec (dec y) + +x ? y = y + (x + x) + +x ? y = y + (x + y) + +x ? y = y + (y + y) + +x ? y = y + dec (dec x) + +x ? y = y + dec (dec y) + +x ? y = dec x + dec x + +x ? y = dec x + dec y + +x ? y = dec y + dec y + +x ? 0 = x +x ? y = dec (dec (dec x)) + +x ? 0 = x +x ? y = dec (dec (dec y)) + +x ? 0 = x +x ? y = x + dec x + +x ? 0 = x +x ? y = x + dec y + +x ? 0 = x +x ? y = y + dec x + +x ? 0 = x +x ? y = y + dec y + +x ? 0 = 0 +x ? y = dec (dec (dec x)) + +x ? 0 = 0 +x ? y = dec (dec (dec y)) + +x ? 0 = 0 +x ? y = x + dec x + +x ? 0 = 0 +x ? y = x + dec y + +x ? 0 = 0 +x ? y = y + dec x + +x ? 0 = 0 +x ? y = y + dec y + +x ? 0 = dec x +x ? y = x + x + +x ? 0 = dec x +x ? y = x + y + +x ? 0 = dec x +x ? y = y + y + +x ? 0 = dec x +x ? y = dec (dec x) + +x ? 0 = dec x +x ? y = dec (dec y) + +x ? 0 = x + x +x ? y = dec x + +x ? 0 = x + x +x ? y = dec y + +x ? 0 = dec (dec x) +x ? y = dec x + +x ? 0 = dec (dec x) +x ? y = dec y + +x ? 0 = dec (dec (dec x)) +x ? y = x + +x ? 0 = dec (dec (dec x)) +x ? y = y + +x ? 0 = dec (dec (dec x)) +x ? y = 0 + +x ? 0 = x + dec x +x ? y = x + +x ? 0 = x + dec x +x ? y = y + +x ? 0 = x + dec x +x ? y = 0 + +0 ? x = x +x ? y = dec (dec (dec x)) + +0 ? x = x +x ? y = dec (dec (dec y)) + +0 ? x = x +x ? y = x + dec x + +0 ? x = x +x ? y = x + dec y + +0 ? x = x +x ? y = y + dec x + +0 ? x = x +x ? y = y + dec y + +0 ? x = 0 +x ? y = dec (dec (dec x)) + +0 ? x = 0 +x ? y = dec (dec (dec y)) + +0 ? x = 0 +x ? y = x + dec x + +0 ? x = 0 +x ? y = x + dec y + +0 ? x = 0 +x ? y = y + dec x + +0 ? x = 0 +x ? y = y + dec y + +0 ? x = dec x +x ? y = x + x + +0 ? x = dec x +x ? y = x + y + +0 ? x = dec x +x ? y = y + y + +0 ? x = dec x +x ? y = dec (dec x) + +0 ? x = dec x +x ? y = dec (dec y) + +0 ? x = x + x +x ? y = dec x + +0 ? x = x + x +x ? y = dec y + +0 ? x = dec (dec x) +x ? y = dec x + +0 ? x = dec (dec x) +x ? y = dec y + +0 ? x = dec (dec (dec x)) +x ? y = x + +0 ? x = dec (dec (dec x)) +x ? y = y + +0 ? x = dec (dec (dec x)) +x ? y = 0 + +0 ? x = x + dec x +x ? y = x + +0 ? x = x + dec x +x ? y = y + +0 ? x = x + dec x +x ? y = 0 + +0 ? x = x +x ? 0 = x +x ? y = x + x + +0 ? x = x +x ? 0 = x +x ? y = y + y + +0 ? x = x +x ? 0 = x +x ? y = dec (dec x) + +0 ? x = x +x ? 0 = x +x ? y = dec (dec y) + +0 ? x = x +x ? 0 = 0 +x ? y = x + x + +0 ? x = x +x ? 0 = 0 +x ? y = dec (dec x) + +0 ? x = x +x ? 0 = 0 +x ? y = dec (dec y) + +0 ? x = x +x ? 0 = dec x +x ? y = dec y + +0 ? x = x +x ? 0 = x + x +x ? y = x + +0 ? x = x +x ? 0 = x + x +x ? y = 0 + +0 ? x = x +x ? 0 = dec (dec x) +x ? y = x + +0 ? x = x +x ? 0 = dec (dec x) +x ? y = 0 + +0 ? x = 0 +x ? 0 = x +x ? y = y + y + +0 ? x = 0 +x ? 0 = x +x ? y = dec (dec x) + +0 ? x = 0 +x ? 0 = x +x ? y = dec (dec y) + +0 ? x = 0 +x ? 0 = 0 +x ? y = x + y + +0 ? x = 0 +x ? 0 = 0 +x ? y = dec (dec x) + +0 ? x = 0 +x ? 0 = 0 +x ? y = dec (dec y) + +0 ? x = 0 +x ? 0 = dec x +x ? y = dec y + +0 ? x = 0 +x ? 0 = x + x +x ? y = y + +0 ? x = 0 +x ? 0 = dec (dec x) +x ? y = y + +0 ? x = dec x +x ? 0 = x +x ? y = dec x + +0 ? x = dec x +x ? 0 = 0 +x ? y = dec x + +0 ? x = dec x +x ? 0 = dec x +x ? y = x + +0 ? x = dec x +x ? 0 = dec x +x ? y = y + +0 ? x = dec x +x ? 0 = dec x +x ? y = 0 + +0 ? x = x + x +x ? 0 = x +x ? y = y + +0 ? x = x + x +x ? 0 = x +x ? y = 0 + +0 ? x = x + x +x ? 0 = 0 +x ? y = x + +0 ? x = dec (dec x) +x ? 0 = x +x ? y = y + +0 ? x = dec (dec x) +x ? 0 = x +x ? y = 0 + +0 ? x = dec (dec x) +x ? 0 = 0 +x ? y = x + +0 ? 0 = 0 +0 ? x = dec x +x ? y = dec x + +x ? 0 = x +x ? y = x ? dec (dec y) + +x ? 0 = x +x ? y = y ? dec (dec x) + +x ? 0 = x +x ? y = y ? dec (dec y) + +x ? 0 = x +x ? y = 0 ? dec (dec y) + +x ? 0 = x +x ? y = dec x ? dec x + +x ? 0 = x +x ? y = dec x ? dec y + +x ? 0 = x +x ? y = dec y ? dec x + +x ? 0 = x +x ? y = dec y ? dec y + +x ? 0 = x +x ? y = dec (dec x) ? x + +x ? 0 = x +x ? y = dec (dec x) ? y + +x ? 0 = x +x ? y = dec (dec y) ? x + +0 ? x = x +x ? y = x ? dec (dec y) + +0 ? x = x +x ? y = y ? dec (dec x) + +0 ? x = x +x ? y = y ? dec (dec y) + +0 ? x = x +x ? y = dec x ? dec x + +0 ? x = x +x ? y = dec x ? dec y + +0 ? x = x +x ? y = dec y ? dec x + +0 ? x = x +x ? y = dec y ? dec y + +0 ? x = x +x ? y = dec (dec x) ? x + +0 ? x = x +x ? y = dec (dec x) ? y + +0 ? x = x +x ? y = dec (dec x) ? 0 + +0 ? x = x +x ? y = dec (dec y) ? x + +x ? 0 = x +x ? y = dec (x ? dec y) + +x ? 0 = x +x ? y = dec (y ? dec x) + +x ? 0 = x +x ? y = dec (y ? dec y) + +x ? 0 = x +x ? y = dec (0 ? dec y) + +x ? 0 = x +x ? y = dec (dec x ? x) + +x ? 0 = x +x ? y = dec (dec x ? y) + +x ? 0 = x +x ? y = dec (dec y ? x) + +x ? 0 = 0 +x ? y = dec (x ? dec y) + +x ? 0 = 0 +x ? y = dec (y ? dec x) + +x ? 0 = 0 +x ? y = dec (y ? dec y) + +x ? 0 = 0 +x ? y = dec (0 ? dec y) + +x ? 0 = 0 +x ? y = dec (dec x ? x) + +x ? 0 = 0 +x ? y = dec (dec x ? y) + +x ? 0 = 0 +x ? y = dec (dec y ? x) + +x ? 0 = dec x +x ? y = x ? dec y + +x ? 0 = dec x +x ? y = y ? dec x + +x ? 0 = dec x +x ? y = y ? dec y + +x ? 0 = dec x +x ? y = 0 ? dec y + +x ? 0 = dec x +x ? y = dec x ? x + +x ? 0 = dec x +x ? y = dec x ? y + +x ? 0 = dec x +x ? y = dec y ? x + +0 ? x = x +x ? y = dec (x ? dec y) + +0 ? x = x +x ? y = dec (y ? dec x) + +0 ? x = x +x ? y = dec (y ? dec y) + +0 ? x = x +x ? y = dec (dec x ? x) + +0 ? x = x +x ? y = dec (dec x ? y) + +0 ? x = x +x ? y = dec (dec x ? 0) + +0 ? x = x +x ? y = dec (dec y ? x) + +0 ? x = 0 +x ? y = dec (x ? dec y) + +0 ? x = 0 +x ? y = dec (y ? dec x) + +0 ? x = 0 +x ? y = dec (y ? dec y) + +0 ? x = 0 +x ? y = dec (dec x ? x) + +0 ? x = 0 +x ? y = dec (dec x ? y) + +0 ? x = 0 +x ? y = dec (dec x ? 0) + +0 ? x = 0 +x ? y = dec (dec y ? x) + +0 ? x = dec x +x ? y = x ? dec y + +0 ? x = dec x +x ? y = y ? dec x + +0 ? x = dec x +x ? y = y ? dec y + +0 ? x = dec x +x ? y = dec x ? x + +0 ? x = dec x +x ? y = dec x ? y + +0 ? x = dec x +x ? y = dec x ? 0 + +0 ? x = dec x +x ? y = dec y ? x + +0 ? x = x +x ? 0 = x +x ? y = x ? dec y + +0 ? x = x +x ? 0 = x +x ? y = y ? dec x + +0 ? x = x +x ? 0 = x +x ? y = y ? dec y + +0 ? x = x +x ? 0 = x +x ? y = dec x ? x + +0 ? x = x +x ? 0 = x +x ? y = dec x ? y + +0 ? x = x +x ? 0 = x +x ? y = dec y ? x + +0 ? x = x +x ? 0 = 0 +x ? y = x ? dec y + +0 ? x = x +x ? 0 = 0 +x ? y = y ? dec x + +0 ? x = x +x ? 0 = 0 +x ? y = y ? dec y + +0 ? x = x +x ? 0 = 0 +x ? y = dec x ? x + +0 ? x = x +x ? 0 = 0 +x ? y = dec x ? y + +0 ? x = x +x ? 0 = 0 +x ? y = dec y ? x + +0 ? x = 0 +x ? 0 = x +x ? y = x ? dec y + +0 ? x = 0 +x ? 0 = x +x ? y = y ? dec x + +0 ? x = 0 +x ? 0 = x +x ? y = y ? dec y + +0 ? x = 0 +x ? 0 = x +x ? y = dec x ? x + +0 ? x = 0 +x ? 0 = x +x ? y = dec x ? y + +0 ? x = 0 +x ? 0 = x +x ? y = dec y ? x + +x ? y = dec (dec (dec (dec (dec x)))) + +x ? y = dec (dec (dec (dec (dec y)))) + +x ? y = x + dec (dec (dec x)) + +x ? y = x + dec (dec (dec y)) + +x ? y = x + (x + dec x) + +x ? y = x + (x + dec y) + +x ? y = x + (y + dec x) + +x ? y = x + (y + dec y) + +x ? y = y + dec (dec (dec x)) + +x ? y = y + dec (dec (dec y)) + +x ? y = y + (x + dec x) + +x ? y = y + (x + dec y) + +x ? y = y + (y + dec x) + +x ? y = y + (y + dec y) + +x ? y = dec x + (x + x) + +x ? y = dec x + (x + y) + +x ? y = dec x + (y + y) + +x ? y = dec x + dec (dec x) + +x ? y = dec x + dec (dec y) + +x ? y = dec y + (x + x) + +x ? y = dec y + (x + y) + +x ? y = dec y + (y + y) + +x ? y = dec y + dec (dec x) + +x ? y = dec y + dec (dec y) + +x ? 0 = x +x ? y = dec (dec (dec (dec x))) + +x ? 0 = x +x ? y = dec (dec (dec (dec y))) + +x ? 0 = x +x ? y = x + (x + x) + +x ? 0 = x +x ? y = x + (x + y) + +x ? 0 = x +x ? y = x + dec (dec x) + +x ? 0 = x +x ? y = x + dec (dec y) + +x ? 0 = x +x ? y = y + (x + x) + +x ? 0 = x +x ? y = y + (y + y) + +x ? 0 = x +x ? y = y + dec (dec x) + +x ? 0 = x +x ? y = y + dec (dec y) + +x ? 0 = x +x ? y = dec x + dec x + +x ? 0 = x +x ? y = dec x + dec y + +x ? 0 = x +x ? y = dec y + dec y + +x ? 0 = 0 +x ? y = dec (dec (dec (dec x))) + +x ? 0 = 0 +x ? y = dec (dec (dec (dec y))) + +x ? 0 = 0 +x ? y = x + (x + x) + +x ? 0 = 0 +x ? y = x + (x + y) + +x ? 0 = 0 +x ? y = x + (y + y) + +x ? 0 = 0 +x ? y = x + dec (dec x) + +x ? 0 = 0 +x ? y = x + dec (dec y) + +x ? 0 = 0 +x ? y = y + (x + x) + +x ? 0 = 0 +x ? y = y + (x + y) + +x ? 0 = 0 +x ? y = y + dec (dec x) + +x ? 0 = 0 +x ? y = y + dec (dec y) + +x ? 0 = 0 +x ? y = dec x + dec x + +x ? 0 = 0 +x ? y = dec x + dec y + +x ? 0 = 0 +x ? y = dec y + dec y + +x ? 0 = dec x +x ? y = dec (dec (dec x)) + +x ? 0 = dec x +x ? y = dec (dec (dec y)) + +x ? 0 = dec x +x ? y = x + dec x + +x ? 0 = dec x +x ? y = x + dec y + +x ? 0 = dec x +x ? y = y + dec y + +x ? 0 = x + x +x ? y = x + y + +x ? 0 = x + x +x ? y = y + y + +x ? 0 = x + x +x ? y = dec (dec x) + +x ? 0 = x + x +x ? y = dec (dec y) + +x ? 0 = dec (dec x) +x ? y = x + x + +x ? 0 = dec (dec x) +x ? y = x + y + +x ? 0 = dec (dec x) +x ? y = y + y + +x ? 0 = dec (dec x) +x ? y = dec (dec y) + +x ? 0 = dec (dec (dec x)) +x ? y = dec x + +x ? 0 = dec (dec (dec x)) +x ? y = dec y + +x ? 0 = x + dec x +x ? y = dec x + +x ? 0 = x + dec x +x ? y = dec y + +x ? 0 = dec (dec (dec (dec x))) +x ? y = x + +x ? 0 = dec (dec (dec (dec x))) +x ? y = y + +x ? 0 = dec (dec (dec (dec x))) +x ? y = 0 + +x ? 0 = x + (x + x) +x ? y = x + +x ? 0 = x + (x + x) +x ? y = y + +x ? 0 = x + (x + x) +x ? y = 0 + +x ? 0 = x + dec (dec x) +x ? y = x + +x ? 0 = x + dec (dec x) +x ? y = y + +x ? 0 = x + dec (dec x) +x ? y = 0 + +x ? 0 = dec x + dec x +x ? y = x + +x ? 0 = dec x + dec x +x ? y = y + +x ? 0 = dec x + dec x +x ? y = 0 + +0 ? x = x +x ? y = dec (dec (dec (dec x))) + +0 ? x = x +x ? y = dec (dec (dec (dec y))) + +0 ? x = x +x ? y = x + (x + x) + +0 ? x = x +x ? y = x + (y + y) + +0 ? x = x +x ? y = x + dec (dec x) + +0 ? x = x +x ? y = x + dec (dec y) + +0 ? x = x +x ? y = y + (x + y) + +0 ? x = x +x ? y = y + (y + y) + +0 ? x = x +x ? y = y + dec (dec x) + +0 ? x = x +x ? y = y + dec (dec y) + +0 ? x = x +x ? y = dec x + dec x + +0 ? x = x +x ? y = dec x + dec y + +0 ? x = x +x ? y = dec y + dec y + +0 ? x = 0 +x ? y = dec (dec (dec (dec x))) + +0 ? x = 0 +x ? y = dec (dec (dec (dec y))) + +0 ? x = 0 +x ? y = x + (x + y) + +0 ? x = 0 +x ? y = x + (y + y) + +0 ? x = 0 +x ? y = x + dec (dec x) + +0 ? x = 0 +x ? y = x + dec (dec y) + +0 ? x = 0 +x ? y = y + (x + x) + +0 ? x = 0 +x ? y = y + (x + y) + +0 ? x = 0 +x ? y = y + (y + y) + +0 ? x = 0 +x ? y = y + dec (dec x) + +0 ? x = 0 +x ? y = y + dec (dec y) + +0 ? x = 0 +x ? y = dec x + dec x + +0 ? x = 0 +x ? y = dec x + dec y + +0 ? x = 0 +x ? y = dec y + dec y + +0 ? x = dec x +x ? y = dec (dec (dec x)) + +0 ? x = dec x +x ? y = dec (dec (dec y)) + +0 ? x = dec x +x ? y = x + dec x + +0 ? x = dec x +x ? y = y + dec x + +0 ? x = dec x +x ? y = y + dec y + +0 ? x = x + x +x ? y = x + x + +0 ? x = x + x +x ? y = x + y + +0 ? x = x + x +x ? y = dec (dec x) + +0 ? x = x + x +x ? y = dec (dec y) + +0 ? x = dec (dec x) +x ? y = x + x + +0 ? x = dec (dec x) +x ? y = x + y + +0 ? x = dec (dec x) +x ? y = y + y + +0 ? x = dec (dec x) +x ? y = dec (dec x) + +0 ? x = dec (dec (dec x)) +x ? y = dec x + +0 ? x = dec (dec (dec x)) +x ? y = dec y + +0 ? x = x + dec x +x ? y = dec x + +0 ? x = x + dec x +x ? y = dec y + +0 ? x = dec (dec (dec (dec x))) +x ? y = x + +0 ? x = dec (dec (dec (dec x))) +x ? y = y + +0 ? x = dec (dec (dec (dec x))) +x ? y = 0 + +0 ? x = x + (x + x) +x ? y = x + +0 ? x = x + (x + x) +x ? y = y + +0 ? x = x + (x + x) +x ? y = 0 + +0 ? x = x + dec (dec x) +x ? y = x + +0 ? x = x + dec (dec x) +x ? y = y + +0 ? x = x + dec (dec x) +x ? y = 0 + +0 ? x = dec x + dec x +x ? y = x + +0 ? x = dec x + dec x +x ? y = y + +0 ? x = dec x + dec x +x ? y = 0 + +0 ? x = x +x ? 0 = x +x ? y = dec (dec (dec x)) + +0 ? x = x +x ? 0 = x +x ? y = dec (dec (dec y)) + +0 ? x = x +x ? 0 = x +x ? y = x + dec x + +0 ? x = x +x ? 0 = x +x ? y = x + dec y + +0 ? x = x +x ? 0 = x +x ? y = y + dec x + +0 ? x = x +x ? 0 = x +x ? y = y + dec y + +0 ? x = x +x ? 0 = 0 +x ? y = dec (dec (dec x)) + +0 ? x = x +x ? 0 = 0 +x ? y = dec (dec (dec y)) + +0 ? x = x +x ? 0 = 0 +x ? y = x + dec x + +0 ? x = x +x ? 0 = 0 +x ? y = x + dec y + +0 ? x = x +x ? 0 = 0 +x ? y = y + dec x + +0 ? x = x +x ? 0 = 0 +x ? y = y + dec y + +0 ? x = x +x ? 0 = dec x +x ? y = x + x + +0 ? x = x +x ? 0 = dec x +x ? y = y + y + +0 ? x = x +x ? 0 = dec x +x ? y = dec (dec x) + +0 ? x = x +x ? 0 = dec x +x ? y = dec (dec y) + +0 ? x = x +x ? 0 = x + x +x ? y = dec x + +0 ? x = x +x ? 0 = x + x +x ? y = dec y + +0 ? x = x +x ? 0 = dec (dec x) +x ? y = dec x + +0 ? x = x +x ? 0 = dec (dec x) +x ? y = dec y + +0 ? x = x +x ? 0 = dec (dec (dec x)) +x ? y = x + +0 ? x = x +x ? 0 = dec (dec (dec x)) +x ? y = 0 + +0 ? x = x +x ? 0 = x + dec x +x ? y = x + +0 ? x = x +x ? 0 = x + dec x +x ? y = 0 + +0 ? x = 0 +x ? 0 = x +x ? y = dec (dec (dec x)) + +0 ? x = 0 +x ? 0 = x +x ? y = dec (dec (dec y)) + +0 ? x = 0 +x ? 0 = x +x ? y = x + dec x + +0 ? x = 0 +x ? 0 = x +x ? y = x + dec y + +0 ? x = 0 +x ? 0 = x +x ? y = y + dec x + +0 ? x = 0 +x ? 0 = x +x ? y = y + dec y + +0 ? x = 0 +x ? 0 = 0 +x ? y = dec (dec (dec x)) + +0 ? x = 0 +x ? 0 = 0 +x ? y = dec (dec (dec y)) + +0 ? x = 0 +x ? 0 = 0 +x ? y = x + dec x + +0 ? x = 0 +x ? 0 = 0 +x ? y = x + dec y + +0 ? x = 0 +x ? 0 = 0 +x ? y = y + dec x + +0 ? x = 0 +x ? 0 = 0 +x ? y = y + dec y + +0 ? x = 0 +x ? 0 = dec x +x ? y = x + y + +0 ? x = 0 +x ? 0 = dec x +x ? y = y + y + +0 ? x = 0 +x ? 0 = dec x +x ? y = dec (dec x) + +0 ? x = 0 +x ? 0 = dec x +x ? y = dec (dec y) + +0 ? x = 0 +x ? 0 = x + x +x ? y = dec x + +0 ? x = 0 +x ? 0 = x + x +x ? y = dec y + +0 ? x = 0 +x ? 0 = dec (dec x) +x ? y = dec x + +0 ? x = 0 +x ? 0 = dec (dec x) +x ? y = dec y + +0 ? x = 0 +x ? 0 = dec (dec (dec x)) +x ? y = y + +0 ? x = 0 +x ? 0 = x + dec x +x ? y = y + +0 ? x = dec x +x ? 0 = x +x ? y = x + x + +0 ? x = dec x +x ? 0 = x +x ? y = y + y + +0 ? x = dec x +x ? 0 = x +x ? y = dec (dec x) + +0 ? x = dec x +x ? 0 = x +x ? y = dec (dec y) + +0 ? x = dec x +x ? 0 = 0 +x ? y = x + x + +0 ? x = dec x +x ? 0 = 0 +x ? y = x + y + +0 ? x = dec x +x ? 0 = 0 +x ? y = dec (dec x) + +0 ? x = dec x +x ? 0 = 0 +x ? y = dec (dec y) + +0 ? x = dec x +x ? 0 = x + x +x ? y = x + +0 ? x = dec x +x ? 0 = x + x +x ? y = y + +0 ? x = dec x +x ? 0 = x + x +x ? y = 0 + +0 ? x = dec x +x ? 0 = dec (dec x) +x ? y = x + +0 ? x = dec x +x ? 0 = dec (dec x) +x ? y = y + +0 ? x = dec x +x ? 0 = dec (dec x) +x ? y = 0 + +0 ? x = x + x +x ? 0 = x +x ? y = dec x + +0 ? x = x + x +x ? 0 = x +x ? y = dec y + +0 ? x = x + x +x ? 0 = 0 +x ? y = dec x + +0 ? x = x + x +x ? 0 = 0 +x ? y = dec y + +0 ? x = x + x +x ? 0 = dec x +x ? y = x + +0 ? x = x + x +x ? 0 = dec x +x ? y = y + +0 ? x = x + x +x ? 0 = dec x +x ? y = 0 + +0 ? x = dec (dec x) +x ? 0 = x +x ? y = dec x + +0 ? x = dec (dec x) +x ? 0 = x +x ? y = dec y + +0 ? x = dec (dec x) +x ? 0 = 0 +x ? y = dec x + +0 ? x = dec (dec x) +x ? 0 = 0 +x ? y = dec y + +0 ? x = dec (dec x) +x ? 0 = dec x +x ? y = x + +0 ? x = dec (dec x) +x ? 0 = dec x +x ? y = y + +0 ? x = dec (dec x) +x ? 0 = dec x +x ? y = 0 + +0 ? x = dec (dec (dec x)) +x ? 0 = x +x ? y = y + +0 ? x = dec (dec (dec x)) +x ? 0 = x +x ? y = 0 + +0 ? x = dec (dec (dec x)) +x ? 0 = 0 +x ? y = x + +0 ? x = x + dec x +x ? 0 = x +x ? y = y + +0 ? x = x + dec x +x ? 0 = x +x ? y = 0 + +0 ? x = x + dec x +x ? 0 = 0 +x ? y = x + +0 ? 0 = 0 +0 ? x = dec x +x ? y = dec (dec x) + +0 ? 0 = 0 +0 ? x = dec x +x ? y = dec (dec y) + +0 ? 0 = 0 +0 ? x = dec (dec x) +x ? y = dec x + +0 ? 0 = 0 +0 ? x = dec (dec x) +x ? y = dec y + + +Candidates for: goo :: [Int] -> [Int] + pruning with 4/4 rules + [2,0,1,0,1,0,1,0,1] direct candidates, 0 duplicates + [2,1,1,3,4,7,10,17,26] pattern candidates, 0 duplicates + +rules: +xs ++ [] == xs +[] ++ xs == xs +(xs ++ ys) ++ zs == xs ++ (ys ++ zs) +(x:xs) ++ ys == x:(xs ++ ys) + +direct candidates: + +goo xs = xs + +goo xs = [] + +goo xs = xs ++ xs + +goo xs = xs ++ (xs ++ xs) + + +pattern candidates: + +goo xs = xs + +goo xs = [] + +goo [] = [] +goo (x:xs) = xs + +goo xs = xs ++ xs + +goo [] = [] +goo (x:xs) = x:xs + +goo [] = [] +goo (x:xs) = [x] + +goo [] = [] +goo (x:xs) = xs ++ xs + +goo [] = [] +goo (x:xs) = x:goo xs + +goo [] = [] +goo (x:xs) = xs ++ goo xs + +goo [] = [] +goo (x:xs) = goo xs ++ xs + +goo xs = xs ++ (xs ++ xs) + +goo [] = [] +goo (x:xs) = goo xs ++ goo xs + +goo [] = [] +goo (x:xs) = x:x:xs + +goo [] = [] +goo (x:xs) = [x,x] + +goo [] = [] +goo (x:xs) = x:(xs ++ xs) + +goo [] = [] +goo (x:xs) = xs ++ (x:xs) + +goo [] = [] +goo (x:xs) = xs ++ [x] + +goo [] = [] +goo (x:xs) = xs ++ (xs ++ xs) + + +Candidates for: ?? :: [Int] -> [Int] -> [Int] + pruning with 4/4 rules + [3,0,4,0,8,0,16,0,32] direct candidates, 0 duplicates + [3,8,15,45,127,268,845,1565,5692] pattern candidates, 0 duplicates + +rules: +xs ++ [] == xs +[] ++ xs == xs +(xs ++ ys) ++ zs == xs ++ (ys ++ zs) +(x:xs) ++ ys == x:(xs ++ ys) + +direct candidates: + +xs ?? ys = xs + +xs ?? ys = ys + +xs ?? ys = [] + +xs ?? ys = xs ++ xs + +xs ?? ys = xs ++ ys + +xs ?? ys = ys ++ xs + +xs ?? ys = ys ++ ys + +xs ?? ys = xs ++ (xs ++ xs) + +xs ?? ys = xs ++ (xs ++ ys) + +xs ?? ys = xs ++ (ys ++ xs) + +xs ?? ys = xs ++ (ys ++ ys) + +xs ?? ys = ys ++ (xs ++ xs) + +xs ?? ys = ys ++ (xs ++ ys) + +xs ?? ys = ys ++ (ys ++ xs) + +xs ?? ys = ys ++ (ys ++ ys) + + +pattern candidates: + +xs ?? ys = xs + +xs ?? ys = ys + +xs ?? ys = [] + +xs ?? [] = xs +xs ?? (x:ys) = ys + +xs ?? [] = xs +xs ?? (x:ys) = [] + +xs ?? [] = [] +xs ?? (x:ys) = xs + +xs ?? [] = [] +xs ?? (x:ys) = ys + +[] ?? xs = xs +(x:xs) ?? ys = xs + +[] ?? xs = xs +(x:xs) ?? ys = [] + +[] ?? xs = [] +(x:xs) ?? ys = xs + +[] ?? xs = [] +(x:xs) ?? ys = ys + +xs ?? ys = xs ++ xs + +xs ?? ys = xs ++ ys + +xs ?? ys = ys ++ xs + +xs ?? ys = ys ++ ys + +[] ?? xs = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? xs = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? xs = xs +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = xs + +[] ?? xs = xs +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = ys + +[] ?? xs = [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? xs = [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = xs + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = [] + +xs ?? [] = xs +xs ?? (x:ys) = xs ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = ys ?? xs + +xs ?? [] = xs +xs ?? (x:ys) = ys ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = [] ?? xs + +xs ?? [] = xs +xs ?? (x:ys) = [] ?? ys + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? ys + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? [] + +[] ?? xs = xs +(x:xs) ?? ys = ys ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = ys ?? [] + +xs ?? [] = xs +xs ?? (x:ys) = x:xs + +xs ?? [] = xs +xs ?? (x:ys) = x:ys + +xs ?? [] = xs +xs ?? (x:ys) = [x] + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ xs + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ ys + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ xs + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ ys + +xs ?? [] = [] +xs ?? (x:ys) = x:xs + +xs ?? [] = [] +xs ?? (x:ys) = x:ys + +xs ?? [] = [] +xs ?? (x:ys) = [x] + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ xs + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ ys + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ xs + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ ys + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = xs + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = ys + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = [] + +[] ?? xs = xs +(x:xs) ?? ys = x:xs + +[] ?? xs = xs +(x:xs) ?? ys = x:ys + +[] ?? xs = xs +(x:xs) ?? ys = [x] + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ xs + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ ys + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ xs + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ ys + +[] ?? xs = [] +(x:xs) ?? ys = x:xs + +[] ?? xs = [] +(x:xs) ?? ys = x:ys + +[] ?? xs = [] +(x:xs) ?? ys = [x] + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ xs + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ ys + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ xs + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ ys + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = xs + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = ys + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? xs = xs +(x:xs) ?? [] = xs +(x:xs) ?? 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[] = xs +(x:xs) ?? (y:ys) = [y] + +[] ?? xs = [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = xs ++ xs + +[] ?? xs = [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = xs ++ ys + +[] ?? xs = [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys ++ xs + +[] ?? xs = [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys ++ ys + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = x:xs + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = x:ys + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = [x] + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = y:xs + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = y:ys + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = [y] + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = xs ++ xs + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = xs ++ ys + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = ys ++ xs + +[] ?? xs = [] +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = ys ++ ys + +[] ?? xs = [] +(x:xs) ?? [] = x:xs +(x:xs) ?? (y:ys) = xs + +[] ?? xs = [] +(x:xs) ?? [] = x:xs +(x:xs) ?? (y:ys) = ys + +[] ?? xs = [] +(x:xs) ?? [] = x:xs +(x:xs) ?? (y:ys) = [] + +[] ?? xs = [] +(x:xs) ?? [] = [x] +(x:xs) ?? (y:ys) = xs + +[] ?? xs = [] +(x:xs) ?? [] = [x] +(x:xs) ?? (y:ys) = ys + +[] ?? xs = [] +(x:xs) ?? [] = [x] +(x:xs) ?? (y:ys) = [] + +[] ?? xs = [] +(x:xs) ?? [] = xs ++ xs +(x:xs) ?? (y:ys) = xs + +[] ?? xs = [] +(x:xs) ?? [] = xs ++ xs +(x:xs) ?? (y:ys) = ys + +[] ?? xs = [] +(x:xs) ?? [] = xs ++ xs +(x:xs) ?? (y:ys) = [] + +[] ?? xs = xs ++ xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? xs = xs ++ xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? xs = xs ++ xs +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = xs + +[] ?? xs = xs ++ xs +(x:xs) ?? [] = [] +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = x:xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = x:ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = [x] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = xs ++ xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = xs ++ ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = ys ++ xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? ys = ys ++ ys + +[] ?? [] = [] +[] ?? (x:xs) = x:xs +(x:xs) ?? ys = xs + +[] ?? [] = [] +[] ?? (x:xs) = x:xs +(x:xs) ?? ys = ys + +[] ?? [] = [] +[] ?? (x:xs) = x:xs +(x:xs) ?? ys = [] + +[] ?? [] = [] +[] ?? (x:xs) = [x] +(x:xs) ?? ys = xs + +[] ?? [] = [] +[] ?? (x:xs) = [x] +(x:xs) ?? ys = ys + +[] ?? [] = [] +[] ?? (x:xs) = [x] +(x:xs) ?? ys = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs ++ xs +(x:xs) ?? ys = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs ++ xs +(x:xs) ?? ys = ys + +[] ?? [] = [] +[] ?? (x:xs) = xs ++ xs +(x:xs) ?? ys = [] + +xs ?? [] = xs +xs ?? (x:ys) = (x:xs) ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = (x:ys) ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = [x] ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = (xs ++ xs) ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = (xs ++ ys) ?? ys + +xs ?? 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[] = xs +xs ?? (x:ys) = ys ++ ys ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ [] ?? xs + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ [] ?? ys + +xs ?? [] = xs +xs ?? (x:ys) = xs ?? ys ++ xs + +xs ?? [] = xs +xs ?? (x:ys) = ys ?? xs ++ xs + +xs ?? [] = xs +xs ?? (x:ys) = ys ?? ys ++ xs + +xs ?? [] = xs +xs ?? (x:ys) = [] ?? xs ++ xs + +xs ?? [] = xs +xs ?? (x:ys) = [] ?? ys ++ xs + +xs ?? [] = xs +xs ?? (x:ys) = xs ?? ys ++ ys + +xs ?? [] = xs +xs ?? (x:ys) = ys ?? xs ++ ys + +xs ?? [] = xs +xs ?? (x:ys) = ys ?? ys ++ ys + +xs ?? [] = xs +xs ?? (x:ys) = [] ?? xs ++ ys + +xs ?? [] = xs +xs ?? (x:ys) = [] ?? ys ++ ys + +xs ?? [] = [] +xs ?? (x:ys) = x:xs ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = x:ys ?? xs + +xs ?? [] = [] +xs ?? (x:ys) = x:ys ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = x:[] ?? xs + +xs ?? [] = [] +xs ?? (x:ys) = x:[] ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ xs ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ ys ?? xs + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ ys ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ [] ?? xs + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ [] ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ xs ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ ys ?? xs + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ ys ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ [] ?? xs + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ [] ?? ys + +xs ?? [] = [] +xs ?? (x:ys) = xs ?? ys ++ xs + +xs ?? [] = [] +xs ?? (x:ys) = ys ?? xs ++ xs + +xs ?? [] = [] +xs ?? (x:ys) = ys ?? ys ++ xs + +xs ?? [] = [] +xs ?? (x:ys) = [] ?? xs ++ xs + +xs ?? [] = [] +xs ?? (x:ys) = [] ?? ys ++ xs + +xs ?? [] = [] +xs ?? (x:ys) = xs ?? ys ++ ys + +xs ?? [] = [] +xs ?? (x:ys) = ys ?? xs ++ ys + +xs ?? [] = [] +xs ?? (x:ys) = ys ?? ys ++ ys + +xs ?? [] = [] +xs ?? (x:ys) = [] ?? xs ++ ys + +xs ?? [] = [] +xs ?? (x:ys) = [] ?? ys ++ ys + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = xs ?? ys + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = ys ?? xs + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = ys ?? ys + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = [] ?? xs + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = [] ?? ys + +[] ?? xs = xs +(x:xs) ?? ys = x:xs ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = x:xs ?? ys + +[] ?? xs = xs +(x:xs) ?? ys = x:xs ?? [] + +[] ?? xs = xs +(x:xs) ?? ys = x:ys ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = x:ys ?? [] + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ xs ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ xs ?? ys + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ xs ?? [] + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ ys ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ ys ?? [] + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ xs ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ xs ?? ys + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ xs ?? [] + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ ys ?? xs + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ ys ?? [] + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? xs ++ xs + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? ys ++ xs + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? [] ++ xs + +[] ?? xs = xs +(x:xs) ?? ys = ys ?? xs ++ xs + +[] ?? xs = xs +(x:xs) ?? ys = ys ?? [] ++ xs + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? xs ++ ys + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? ys ++ ys + +[] ?? xs = xs +(x:xs) ?? ys = xs ?? [] ++ ys + +[] ?? xs = xs +(x:xs) ?? ys = ys ?? xs ++ ys + +[] ?? xs = xs +(x:xs) ?? ys = ys ?? [] ++ ys + +[] ?? xs = [] +(x:xs) ?? ys = x:xs ?? xs + +[] ?? xs = [] +(x:xs) ?? ys = x:xs ?? ys + +[] ?? xs = [] +(x:xs) ?? ys = x:xs ?? [] + +[] ?? xs = [] +(x:xs) ?? ys = x:ys ?? xs + +[] ?? xs = [] +(x:xs) ?? ys = x:ys ?? [] + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ xs ?? xs + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ xs ?? ys + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ xs ?? [] + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ ys ?? xs + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ ys ?? [] + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ xs ?? xs + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ xs ?? ys + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ xs ?? [] + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ ys ?? xs + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ ys ?? [] + +[] ?? xs = [] +(x:xs) ?? ys = xs ?? xs ++ xs + +[] ?? xs = [] +(x:xs) ?? ys = xs ?? ys ++ xs + +[] ?? xs = [] +(x:xs) ?? ys = xs ?? [] ++ xs + +[] ?? xs = [] +(x:xs) ?? ys = ys ?? xs ++ xs + +[] ?? xs = [] +(x:xs) ?? ys = ys ?? [] ++ xs + +[] ?? xs = [] +(x:xs) ?? ys = xs ?? xs ++ ys + +[] ?? xs = [] +(x:xs) ?? ys = xs ?? ys ++ ys + +[] ?? xs = [] +(x:xs) ?? ys = xs ?? [] ++ ys + +[] ?? xs = [] +(x:xs) ?? ys = ys ?? xs ++ ys + +[] ?? xs = [] +(x:xs) ?? ys = ys ?? [] ++ ys + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = xs ?? xs + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = xs ?? ys + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = xs ?? [] + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = ys ?? xs + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = ys ?? [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = xs ?? xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = xs ?? ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = xs ?? [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys ?? xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys ?? ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys ?? [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] ?? xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] ?? ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs ?? xs +(x:xs) ?? (y:ys) = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs ?? [] +(x:xs) ?? (y:ys) = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = [] ?? xs +(x:xs) ?? (y:ys) = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs ?? xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs ?? [] +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = [] ?? xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs ?? xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = xs ?? [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = [] ?? xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = xs ?? xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs ?? [] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = [] ?? xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +xs ?? [] = xs +xs ?? (x:ys) = x:x:xs + +xs ?? [] = xs +xs ?? (x:ys) = x:x:ys + +xs ?? [] = xs +xs ?? (x:ys) = [x,x] + +xs ?? [] = xs +xs ?? (x:ys) = x:(xs ++ xs) + +xs ?? [] = xs +xs ?? (x:ys) = x:(xs ++ ys) + +xs ?? [] = xs +xs ?? (x:ys) = x:(ys ++ xs) + +xs ?? [] = xs +xs ?? (x:ys) = x:(ys ++ ys) + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ (x:xs) + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ (x:ys) + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ [x] + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ (xs ++ xs) + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ (xs ++ ys) + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ (ys ++ xs) + +xs ?? [] = xs +xs ?? (x:ys) = xs ++ (ys ++ ys) + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ (x:xs) + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ (x:ys) + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ [x] + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ (xs ++ xs) + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ (xs ++ ys) + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ (ys ++ xs) + +xs ?? [] = xs +xs ?? (x:ys) = ys ++ (ys ++ ys) + +xs ?? [] = [] +xs ?? (x:ys) = x:x:xs + +xs ?? [] = [] +xs ?? (x:ys) = x:x:ys + +xs ?? [] = [] +xs ?? (x:ys) = [x,x] + +xs ?? [] = [] +xs ?? (x:ys) = x:(xs ++ xs) + +xs ?? [] = [] +xs ?? (x:ys) = x:(xs ++ ys) + +xs ?? [] = [] +xs ?? (x:ys) = x:(ys ++ xs) + +xs ?? [] = [] +xs ?? (x:ys) = x:(ys ++ ys) + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ (x:xs) + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ (x:ys) + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ [x] + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ (xs ++ xs) + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ (xs ++ ys) + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ (ys ++ xs) + +xs ?? [] = [] +xs ?? (x:ys) = xs ++ (ys ++ ys) + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ (x:xs) + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ (x:ys) + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ [x] + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ (xs ++ xs) + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ (xs ++ ys) + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ (ys ++ xs) + +xs ?? [] = [] +xs ?? (x:ys) = ys ++ (ys ++ ys) + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = x:xs + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = x:ys + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = [x] + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = xs ++ ys + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = ys ++ xs + +xs ?? [] = xs ++ xs +xs ?? (x:ys) = ys ++ ys + +xs ?? [] = xs ++ (xs ++ xs) +xs ?? (x:ys) = xs + +xs ?? [] = xs ++ (xs ++ xs) +xs ?? (x:ys) = ys + +xs ?? [] = xs ++ (xs ++ xs) +xs ?? (x:ys) = [] + +[] ?? xs = xs +(x:xs) ?? ys = x:x:xs + +[] ?? xs = xs +(x:xs) ?? ys = x:x:ys + +[] ?? xs = xs +(x:xs) ?? ys = [x,x] + +[] ?? xs = xs +(x:xs) ?? ys = x:(xs ++ xs) + +[] ?? xs = xs +(x:xs) ?? ys = x:(xs ++ ys) + +[] ?? xs = xs +(x:xs) ?? ys = x:(ys ++ xs) + +[] ?? xs = xs +(x:xs) ?? ys = x:(ys ++ ys) + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ (x:xs) + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ (x:ys) + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ [x] + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ (xs ++ xs) + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ (xs ++ ys) + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ (ys ++ xs) + +[] ?? xs = xs +(x:xs) ?? ys = xs ++ (ys ++ ys) + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ (x:xs) + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ (x:ys) + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ [x] + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ (xs ++ xs) + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ (xs ++ ys) + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ (ys ++ xs) + +[] ?? xs = xs +(x:xs) ?? ys = ys ++ (ys ++ ys) + +[] ?? xs = [] +(x:xs) ?? ys = x:x:xs + +[] ?? xs = [] +(x:xs) ?? ys = x:x:ys + +[] ?? xs = [] +(x:xs) ?? ys = [x,x] + +[] ?? xs = [] +(x:xs) ?? ys = x:(xs ++ xs) + +[] ?? xs = [] +(x:xs) ?? ys = x:(xs ++ ys) + +[] ?? xs = [] +(x:xs) ?? ys = x:(ys ++ xs) + +[] ?? xs = [] +(x:xs) ?? ys = x:(ys ++ ys) + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ (x:xs) + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ (x:ys) + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ [x] + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ (xs ++ xs) + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ (xs ++ ys) + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ (ys ++ xs) + +[] ?? xs = [] +(x:xs) ?? ys = xs ++ (ys ++ ys) + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ (x:xs) + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ (x:ys) + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ [x] + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ (xs ++ xs) + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ (xs ++ ys) + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ (ys ++ xs) + +[] ?? xs = [] +(x:xs) ?? ys = ys ++ (ys ++ ys) + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = x:xs + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = x:ys + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = [x] + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = xs ++ xs + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = xs ++ ys + +[] ?? xs = xs ++ xs +(x:xs) ?? ys = ys ++ xs + +[] ?? xs = xs ++ (xs ++ xs) +(x:xs) ?? ys = xs + +[] ?? xs = xs ++ (xs ++ xs) +(x:xs) ?? ys = ys + +[] ?? xs = xs ++ (xs ++ xs) +(x:xs) ?? ys = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = x:xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = x:ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [x] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = y:xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = y:ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [y] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = xs ++ xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = xs ++ ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys ++ xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys ++ ys + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = x:xs +(x:xs) ?? (y:ys) = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = x:xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = [x] +(x:xs) ?? (y:ys) = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = [x] +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs ++ xs +(x:xs) ?? (y:ys) = xs + +[] ?? [] = [] +[] ?? (x:xs) = xs +(x:xs) ?? [] = xs ++ xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = x:xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = x:xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = [x] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = [x] +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + +[] ?? [] = [] +[] ?? (x:xs) = xs ++ xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = ys + +[] ?? [] = [] +[] ?? (x:xs) = xs ++ xs +(x:xs) ?? [] = xs +(x:xs) ?? (y:ys) = [] + + +Candidates for: ton :: Bool -> Bool + pruning with 39/49 rules + [3,1,0,0,0,0,0,0,0] direct candidates, 0 duplicates + [3,3,0,0,0,0,0,0,0] pattern candidates, 0 duplicates + +rules: +not False == True +not True == False +p && p == p +p || p == p +not (not p) == p +p && False == False +p && True == p +False && p == False +True && p == p +p || False == p +p || True == True +False || p == p +True || p == True +not (p && q) == not p || not q +not (p && q) == not q || not p +not (p || q) == not p && not q +not (p || q) == not q && not p +p && not p == False +not p && p == False +p || not p == True +not p || p == True +(p && q) && r == p && (q && r) +(p && q) && r == q && (p && r) +(p || q) || r == p || (q || r) +(p || q) || r == q || (p || r) +p && (p && q) == p && q +p && (q && p) == p && q +p && (q && p) == q && p +p || (p || q) == p || q +p || (q || p) == p || q +p || (q || p) == q || p +p && (p || q) == p +p && (q || p) == p +(p || q) && p == p +(p || q) && q == q +p || p && q == p +p || q && p == p +p && q || p == p +p && q || q == q +equations: +q && p == p && q +q || p == p || q +q && (p && r) == p && (q && r) +r && (p && q) == p && (q && r) +r && (q && p) == p && (q && r) +q || (p || r) == p || (q || r) +r || (p || q) == p || (q || r) +r || (q || p) == p || (q || r) +(r || q) && p == p && (q || r) +r && q || p == p || q && r + +direct candidates: + +ton p = p + +ton p = False + +ton p = True + +ton p = not p + + +pattern candidates: + +ton p = p + +ton p = False + +ton p = True + +ton p = not p + +ton False = False +ton True = True + +ton False = True +ton True = False + + +Candidates for: &| :: Bool -> Bool -> Bool + pruning with 39/49 rules + [4,2,2,4,2,16,18,60,120] direct candidates, 0 duplicates + [4,14,26,10,2,16,18,60,120] pattern candidates, 0 duplicates + +rules: +not False == True +not True == False +p && p == p +p || p == p +not (not p) == p +p && False == False +p && True == p +False && p == False +True && p == p +p || False == p +p || True == True +False || p == p +True || p == True +not (p && q) == not p || not q +not (p && q) == not q || not p +not (p || q) == not p && not q +not (p || q) == not q && not p +p && not p == False +not p && p == False +p || not p == True +not p || p == True +(p && q) && r == p && (q && r) +(p && q) && r == q && (p && r) +(p || q) || r == p || (q || r) +(p || q) || r == q || (p || r) +p && (p && q) == p && q +p && (q && p) == p && q +p && (q && p) == q && p +p || (p || q) == p || q +p || (q || p) == p || q +p || (q || p) == q || p +p && (p || q) == p +p && (q || p) == p +(p || q) && p == p +(p || q) && q == q +p || p && q == p +p || q && p == p +p && q || p == p +p && q || q == q +equations: +q && p == p && q +q || p == p || q +q && (p && r) == p && (q && r) +r && (p && q) == p && (q && r) +r && (q && p) == p && (q && r) +q || (p || r) == p || (q || r) +r || (p || q) == p || (q || r) +r || (q || p) == p || (q || r) +(r || q) && p == p && (q || r) +r && q || p == p || q && r + +direct candidates: + +p &| q = p + +p &| q = q + +p &| q = False + +p &| q = True + +p &| q = not p + +p &| q = not q + +p &| q = p && q + +p &| q = p || q + +p &| q = p && not q + +p &| q = q && not p + +p &| q = p || not q + +p &| q = q || not p + +p &| q = not p && not q + +p &| q = not p || not q + +p &| q = p && (q && not p) + +p &| q = p && (q || not p) + +p &| q = q && (p && not q) + +p &| q = q && (p || not q) + +p &| q = p || q && not p + +p &| q = p || (q || not p) + +p &| q = q || p && not q + +p &| q = q || (p || not q) + +p &| q = not p && (p && q) + +p &| q = not p && (p || q) + +p &| q = not q && (p && q) + +p &| q = not q && (p || q) + +p &| q = not p || p && q + +p &| q = not p || (p || q) + +p &| q = not q || p && q + +p &| q = not q || (p || q) + + +pattern candidates: + +p &| q = p + +p &| q = q + +p &| q = False + +p &| q = True + +p &| q = not p + +p &| q = not q + +p &| False = p +p &| True = False + +p &| False = p +p &| True = True + +p &| False = False +p &| True = p + +p &| False = False +p &| True = True + +p &| False = True +p &| True = p + +p &| False = True +p &| True = False + +False &| p = p +True &| p = False + +False &| p = p +True &| p = True + +False &| p = False +True &| p = p + +False &| p = False +True &| p = True + +False &| p = True +True &| p = p + +False &| p = True +True &| p = False + +p &| q = p && q + +p &| q = p || q + +p &| False = p +p &| True = not p + +p &| False = False +p &| True = not p + +p &| False = True +p &| True = not p + +p &| False = not p +p &| True = p + +p &| False = not p +p &| True = False + +p &| False = not p +p &| True = True + +False &| p = p +True &| p = not p + +False &| p = False +True &| p = not p + +False &| p = True +True &| p = not p + +False &| p = not p +True &| p = p + +False &| p = not p +True &| p = False + +False &| p = not p +True &| p = True + +False &| p = p +True &| False = False +True &| True = True + +False &| p = p +True &| False = True +True &| True = False + +False &| p = False +True &| False = False +True &| True = True + +False &| p = False +True &| False = True +True &| True = False + +False &| p = True +True &| False = False +True &| True = True + +False &| p = True +True &| False = True +True &| True = False + +False &| False = False +False &| True = True +True &| p = p + +False &| False = False +False &| True = True +True &| p = False + +False &| False = False +False &| True = True +True &| p = True + +False &| False = True +False &| True = False +True &| p = p + +False &| False = True +False &| True = False +True &| p = False + +False &| False = True +False &| True = False +True &| p = True + +p &| q = p && not q + +p &| q = q && not p + +p &| q = p || not q + +p &| q = q || not p + +False &| p = not p +True &| False = False +True &| True = True + +False &| p = not p +True &| False = True +True &| True = False + +False &| False = False +False &| True = True +True &| p = not p + +False &| False = True +False &| True = False +True &| p = not p + +False &| False = False +False &| True = True +True &| False = True +True &| True = False + +False &| False = True +False &| True = False +True &| False = False +True &| True = True + +p &| q = not p && not q + +p &| q = not p || not q + +p &| q = p && (q && not p) + +p &| q = p && (q || not p) + +p &| q = q && (p && not q) + +p &| q = q && (p || not q) + +p &| q = p || q && not p + +p &| q = p || (q || not p) + +p &| q = q || p && not q + +p &| q = q || (p || not q) + +p &| q = not p && (p && q) + +p &| q = not p && (p || q) + +p &| q = not q && (p && q) + +p &| q = not q && (p || q) + +p &| q = not p || p && q + +p &| q = not p || (p || q) + +p &| q = not q || p && q + +p &| q = not q || (p || q) + + +Candidates for: gcd :: Int -> Int -> Int + pruning with 0/0 rules + [3,0,9,0,54,0,405,0,3402] direct candidates, 0 duplicates + [3,6,11,50,98,344,792,2956,6945] pattern candidates, 0 duplicates + +no rules. + +direct candidates: + +gcd x y = x + +gcd x y = y + +gcd x y = 0 + +gcd x y = x `mod` x + +gcd x y = x `mod` y + +gcd x y = x `mod` 0 + +gcd x y = y `mod` x + +gcd x y = y `mod` y + +gcd x y = y `mod` 0 + +gcd x y = 0 `mod` x + +gcd x y = 0 `mod` y + +gcd x y = 0 `mod` 0 + +gcd x y = (x `mod` x) `mod` x + +gcd x y = (x `mod` x) `mod` y + +gcd x y = (x `mod` x) `mod` 0 + +gcd x y = (x `mod` y) `mod` x + +gcd x y = (x `mod` y) `mod` y + +gcd x y = (x `mod` y) `mod` 0 + +gcd x y = (x `mod` 0) `mod` x + +gcd x y = (x `mod` 0) `mod` y + +gcd x y = (x `mod` 0) `mod` 0 + +gcd x y = (y `mod` x) `mod` x + +gcd x y = (y `mod` x) `mod` y + +gcd x y = (y `mod` x) `mod` 0 + +gcd x y = (y `mod` y) `mod` x + +gcd x y = (y `mod` y) `mod` y + +gcd x y = (y `mod` y) `mod` 0 + +gcd x y = (y `mod` 0) `mod` x + +gcd x y = (y `mod` 0) `mod` y + +gcd x y = (y `mod` 0) `mod` 0 + +gcd x y = (0 `mod` x) `mod` x + +gcd x y = (0 `mod` x) `mod` y + +gcd x y = (0 `mod` x) `mod` 0 + +gcd x y = (0 `mod` y) `mod` x + +gcd x y = (0 `mod` y) `mod` y + +gcd x y = (0 `mod` y) `mod` 0 + +gcd x y = (0 `mod` 0) `mod` x + +gcd x y = (0 `mod` 0) `mod` y + +gcd x y = (0 `mod` 0) `mod` 0 + +gcd x y = x `mod` (x `mod` x) + +gcd x y = x `mod` (x `mod` y) + +gcd x y = x `mod` (x `mod` 0) + +gcd x y = x `mod` (y `mod` x) + +gcd x y = x `mod` (y `mod` y) + +gcd x y = x `mod` (y `mod` 0) + +gcd x y = x `mod` (0 `mod` x) + +gcd x y = x `mod` (0 `mod` y) + +gcd x y = x `mod` (0 `mod` 0) + +gcd x y = y `mod` (x `mod` x) + +gcd x y = y `mod` (x `mod` y) + +gcd x y = y `mod` (x `mod` 0) + +gcd x y = y `mod` (y `mod` x) + +gcd x y = y `mod` (y `mod` y) + +gcd x y = y `mod` (y `mod` 0) + +gcd x y = y `mod` (0 `mod` x) + +gcd x y = y `mod` (0 `mod` y) + +gcd x y = y `mod` (0 `mod` 0) + +gcd x y = 0 `mod` (x `mod` x) + +gcd x y = 0 `mod` (x `mod` y) + +gcd x y = 0 `mod` (x `mod` 0) + +gcd x y = 0 `mod` (y `mod` x) + +gcd x y = 0 `mod` (y `mod` y) + +gcd x y = 0 `mod` (y `mod` 0) + +gcd x y = 0 `mod` (0 `mod` x) + +gcd x y = 0 `mod` (0 `mod` y) + +gcd x y = 0 `mod` (0 `mod` 0) + + +pattern candidates: + +gcd x y = x + +gcd x y = y + +gcd x y = 0 + +gcd x 0 = x +gcd x y = y + +gcd x 0 = x +gcd x y = 0 + +gcd x 0 = 0 +gcd x y = x + +gcd 0 x = x +gcd x y = x + +gcd 0 x = x +gcd x y = 0 + +gcd 0 x = 0 +gcd x y = y + +gcd x y = x `mod` x + +gcd x y = x `mod` y + +gcd x y = x `mod` 0 + +gcd x y = y `mod` x + +gcd x y = y `mod` y + +gcd x y = y `mod` 0 + +gcd x y = 0 `mod` x + +gcd x y = 0 `mod` y + +gcd 0 x = x +gcd x 0 = x +gcd x y = 0 + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = x + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = y + +gcd x 0 = x +gcd x y = x `mod` x + +gcd x 0 = x +gcd x y = x `mod` y + +gcd x 0 = x +gcd x y = x `mod` 0 + +gcd x 0 = x +gcd x y = y `mod` x + +gcd x 0 = x +gcd x y = y `mod` y + +gcd x 0 = x +gcd x y = y `mod` 0 + +gcd x 0 = x +gcd x y = 0 `mod` x + +gcd x 0 = x +gcd x y = 0 `mod` y + +gcd x 0 = 0 +gcd x y = x `mod` x + +gcd x 0 = 0 +gcd x y = x `mod` y + +gcd x 0 = 0 +gcd x y = x `mod` 0 + +gcd x 0 = 0 +gcd x y = y `mod` x + +gcd x 0 = 0 +gcd x y = y `mod` y + +gcd x 0 = 0 +gcd x y = y `mod` 0 + +gcd x 0 = 0 +gcd x y = 0 `mod` x + +gcd x 0 = 0 +gcd x y = 0 `mod` y + +gcd x 0 = x `mod` x +gcd x y = x + +gcd x 0 = x `mod` x +gcd x y = y + +gcd x 0 = x `mod` x +gcd x y = 0 + +gcd x 0 = x `mod` 0 +gcd x y = x + +gcd x 0 = x `mod` 0 +gcd x y = y + +gcd x 0 = x `mod` 0 +gcd x y = 0 + +gcd x 0 = 0 `mod` x +gcd x y = x + +gcd x 0 = 0 `mod` x +gcd x y = y + +gcd x 0 = 0 `mod` x +gcd x y = 0 + +gcd 0 x = x +gcd x y = x `mod` x + +gcd 0 x = x +gcd x y = x `mod` y + +gcd 0 x = x +gcd x y = x `mod` 0 + +gcd 0 x = x +gcd x y = y `mod` x + +gcd 0 x = x +gcd x y = y `mod` y + +gcd 0 x = x +gcd x y = y `mod` 0 + +gcd 0 x = x +gcd x y = 0 `mod` x + +gcd 0 x = x +gcd x y = 0 `mod` y + +gcd 0 x = 0 +gcd x y = x `mod` x + +gcd 0 x = 0 +gcd x y = x `mod` y + +gcd 0 x = 0 +gcd x y = x `mod` 0 + +gcd 0 x = 0 +gcd x y = y `mod` x + +gcd 0 x = 0 +gcd x y = y `mod` y + +gcd 0 x = 0 +gcd x y = y `mod` 0 + +gcd 0 x = 0 +gcd x y = 0 `mod` x + +gcd 0 x = 0 +gcd x y = 0 `mod` y + +gcd 0 x = x `mod` x +gcd x y = x + +gcd 0 x = x `mod` x +gcd x y = y + +gcd 0 x = x `mod` x +gcd x y = 0 + +gcd 0 x = x `mod` 0 +gcd x y = x + +gcd 0 x = x `mod` 0 +gcd x y = y + +gcd 0 x = x `mod` 0 +gcd x y = 0 + +gcd 0 x = 0 `mod` x +gcd x y = x + +gcd 0 x = 0 `mod` x +gcd x y = y + +gcd 0 x = 0 `mod` x +gcd x y = 0 + +gcd x y = (x `mod` x) `mod` x + +gcd x y = (x `mod` x) `mod` y + +gcd x y = (x `mod` x) `mod` 0 + +gcd x y = (x `mod` y) `mod` x + +gcd x y = (x `mod` y) `mod` y + +gcd x y = (x `mod` y) `mod` 0 + +gcd x y = (x `mod` 0) `mod` x + +gcd x y = (x `mod` 0) `mod` y + +gcd x y = (x `mod` 0) `mod` 0 + +gcd x y = (y `mod` x) `mod` x + +gcd x y = (y `mod` x) `mod` y + +gcd x y = (y `mod` x) `mod` 0 + +gcd x y = (y `mod` y) `mod` x + +gcd x y = (y `mod` y) `mod` y + +gcd x y = (y `mod` y) `mod` 0 + +gcd x y = (y `mod` 0) `mod` x + +gcd x y = (y `mod` 0) `mod` y + +gcd x y = (y `mod` 0) `mod` 0 + +gcd x y = (0 `mod` x) `mod` x + +gcd x y = (0 `mod` x) `mod` y + +gcd x y = (0 `mod` x) `mod` 0 + +gcd x y = (0 `mod` y) `mod` x + +gcd x y = (0 `mod` y) `mod` y + +gcd x y = (0 `mod` y) `mod` 0 + +gcd x y = x `mod` (x `mod` x) + +gcd x y = x `mod` (x `mod` y) + +gcd x y = x `mod` (x `mod` 0) + +gcd x y = x `mod` (y `mod` x) + +gcd x y = x `mod` (y `mod` y) + +gcd x y = x `mod` (y `mod` 0) + +gcd x y = x `mod` (0 `mod` x) + +gcd x y = x `mod` (0 `mod` y) + +gcd x y = y `mod` (x `mod` x) + +gcd x y = y `mod` (x `mod` y) + +gcd x y = y `mod` (x `mod` 0) + +gcd x y = y `mod` (y `mod` x) + +gcd x y = y `mod` (y `mod` y) + +gcd x y = y `mod` (y `mod` 0) + +gcd x y = y `mod` (0 `mod` x) + +gcd x y = y `mod` (0 `mod` y) + +gcd x y = 0 `mod` (x `mod` x) + +gcd x y = 0 `mod` (x `mod` y) + +gcd x y = 0 `mod` (x `mod` 0) + +gcd x y = 0 `mod` (y `mod` x) + +gcd x y = 0 `mod` (y `mod` y) + +gcd x y = 0 `mod` (y `mod` 0) + +gcd x y = 0 `mod` (0 `mod` x) + +gcd x y = 0 `mod` (0 `mod` y) + +gcd 0 x = x +gcd x 0 = x +gcd x y = x `mod` x + +gcd 0 x = x +gcd x 0 = x +gcd x y = x `mod` y + +gcd 0 x = x +gcd x 0 = x +gcd x y = x `mod` 0 + +gcd 0 x = x +gcd x 0 = x +gcd x y = y `mod` x + +gcd 0 x = x +gcd x 0 = x +gcd x y = y `mod` y + +gcd 0 x = x +gcd x 0 = x +gcd x y = y `mod` 0 + +gcd 0 x = x +gcd x 0 = x +gcd x y = 0 `mod` x + +gcd 0 x = x +gcd x 0 = x +gcd x y = 0 `mod` y + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = x `mod` x + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = x `mod` y + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = x `mod` 0 + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = y `mod` x + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = y `mod` y + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = y `mod` 0 + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = 0 `mod` x + +gcd 0 x = x +gcd x 0 = 0 +gcd x y = 0 `mod` y + +gcd 0 x = x +gcd x 0 = x `mod` x +gcd x y = x + +gcd 0 x = x +gcd x 0 = x `mod` x +gcd x y = 0 + +gcd 0 x = x +gcd x 0 = x `mod` 0 +gcd x y = x + +gcd 0 x = x +gcd x 0 = x `mod` 0 +gcd x y = 0 + +gcd 0 x = x +gcd x 0 = 0 `mod` x +gcd x y = x + +gcd 0 x = x +gcd x 0 = 0 `mod` x +gcd x y = 0 + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = x `mod` x + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = x `mod` y + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = x `mod` 0 + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = y `mod` x + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = y `mod` y + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = y `mod` 0 + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = 0 `mod` x + +gcd 0 x = 0 +gcd x 0 = x +gcd x y = 0 `mod` y + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = x `mod` x + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = x `mod` y + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = x `mod` 0 + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = y `mod` x + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = y `mod` y + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = y `mod` 0 + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = 0 `mod` x + +gcd 0 x = 0 +gcd x 0 = 0 +gcd x y = 0 `mod` y + +gcd 0 x = 0 +gcd x 0 = x `mod` x +gcd x y = y + +gcd 0 x = 0 +gcd x 0 = x `mod` 0 +gcd x y = y + +gcd 0 x = 0 +gcd x 0 = 0 `mod` x +gcd x y = y + +gcd 0 x = x `mod` x +gcd x 0 = x +gcd x y = y + +gcd 0 x = x `mod` x +gcd x 0 = x +gcd x y = 0 + +gcd 0 x = x `mod` x +gcd x 0 = 0 +gcd x y = x + +gcd 0 x = x `mod` 0 +gcd x 0 = x +gcd x y = y + +gcd 0 x = x `mod` 0 +gcd x 0 = x +gcd x y = 0 + +gcd 0 x = x `mod` 0 +gcd x 0 = 0 +gcd x y = x + +gcd 0 x = 0 `mod` x +gcd x 0 = x +gcd x y = y + +gcd 0 x = 0 `mod` x +gcd x 0 = x +gcd x y = 0 + +gcd 0 x = 0 `mod` x +gcd x 0 = 0 +gcd x y = x + +gcd x 0 = x +gcd x y = gcd x (x `mod` y) + +gcd x 0 = x +gcd x y = gcd x (y `mod` y) + +gcd x 0 = x +gcd x y = gcd x (0 `mod` y) + +gcd x 0 = x +gcd x y = gcd y (x `mod` x) + +gcd x 0 = x +gcd x y = gcd y (x `mod` y) + +gcd x 0 = x +gcd x y = gcd y (y `mod` x) + +gcd x 0 = x +gcd x y = gcd y (y `mod` y) + +gcd x 0 = x +gcd x y = gcd y (0 `mod` x) + +gcd x 0 = x +gcd x y = gcd y (0 `mod` y) + +gcd x 0 = x +gcd x y = gcd 0 (x `mod` y) + +gcd x 0 = x +gcd x y = gcd 0 (y `mod` y) + +gcd x 0 = x +gcd x y = gcd 0 (0 `mod` y) + +gcd x 0 = x +gcd x y = gcd (x `mod` x) x + +gcd x 0 = x +gcd x y = gcd (x `mod` x) y + +gcd x 0 = x +gcd x y = gcd (x `mod` y) x + +gcd x 0 = x +gcd x y = gcd (y `mod` x) x + +gcd x 0 = x +gcd x y = gcd (y `mod` x) y + +gcd x 0 = x +gcd x y = gcd (y `mod` y) x + +gcd x 0 = x +gcd x y = gcd (0 `mod` x) x + +gcd x 0 = x +gcd x y = gcd (0 `mod` x) y + +gcd x 0 = x +gcd x y = gcd (0 `mod` y) x + +gcd 0 x = x +gcd x y = gcd x (x `mod` y) + +gcd 0 x = x +gcd x y = gcd x (y `mod` y) + +gcd 0 x = x +gcd x y = gcd x (0 `mod` y) + +gcd 0 x = x +gcd x y = gcd y (x `mod` x) + +gcd 0 x = x +gcd x y = gcd y (x `mod` y) + +gcd 0 x = x +gcd x y = gcd y (y `mod` x) + +gcd 0 x = x +gcd x y = gcd y (y `mod` y) + +gcd 0 x = x +gcd x y = gcd y (0 `mod` x) + +gcd 0 x = x +gcd x y = gcd y (0 `mod` y) + +gcd 0 x = x +gcd x y = gcd (x `mod` x) x + +gcd 0 x = x +gcd x y = gcd (x `mod` x) y + +gcd 0 x = x +gcd x y = gcd (x `mod` x) 0 + +gcd 0 x = x +gcd x y = gcd (x `mod` y) x + +gcd 0 x = x +gcd x y = gcd (y `mod` x) x + +gcd 0 x = x +gcd x y = gcd (y `mod` x) y + +gcd 0 x = x +gcd x y = gcd (y `mod` x) 0 + +gcd 0 x = x +gcd x y = gcd (y `mod` y) x + +gcd 0 x = x +gcd x y = gcd (0 `mod` x) x + +gcd 0 x = x +gcd x y = gcd (0 `mod` x) y + +gcd 0 x = x +gcd x y = gcd (0 `mod` x) 0 + +gcd 0 x = x +gcd x y = gcd (0 `mod` y) x + +gcd x 0 = x +gcd x y = (x `mod` x) `mod` x + +gcd x 0 = x +gcd x y = (x `mod` x) `mod` y + +gcd x 0 = x +gcd x y = (x `mod` x) `mod` 0 + +gcd x 0 = x +gcd x y = (x `mod` y) `mod` x + +gcd x 0 = x +gcd x y = (x `mod` y) `mod` y + +gcd x 0 = x +gcd x y = (x `mod` y) `mod` 0 + +gcd x 0 = x +gcd x y = (x `mod` 0) `mod` x + +gcd x 0 = x +gcd x y = (x `mod` 0) `mod` y + +gcd x 0 = x +gcd x y = (x `mod` 0) `mod` 0 + +gcd x 0 = x +gcd x y = (y `mod` x) `mod` x + +gcd x 0 = x +gcd x y = (y `mod` x) `mod` y + +gcd x 0 = x +gcd x y = (y `mod` x) `mod` 0 + +gcd x 0 = x +gcd x y = (y `mod` y) `mod` x + +gcd x 0 = x +gcd x y = (y `mod` y) `mod` y + +gcd x 0 = x +gcd x y = (y `mod` y) `mod` 0 + +gcd x 0 = x +gcd x y = (y `mod` 0) `mod` x + +gcd x 0 = x +gcd x y = (y `mod` 0) `mod` y + +gcd x 0 = x +gcd x y = (y `mod` 0) `mod` 0 + +gcd x 0 = x +gcd x y = (0 `mod` x) `mod` x + +gcd x 0 = x +gcd x y = (0 `mod` x) `mod` y + +gcd x 0 = x +gcd x y = (0 `mod` x) `mod` 0 + +gcd x 0 = x +gcd x y = (0 `mod` y) `mod` x + +gcd x 0 = x +gcd x y = (0 `mod` y) `mod` y + +gcd x 0 = x +gcd x y = (0 `mod` y) `mod` 0 + +gcd x 0 = x +gcd x y = x `mod` (x `mod` x) + +gcd x 0 = x +gcd x y = x `mod` (x `mod` y) + +gcd x 0 = x +gcd x y = x `mod` (x `mod` 0) + +gcd x 0 = x +gcd x y = x `mod` (y `mod` x) + +gcd x 0 = x +gcd x y = x `mod` (y `mod` y) + +gcd x 0 = x +gcd x y = x `mod` (y `mod` 0) + +gcd x 0 = x +gcd x y = x `mod` (0 `mod` x) + +gcd x 0 = x +gcd x y = x `mod` (0 `mod` y) + +gcd x 0 = x +gcd x y = y `mod` (x `mod` x) + +gcd x 0 = x +gcd x y = y `mod` (x `mod` y) + +gcd x 0 = x +gcd x y = y `mod` (x `mod` 0) + +gcd x 0 = x +gcd x y = y `mod` (y `mod` x) + +gcd x 0 = x +gcd x y = y `mod` (y `mod` y) + +gcd x 0 = x +gcd x y = y `mod` (y `mod` 0) + +gcd x 0 = x +gcd x y = y `mod` (0 `mod` x) + +gcd x 0 = x +gcd x y = y `mod` (0 `mod` y) + +gcd x 0 = x +gcd x y = 0 `mod` (x `mod` x) + +gcd x 0 = x +gcd x y = 0 `mod` (x `mod` y) + +gcd x 0 = x +gcd x y = 0 `mod` (x `mod` 0) + +gcd x 0 = x +gcd x y = 0 `mod` (y `mod` x) + +gcd x 0 = x +gcd x y = 0 `mod` (y `mod` y) + +gcd x 0 = x +gcd x y = 0 `mod` (y `mod` 0) + +gcd x 0 = x +gcd x y = 0 `mod` (0 `mod` x) + +gcd x 0 = x +gcd x y = 0 `mod` (0 `mod` y) + +gcd x 0 = 0 +gcd x y = (x `mod` x) `mod` x + +gcd x 0 = 0 +gcd x y = (x `mod` x) `mod` y + +gcd x 0 = 0 +gcd x y = (x `mod` x) `mod` 0 + +gcd x 0 = 0 +gcd x y = (x `mod` y) `mod` x + +gcd x 0 = 0 +gcd x y = (x `mod` y) `mod` y + +gcd x 0 = 0 +gcd x y = (x `mod` y) `mod` 0 + +gcd x 0 = 0 +gcd x y = (x `mod` 0) `mod` x + +gcd x 0 = 0 +gcd x y = (x `mod` 0) `mod` y + +gcd x 0 = 0 +gcd x y = (x `mod` 0) `mod` 0 + +gcd x 0 = 0 +gcd x y = (y `mod` x) `mod` x + +gcd x 0 = 0 +gcd x y = (y `mod` x) `mod` y + +gcd x 0 = 0 +gcd x y = (y `mod` x) `mod` 0 + +gcd x 0 = 0 +gcd x y = (y `mod` y) `mod` x + +gcd x 0 = 0 +gcd x y = (y `mod` y) `mod` y + +gcd x 0 = 0 +gcd x y = (y `mod` y) `mod` 0 + +gcd x 0 = 0 +gcd x y = (y `mod` 0) `mod` x + +gcd x 0 = 0 +gcd x y = (y `mod` 0) `mod` y + +gcd x 0 = 0 +gcd x y = (y `mod` 0) `mod` 0 + +gcd x 0 = 0 +gcd x y = (0 `mod` x) `mod` x + +gcd x 0 = 0 +gcd x y = (0 `mod` x) `mod` y + +gcd x 0 = 0 +gcd x y = (0 `mod` x) `mod` 0 + +gcd x 0 = 0 +gcd x y = (0 `mod` y) `mod` x + +gcd x 0 = 0 +gcd x y = (0 `mod` y) `mod` y + +gcd x 0 = 0 +gcd x y = (0 `mod` y) `mod` 0 + +gcd x 0 = 0 +gcd x y = x `mod` (x `mod` x) + +gcd x 0 = 0 +gcd x y = x `mod` (x `mod` y) + +gcd x 0 = 0 +gcd x y = x `mod` (x `mod` 0) + +gcd x 0 = 0 +gcd x y = x `mod` (y `mod` x) + +gcd x 0 = 0 +gcd x y = x `mod` (y `mod` y) + +gcd x 0 = 0 +gcd x y = x `mod` (y `mod` 0) + +gcd x 0 = 0 +gcd x y = x `mod` (0 `mod` x) + +gcd x 0 = 0 +gcd x y = x `mod` (0 `mod` y) + +gcd x 0 = 0 +gcd x y = y `mod` (x `mod` x) + +gcd x 0 = 0 +gcd x y = y `mod` (x `mod` y) + +gcd x 0 = 0 +gcd x y = y `mod` (x `mod` 0) + +gcd x 0 = 0 +gcd x y = y `mod` (y `mod` x) + +gcd x 0 = 0 +gcd x y = y `mod` (y `mod` y) + +gcd x 0 = 0 +gcd x y = y `mod` (y `mod` 0) + +gcd x 0 = 0 +gcd x y = y `mod` (0 `mod` x) + +gcd x 0 = 0 +gcd x y = y `mod` (0 `mod` y) + +gcd x 0 = 0 +gcd x y = 0 `mod` (x `mod` x) + +gcd x 0 = 0 +gcd x y = 0 `mod` (x `mod` y) + +gcd x 0 = 0 +gcd x y = 0 `mod` (x `mod` 0) + +gcd x 0 = 0 +gcd x y = 0 `mod` (y `mod` x) + +gcd x 0 = 0 +gcd x y = 0 `mod` (y `mod` y) + +gcd x 0 = 0 +gcd x y = 0 `mod` (y `mod` 0) + +gcd x 0 = 0 +gcd x y = 0 `mod` (0 `mod` x) + +gcd x 0 = 0 +gcd x y = 0 `mod` (0 `mod` y) + +gcd x 0 = x `mod` x +gcd x y = x `mod` y + +gcd x 0 = x `mod` x +gcd x y = x `mod` 0 + +gcd x 0 = x `mod` x +gcd x y = y `mod` x + +gcd x 0 = x `mod` x +gcd x y = y `mod` y + +gcd x 0 = x `mod` x +gcd x y = y `mod` 0 + +gcd x 0 = x `mod` x +gcd x y = 0 `mod` x + +gcd x 0 = x `mod` x +gcd x y = 0 `mod` y + +gcd x 0 = x `mod` 0 +gcd x y = x `mod` x + +gcd x 0 = x `mod` 0 +gcd x y = y `mod` x + +gcd x 0 = x `mod` 0 +gcd x y = y `mod` y + +gcd x 0 = x `mod` 0 +gcd x y = y `mod` 0 + +gcd x 0 = x `mod` 0 +gcd x y = 0 `mod` x + +gcd x 0 = x `mod` 0 +gcd x y = 0 `mod` y + +gcd x 0 = 0 `mod` x +gcd x y = x `mod` x + +gcd x 0 = 0 `mod` x +gcd x y = x `mod` y + +gcd x 0 = 0 `mod` x +gcd x y = x `mod` 0 + +gcd x 0 = 0 `mod` x +gcd x y = y `mod` y + +gcd x 0 = 0 `mod` x +gcd x y = y `mod` 0 + +gcd x 0 = 0 `mod` x +gcd x y = 0 `mod` y + +gcd x 0 = (x `mod` x) `mod` x +gcd x y = x + +gcd x 0 = (x `mod` x) `mod` x +gcd x y = y + +gcd x 0 = (x `mod` x) `mod` x +gcd x y = 0 + +gcd x 0 = (x `mod` x) `mod` 0 +gcd x y = x + +gcd x 0 = (x `mod` x) `mod` 0 +gcd x y = y + +gcd x 0 = (x `mod` x) `mod` 0 +gcd x y = 0 + +gcd x 0 = (x `mod` 0) `mod` x +gcd x y = x + +gcd x 0 = (x `mod` 0) `mod` x +gcd x y = y + +gcd x 0 = (x `mod` 0) `mod` x +gcd x y = 0 + +gcd x 0 = (x `mod` 0) `mod` 0 +gcd x y = x + +gcd x 0 = (x `mod` 0) `mod` 0 +gcd x y = y + +gcd x 0 = (x `mod` 0) `mod` 0 +gcd x y = 0 + +gcd x 0 = (0 `mod` x) `mod` x +gcd x y = x + +gcd x 0 = (0 `mod` x) `mod` x +gcd x y = y + +gcd x 0 = (0 `mod` x) `mod` x +gcd x y = 0 + +gcd x 0 = (0 `mod` x) `mod` 0 +gcd x y = x + +gcd x 0 = (0 `mod` x) `mod` 0 +gcd x y = y + +gcd x 0 = (0 `mod` x) `mod` 0 +gcd x y = 0 + +gcd x 0 = x `mod` (x `mod` x) +gcd x y = x + +gcd x 0 = x `mod` (x `mod` x) +gcd x y = y + +gcd x 0 = x `mod` (x `mod` x) +gcd x y = 0 + +gcd x 0 = x `mod` (x `mod` 0) +gcd x y = x + +gcd x 0 = x `mod` (x `mod` 0) +gcd x y = y + +gcd x 0 = x `mod` (x `mod` 0) +gcd x y = 0 + +gcd x 0 = x `mod` (0 `mod` x) +gcd x y = x + +gcd x 0 = x `mod` (0 `mod` x) +gcd x y = y + +gcd x 0 = x `mod` (0 `mod` x) +gcd x y = 0 + +gcd x 0 = 0 `mod` (x `mod` x) +gcd x y = x + +gcd x 0 = 0 `mod` (x `mod` x) +gcd x y = y + +gcd x 0 = 0 `mod` (x `mod` x) +gcd x y = 0 + +gcd x 0 = 0 `mod` (x `mod` 0) +gcd x y = x + +gcd x 0 = 0 `mod` (x `mod` 0) +gcd x y = y + +gcd x 0 = 0 `mod` (x `mod` 0) +gcd x y = 0 + +gcd x 0 = 0 `mod` (0 `mod` x) +gcd x y = x + +gcd x 0 = 0 `mod` (0 `mod` x) +gcd x y = y + +gcd x 0 = 0 `mod` (0 `mod` x) +gcd x y = 0 + +gcd 0 x = x +gcd x y = (x `mod` x) `mod` x + +gcd 0 x = x +gcd x y = (x `mod` x) `mod` y + +gcd 0 x = x +gcd x y = (x `mod` x) `mod` 0 + +gcd 0 x = x +gcd x y = (x `mod` y) `mod` x + +gcd 0 x = x +gcd x y = (x `mod` y) `mod` y + +gcd 0 x = x +gcd x y = (x `mod` y) `mod` 0 + +gcd 0 x = x +gcd x y = (x `mod` 0) `mod` x + +gcd 0 x = x +gcd x y = (x `mod` 0) `mod` y + +gcd 0 x = x +gcd x y = (x `mod` 0) `mod` 0 + +gcd 0 x = x +gcd x y = (y `mod` x) `mod` x + +gcd 0 x = x +gcd x y = (y `mod` x) `mod` y + +gcd 0 x = x +gcd x y = (y `mod` x) `mod` 0 + +gcd 0 x = x +gcd x y = (y `mod` y) `mod` x + +gcd 0 x = x +gcd x y = (y `mod` y) `mod` y + +gcd 0 x = x +gcd x y = (y `mod` y) `mod` 0 + +gcd 0 x = x +gcd x y = (y `mod` 0) `mod` x + +gcd 0 x = x +gcd x y = (y `mod` 0) `mod` y + +gcd 0 x = x +gcd x y = (y `mod` 0) `mod` 0 + +gcd 0 x = x +gcd x y = (0 `mod` x) `mod` x + +gcd 0 x = x +gcd x y = (0 `mod` x) `mod` y + +gcd 0 x = x +gcd x y = (0 `mod` x) `mod` 0 + +gcd 0 x = x +gcd x y = (0 `mod` y) `mod` x + +gcd 0 x = x +gcd x y = (0 `mod` y) `mod` y + +gcd 0 x = x +gcd x y = (0 `mod` y) `mod` 0 + +gcd 0 x = x +gcd x y = x `mod` (x `mod` x) + +gcd 0 x = x +gcd x y = x `mod` (x `mod` y) + +gcd 0 x = x +gcd x y = x `mod` (x `mod` 0) + +gcd 0 x = x +gcd x y = x `mod` (y `mod` x) + +gcd 0 x = x +gcd x y = x `mod` (y `mod` y) + +gcd 0 x = x +gcd x y = x `mod` (y `mod` 0) + +gcd 0 x = x +gcd x y = x `mod` (0 `mod` x) + +gcd 0 x = x +gcd x y = x `mod` (0 `mod` y) + +gcd 0 x = x +gcd x y = y `mod` (x `mod` x) + +gcd 0 x = x +gcd x y = y `mod` (x `mod` y) + +gcd 0 x = x +gcd x y = y `mod` (x `mod` 0) + +gcd 0 x = x +gcd x y = y `mod` (y `mod` x) + +gcd 0 x = x +gcd x y = y `mod` (y `mod` y) + +gcd 0 x = x +gcd x y = y `mod` (y `mod` 0) + +gcd 0 x = x +gcd x y = y `mod` (0 `mod` x) + +gcd 0 x = x +gcd x y = y `mod` (0 `mod` y) + +gcd 0 x = x +gcd x y = 0 `mod` (x `mod` x) + +gcd 0 x = x +gcd x y = 0 `mod` (x `mod` y) + +gcd 0 x = x +gcd x y = 0 `mod` (x `mod` 0) + +gcd 0 x = x +gcd x y = 0 `mod` (y `mod` x) + +gcd 0 x = x +gcd x y = 0 `mod` (y `mod` y) + +gcd 0 x = x +gcd x y = 0 `mod` (y `mod` 0) + +gcd 0 x = x +gcd x y = 0 `mod` (0 `mod` x) + +gcd 0 x = x +gcd x y = 0 `mod` (0 `mod` y) + +gcd 0 x = 0 +gcd x y = (x `mod` x) `mod` x + +gcd 0 x = 0 +gcd x y = (x `mod` x) `mod` y + +gcd 0 x = 0 +gcd x y = (x `mod` x) `mod` 0 + +gcd 0 x = 0 +gcd x y = (x `mod` y) `mod` x + +gcd 0 x = 0 +gcd x y = (x `mod` y) `mod` y + +gcd 0 x = 0 +gcd x y = (x `mod` y) `mod` 0 + +gcd 0 x = 0 +gcd x y = (x `mod` 0) `mod` x + +gcd 0 x = 0 +gcd x y = (x `mod` 0) `mod` y + +gcd 0 x = 0 +gcd x y = (x `mod` 0) `mod` 0 + +gcd 0 x = 0 +gcd x y = (y `mod` x) `mod` x + +gcd 0 x = 0 +gcd x y = (y `mod` x) `mod` y + +gcd 0 x = 0 +gcd x y = (y `mod` x) `mod` 0 + +gcd 0 x = 0 +gcd x y = (y `mod` y) `mod` x + +gcd 0 x = 0 +gcd x y = (y `mod` y) `mod` y + +gcd 0 x = 0 +gcd x y = (y `mod` y) `mod` 0 + +gcd 0 x = 0 +gcd x y = (y `mod` 0) `mod` x + +gcd 0 x = 0 +gcd x y = (y `mod` 0) `mod` y + +gcd 0 x = 0 +gcd x y = (y `mod` 0) `mod` 0 + +gcd 0 x = 0 +gcd x y = (0 `mod` x) `mod` x + +gcd 0 x = 0 +gcd x y = (0 `mod` x) `mod` y + +gcd 0 x = 0 +gcd x y = (0 `mod` x) `mod` 0 + +gcd 0 x = 0 +gcd x y = (0 `mod` y) `mod` x + +gcd 0 x = 0 +gcd x y = (0 `mod` y) `mod` y + +gcd 0 x = 0 +gcd x y = (0 `mod` y) `mod` 0 + +gcd 0 x = 0 +gcd x y = x `mod` (x `mod` x) + +gcd 0 x = 0 +gcd x y = x `mod` (x `mod` y) + +gcd 0 x = 0 +gcd x y = x `mod` (x `mod` 0) + +gcd 0 x = 0 +gcd x y = x `mod` (y `mod` x) + +gcd 0 x = 0 +gcd x y = x `mod` (y `mod` y) + +gcd 0 x = 0 +gcd x y = x `mod` (y `mod` 0) + +gcd 0 x = 0 +gcd x y = x `mod` (0 `mod` x) + +gcd 0 x = 0 +gcd x y = x `mod` (0 `mod` y) + +gcd 0 x = 0 +gcd x y = y `mod` (x `mod` x) + +gcd 0 x = 0 +gcd x y = y `mod` (x `mod` y) + +gcd 0 x = 0 +gcd x y = y `mod` (x `mod` 0) + +gcd 0 x = 0 +gcd x y = y `mod` (y `mod` x) + +gcd 0 x = 0 +gcd x y = y `mod` (y `mod` y) + +gcd 0 x = 0 +gcd x y = y `mod` (y `mod` 0) + +gcd 0 x = 0 +gcd x y = y `mod` (0 `mod` x) + +gcd 0 x = 0 +gcd x y = y `mod` (0 `mod` y) + +gcd 0 x = 0 +gcd x y = 0 `mod` (x `mod` x) + +gcd 0 x = 0 +gcd x y = 0 `mod` (x `mod` y) + +gcd 0 x = 0 +gcd x y = 0 `mod` (x `mod` 0) + +gcd 0 x = 0 +gcd x y = 0 `mod` (y `mod` x) + +gcd 0 x = 0 +gcd x y = 0 `mod` (y `mod` y) + +gcd 0 x = 0 +gcd x y = 0 `mod` (y `mod` 0) + +gcd 0 x = 0 +gcd x y = 0 `mod` (0 `mod` x) + +gcd 0 x = 0 +gcd x y = 0 `mod` (0 `mod` y) + +gcd 0 x = x `mod` x +gcd x y = x `mod` x + +gcd 0 x = x `mod` x +gcd x y = x `mod` y + +gcd 0 x = x `mod` x +gcd x y = x `mod` 0 + +gcd 0 x = x `mod` x +gcd x y = y `mod` x + +gcd 0 x = x `mod` x +gcd x y = y `mod` 0 + +gcd 0 x = x `mod` x +gcd x y = 0 `mod` x + +gcd 0 x = x `mod` x +gcd x y = 0 `mod` y + +gcd 0 x = x `mod` 0 +gcd x y = x `mod` x + +gcd 0 x = x `mod` 0 +gcd x y = x `mod` y + +gcd 0 x = x `mod` 0 +gcd x y = x `mod` 0 + +gcd 0 x = x `mod` 0 +gcd x y = y `mod` y + +gcd 0 x = x `mod` 0 +gcd x y = 0 `mod` x + +gcd 0 x = x `mod` 0 +gcd x y = 0 `mod` y + +gcd 0 x = 0 `mod` x +gcd x y = x `mod` x + +gcd 0 x = 0 `mod` x +gcd x y = x `mod` 0 + +gcd 0 x = 0 `mod` x +gcd x y = y `mod` x + +gcd 0 x = 0 `mod` x +gcd x y = y `mod` y + +gcd 0 x = 0 `mod` x +gcd x y = y `mod` 0 + +gcd 0 x = 0 `mod` x +gcd x y = 0 `mod` x + +gcd 0 x = (x `mod` x) `mod` x +gcd x y = x + +gcd 0 x = (x `mod` x) `mod` x +gcd x y = y + +gcd 0 x = (x `mod` x) `mod` x +gcd x y = 0 + +gcd 0 x = (x `mod` x) `mod` 0 +gcd x y = x + +gcd 0 x = (x `mod` x) `mod` 0 +gcd x y = y + +gcd 0 x = (x `mod` x) `mod` 0 +gcd x y = 0 + +gcd 0 x = (x `mod` 0) `mod` x +gcd x y = x + +gcd 0 x = (x `mod` 0) `mod` x +gcd x y = y + +gcd 0 x = (x `mod` 0) `mod` x +gcd x y = 0 + +gcd 0 x = (x `mod` 0) `mod` 0 +gcd x y = x + +gcd 0 x = (x `mod` 0) `mod` 0 +gcd x y = y + +gcd 0 x = (x `mod` 0) `mod` 0 +gcd x y = 0 + +gcd 0 x = (0 `mod` x) `mod` x +gcd x y = x + +gcd 0 x = (0 `mod` x) `mod` x +gcd x y = y + +gcd 0 x = (0 `mod` x) `mod` x +gcd x y = 0 + +gcd 0 x = (0 `mod` x) `mod` 0 +gcd x y = x + +gcd 0 x = (0 `mod` x) `mod` 0 +gcd x y = y + +gcd 0 x = (0 `mod` x) `mod` 0 +gcd x y = 0 + +gcd 0 x = x `mod` (x `mod` x) +gcd x y = x + +gcd 0 x = x `mod` (x `mod` x) +gcd x y = y + +gcd 0 x = x `mod` (x `mod` x) +gcd x y = 0 + +gcd 0 x = x `mod` (x `mod` 0) +gcd x y = x + +gcd 0 x = x `mod` (x `mod` 0) +gcd x y = y + +gcd 0 x = x `mod` (x `mod` 0) +gcd x y = 0 + +gcd 0 x = x `mod` (0 `mod` x) +gcd x y = x + +gcd 0 x = x `mod` (0 `mod` x) +gcd x y = y + +gcd 0 x = x `mod` (0 `mod` x) +gcd x y = 0 + +gcd 0 x = 0 `mod` (x `mod` x) +gcd x y = x + +gcd 0 x = 0 `mod` (x `mod` x) +gcd x y = y + +gcd 0 x = 0 `mod` (x `mod` x) +gcd x y = 0 + +gcd 0 x = 0 `mod` (x `mod` 0) +gcd x y = x + +gcd 0 x = 0 `mod` (x `mod` 0) +gcd x y = y + +gcd 0 x = 0 `mod` (x `mod` 0) +gcd x y = 0 + +gcd 0 x = 0 `mod` (0 `mod` x) +gcd x y = x + +gcd 0 x = 0 `mod` (0 `mod` x) +gcd x y = y + +gcd 0 x = 0 `mod` (0 `mod` x) +gcd x y = 0 + + diff --git a/bench/erroneous.hs b/bench/erroneous.hs new file mode 100644 --- /dev/null +++ b/bench/erroneous.hs @@ -0,0 +1,101 @@ +-- Print erroneous candidates +-- +-- Copyright (C) 2024 Rudy Matela +-- Distributed under the 3-Clause BSD licence (see the file LICENSE). +import Conjure + +-- This script needs some internal utilities of Conjure: +import Conjure.Engine +import Conjure.Defn +import Conjure.Defn.Redundancy +import Conjure.Defn.Test +import Conjure.Utils +import Test.LeanCheck.Tiers (discardT) + + +-- | This function prints erroneous candidates, +-- i.e.: candidates that yield errors or loop indefinitely +-- even if for just a single combination of argument values. +-- +-- The arguments are, in their respective order: +-- +-- * maximum candidate size (5 = few seconds, 7 = few minutes); +-- * function name (for pretty-printing purposes); +-- * proxy value to indicate the type of functions to generate; +-- * list of primitives, in Conjure-compatible form. +printErroneousCandidates :: Conjurable f => Int -> String -> f -> [Prim] -> IO () +printErroneousCandidates n nm f ps = do + putStrLn $ "Erroneous candidates for: " ++ nm ++ " :: " ++ show (typeOf f) + putStrLn $ " pruning with " ++ show nRules ++ "/" ++ show nREs ++ " rules" + putStrLn $ " " ++ show (map length css) ++ " candidates" + putStrLn $ " " ++ show numErroneous ++ "/" ++ show numCandidates ++ " erroneous candidates" + putStrLn "" +--printThy thy + putStrLn $ unlines . map showDefnWithError $ erroneous + where + numCandidates = length candidates + numErroneous = length erroneous + erroneous = [(c, e) | c <- candidates, Just e <- [findError c]] + candidates = concat css + css = take n + . discardT isRedundantByIntroduction -- additional pruning rule + $ css' + (css', thy) = candidateDefnsC args nm f ps -- Conjure uses this for listing candidates + nRules = length (rules thy) + nREs = length (equations thy) + nRules + maxTests = 60 -- a hardcoded value probably will not hurt in this simple benchmark + maxEvalRecursions = 60 + findError = findDefnError maxTests maxEvalRecursions nm f + showDefnWithError (d,e) = showDefn d + ++ "-- " ++ showExpr e ++ " = bottom\n" + + +main :: IO () +main = do + + -- This N value limits the maximum size of candidates, + -- increase it to print erroneous candidates of bigger size. + let n = 7 + + printErroneousCandidates n "foo" (undefined :: Int -> Int) + [ pr (0 :: Int) + , pr (1 :: Int) + , prim "+" ((+) :: Int -> Int -> Int) + , prim "*" ((+) :: Int -> Int -> Int) + , prim "-" ((-) :: Int -> Int -> Int) + ] + + printErroneousCandidates n "?" (undefined :: Int -> Int -> Int) + [ pr (0 :: Int) + , prim "+" ((+) :: Int -> Int -> Int) + , prim "*" ((+) :: Int -> Int -> Int) + , prim "dec" (subtract 1 :: Int -> Int) + ] + + printErroneousCandidates n "goo" (undefined :: [Int] -> [Int]) + [ pr ([] :: [Int]) + , prim ":" ((:) :: Int -> [Int] -> [Int]) + , prim "++" ((++) :: [Int] -> [Int] -> [Int]) + ] + + printErroneousCandidates n "??" (undefined :: [Int] -> [Int] -> [Int]) + [ pr ([] :: [Int]) + , prim ":" ((:) :: Int -> [Int] -> [Int]) + , prim "++" ((++) :: [Int] -> [Int] -> [Int]) + ] + + printErroneousCandidates n "ton" (undefined :: Bool -> Bool) + [ pr False + , pr True + , prim "&&" (&&) + , prim "||" (||) + , prim "not" not + ] + + printErroneousCandidates n "&|" (undefined :: Bool -> Bool -> Bool) + [ pr False + , pr True + , prim "&&" (&&) + , prim "||" (||) + , prim "not" not + ] diff --git a/bench/erroneous.txt b/bench/erroneous.txt new file mode 100644 --- /dev/null +++ b/bench/erroneous.txt @@ -0,0 +1,643 @@ +Erroneous candidates for: foo :: Int -> Int + pruning with 15/35 rules + [3,3,8,9,21,27,98] candidates + 0/169 erroneous candidates + + +Erroneous candidates for: ? :: Int -> Int -> Int + pruning with 10/23 rules + [3,8,22,50,116,302,765] candidates + 147/1266 erroneous candidates + +x ? 0 = x +x ? y = dec x ? y +-- 0 ? 1 = bottom + +0 ? x = x +x ? y = x ? dec y +-- 1 ? 0 = bottom + +x ? 0 = x +x ? y = x ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = y ? dec (dec x) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = y ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = 0 ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec x ? dec x +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec y ? dec x +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec x) ? x +-- 1 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec x) ? y +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec y) ? x +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = x ? dec (dec y) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = y ? dec (dec x) +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = y ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = dec y ? dec x +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec y ? dec y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec x) ? x +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec x) ? y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec x) ? 0 +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec y) ? x +-- 1 ? 0 = bottom + +x ? 0 = x +x ? y = dec (dec x ? y) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (dec x ? y) +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = dec x ? y +-- 0 ? 1 = bottom + +0 ? x = x +x ? y = dec (x ? dec y) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (x ? dec y) +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = x ? dec y +-- 1 ? 0 = bottom + +x ? 0 = x +x ? y = x ? dec (dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = y ? dec (dec (dec x)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = y ? dec (dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = 0 ? dec (dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec x ? (x + y) +-- 1 ? 1 = bottom + +x ? 0 = x +x ? y = dec x ? (y + y) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec x ? dec (dec x) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec x ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec y ? dec (dec x) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec y ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec x) ? dec x +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec y) ? dec x +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec (dec x)) ? x +-- 1 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec (dec x)) ? y +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec (dec y)) ? x +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = x ? dec (dec (dec y)) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = y ? dec (dec (dec x)) +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = y ? dec (dec (dec y)) +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = dec y ? dec (dec x) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec y ? dec (dec y) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = (x + x) ? dec y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = (x + y) ? dec y +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = dec (dec x) ? dec x +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec x) ? dec y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec y) ? dec x +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec y) ? dec y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec x)) ? x +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec x)) ? y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec x)) ? 0 +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec y)) ? x +-- 1 ? 0 = bottom + +x ? 0 = x +x ? y = dec (x ? dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (y ? dec (dec x)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (y ? dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (0 ? dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec x ? dec x) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec y ? dec x) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec (dec x) ? x) +-- 1 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec (dec x) ? y) +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec (dec y) ? x) +-- 1 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (x ? dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (y ? dec (dec x)) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (y ? dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (0 ? dec (dec y)) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (dec x ? dec x) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (dec y ? dec x) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (dec (dec x) ? x) +-- 1 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (dec (dec x) ? y) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (dec (dec y) ? x) +-- 1 ? 1 = bottom + +x ? 0 = dec x +x ? y = x ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = y ? dec (dec x) +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = y ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = 0 ? dec (dec y) +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = dec x ? dec x +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = dec y ? dec x +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = dec (dec x) ? x +-- 1 ? 1 = bottom + +x ? 0 = dec x +x ? y = dec (dec x) ? y +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = dec (dec y) ? x +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = dec (x ? dec (dec y)) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (y ? dec (dec x)) +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = dec (y ? dec (dec y)) +-- 1 ? 1 = bottom + +0 ? x = x +x ? y = dec (dec y ? dec x) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec y ? dec y) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec x) ? x) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec x) ? y) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec x) ? 0) +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (dec y) ? x) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (x ? dec (dec y)) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (y ? dec (dec x)) +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? y = dec (y ? dec (dec y)) +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? y = dec (dec y ? dec x) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (dec y ? dec y) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (dec (dec x) ? x) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (dec (dec x) ? y) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (dec (dec x) ? 0) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (dec (dec y) ? x) +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = x ? dec (dec y) +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = y ? dec (dec x) +-- 1 ? 1 = bottom + +0 ? x = dec x +x ? y = y ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = dec x +x ? y = dec y ? dec x +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = dec y ? dec y +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = dec (dec x) ? x +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = dec (dec x) ? y +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = dec (dec x) ? 0 +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = dec (dec y) ? x +-- 1 ? 0 = bottom + +0 ? x = x +x ? 0 = x +x ? y = x ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = x +x ? y = y ? dec (dec x) +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = x +x ? y = y ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = x +x ? y = dec (dec x) ? x +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = x +x ? y = dec (dec x) ? y +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = x +x ? y = dec (dec y) ? x +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = 0 +x ? y = x ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = 0 +x ? y = y ? dec (dec x) +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = 0 +x ? y = y ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = 0 +x ? y = dec (dec x) ? x +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = 0 +x ? y = dec (dec x) ? y +-- 1 ? 1 = bottom + +0 ? x = x +x ? 0 = 0 +x ? y = dec (dec y) ? x +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? 0 = x +x ? y = x ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? 0 = x +x ? y = y ? dec (dec x) +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? 0 = x +x ? y = y ? dec (dec y) +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? 0 = x +x ? y = dec (dec x) ? x +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? 0 = x +x ? y = dec (dec x) ? y +-- 1 ? 1 = bottom + +0 ? x = 0 +x ? 0 = x +x ? y = dec (dec y) ? x +-- 1 ? 1 = bottom + +x ? 0 = x +x ? y = x + dec x ? y +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec x ? y + y +-- 0 ? 1 = bottom + +x ? 0 = x +x ? y = dec (dec (dec x ? y)) +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = x + dec x ? y +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec x ? y + y +-- 0 ? 1 = bottom + +x ? 0 = 0 +x ? y = dec (dec (dec x ? y)) +-- 0 ? 1 = bottom + +x ? 0 = dec x +x ? y = dec (dec x ? y) +-- 0 ? 1 = bottom + +x ? 0 = x + x +x ? y = dec x ? y +-- 0 ? 1 = bottom + +x ? 0 = dec (dec x) +x ? y = dec x ? y +-- 0 ? 1 = bottom + +0 ? x = x +x ? y = x + x ? dec y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = x ? dec y + y +-- 1 ? 0 = bottom + +0 ? x = x +x ? y = dec (dec (x ? dec y)) +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = x + x ? dec y +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = x ? dec y + y +-- 1 ? 0 = bottom + +0 ? x = 0 +x ? y = dec (dec (x ? dec y)) +-- 1 ? 0 = bottom + +0 ? x = dec x +x ? y = dec (x ? dec y) +-- 1 ? 0 = bottom + +0 ? x = x + x +x ? y = x ? dec y +-- 1 ? 0 = bottom + +0 ? x = dec (dec x) +x ? y = x ? dec y +-- 1 ? 0 = bottom + +0 ? 0 = 0 +0 ? x = dec x +x ? y = x ? dec y +-- 1 ? 0 = bottom + + +Erroneous candidates for: goo :: [Int] -> [Int] + pruning with 4/4 rules + [2,1,1,2,4,7,10] candidates + 0/27 erroneous candidates + + +Erroneous candidates for: ?? :: [Int] -> [Int] -> [Int] + pruning with 4/4 rules + [3,8,15,43,122,264,830] candidates + 0/1285 erroneous candidates + + +Erroneous candidates for: ton :: Bool -> Bool + pruning with 39/49 rules + [3,2,0,0,0,0,0] candidates + 0/5 erroneous candidates + + +Erroneous candidates for: &| :: Bool -> Bool -> Bool + pruning with 39/49 rules + [4,12,20,6,2,16,18] candidates + 0/78 erroneous candidates + + diff --git a/bench/gps.hs b/bench/gps.hs --- a/bench/gps.hs +++ b/bench/gps.hs @@ -1,6 +1,6 @@ -- gps.hs: General Program Synthesis Benchmark Suite -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# LANGUAGE CPP #-} import Conjure diff --git a/bench/gps.out b/bench/gps.out deleted file mode 100644 --- a/bench/gps.out +++ /dev/null @@ -1,539 +0,0 @@ -gps1 :: Int -> Float -> Float --- testing 4 combinations of argument values --- pruning with 0/5 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 1 candidates of size 4 --- tested 4 candidates -gps1 x y = y + fromIntegral x - -gps2 :: Int -> Maybe [Char] --- testing 6 combinations of argument values --- pruning with 9/17 rules --- looking through 1 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 32 candidates of size 7 --- looking through 48 candidates of size 8 --- looking through 48 candidates of size 9 --- looking through 48 candidates of size 10 --- looking through 16 candidates of size 11 --- looking through 512 candidates of size 12 --- looking through 1792 candidates of size 13 --- tested 1203 candidates -gps2 x = if 2000 <= x - then Just "large" - else if x < 1000 then Just "small" else Nothing - -gps3 :: Int -> Int -> Int -> [Int] --- testing 2 combinations of argument values --- pruning with 11/33 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 64 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 1248 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 18627 candidates of size 8 --- tested 12358 candidates -gps3 x y z = enumFromThenTo x (x + z) (y - 1) - -gps3 :: Int -> Int -> Int -> [Int] --- testing 2 combinations of argument values --- pruning with 6/18 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 15 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 81 candidates of size 7 --- looking through 36 candidates of size 8 --- tested 136 candidates -cannot conjure - -gps4 :: [Char] -> [Char] -> [Char] -> Bool --- testing 9 combinations of argument values --- pruning with 11/15 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 6 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 0 candidates of size 8 --- looking through 162 candidates of size 9 --- looking through 26 candidates of size 10 --- looking through 15 candidates of size 11 --- tested 197 candidates -gps4 cs ds es = length cs < length ds && length ds < length es - -gps5 :: [Char] -> [Char] --- testing 5 combinations of argument values --- pruning with 2/3 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 5 candidates of size 5 --- looking through 13 candidates of size 6 --- tested 30 candidates -cannot conjure - -gps6 :: Int -> Int --- testing 9 combinations of argument values --- pruning with 16/18 rules --- looking through 4 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 14 candidates of size 3 --- looking through 17 candidates of size 4 --- looking through 188 candidates of size 5 --- looking through 200 candidates of size 6 --- tested 425 candidates -cannot conjure - -gps7 :: [Char] -> ([Char],Int) --- testing 4 combinations of argument values --- pruning with 5/10 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 7 candidates of size 6 --- looking through 16 candidates of size 7 --- looking through 39 candidates of size 8 --- looking through 88 candidates of size 9 --- looking through 201 candidates of size 10 --- looking through 442 candidates of size 11 --- tested 546 candidates -gps7 cs = (init (unlines (words cs)),length (filter (not . isSpace) cs)) - -gps8 :: [Char] -> [Char] -> [(Int,Char,Char)] --- testing 3 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 0 candidates of size 4 --- tested 0 candidates -cannot conjure - -gps9 :: Int -> [Int] --- testing 3 combinations of argument values --- pruning with 13/14 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 10 candidates of size 5 --- looking through 21 candidates of size 6 --- looking through 34 candidates of size 7 --- looking through 83 candidates of size 8 --- looking through 143 candidates of size 9 --- looking through 256 candidates of size 10 --- tested 325 candidates -gps9 x = filter even (filter (x >) (map sq [1..x])) - -wallisNext :: Ratio Integer -> Ratio Integer --- testing 6 combinations of argument values --- pruning with 37/64 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 15 candidates of size 4 --- looking through 4 candidates of size 5 --- looking through 86 candidates of size 6 --- looking through 5 candidates of size 7 --- looking through 537 candidates of size 8 --- tested 588 candidates -wallisNext (x % y) = (y + 1) % (x + 1) - -wallisNext :: Ratio Integer -> Ratio Integer --- testing 6 combinations of argument values --- pruning with 15/26 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 16 candidates of size 4 --- looking through 3 candidates of size 5 --- looking through 71 candidates of size 6 --- looking through 5 candidates of size 7 --- looking through 393 candidates of size 8 --- tested 451 candidates -wallisNext (x % y) = (y + 1) % (x + 1) - -gps10 :: Int -> Ratio Integer --- testing 6 combinations of argument values --- pruning with 3/4 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 5 candidates of size 6 --- looking through 8 candidates of size 7 --- looking through 13 candidates of size 8 --- tested 33 candidates -gps10 x = product (take x (iterate wallisNext (2 % 3))) - -gps11 :: [[Char]] -> [Int] --- testing 4 combinations of argument values --- pruning with 1/1 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 1 candidates of size 4 --- tested 2 candidates -gps11 css = reverse (map length css) - -gps11 :: [[Char]] -> [Int] --- testing 4 combinations of argument values --- pruning with 4/4 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 1 candidates of size 5 --- looking through 2 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 2 candidates of size 8 --- tested 6 candidates -gps11 [] = [] -gps11 (cs:css) = gps11 css ++ [length cs] - -gps12 :: [Int] -> Int --- testing 6 combinations of argument values --- pruning with 13/27 rules --- looking through 2 candidates of size 1 --- looking through 5 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 11 candidates of size 4 --- looking through 22 candidates of size 5 --- looking through 51 candidates of size 6 --- looking through 133 candidates of size 7 --- looking through 318 candidates of size 8 --- looking through 938 candidates of size 9 --- looking through 2418 candidates of size 10 --- looking through 7229 candidates of size 11 --- tested 8246 candidates -gps12 xs = (length xs - fromJust (findIndex (0 ==) (reverse xs))) - 1 - -gps13 :: [Ratio Integer] -> Ratio Integer --- testing 3 combinations of argument values --- pruning with 4/8 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 10 candidates of size 4 --- looking through 14 candidates of size 5 --- looking through 51 candidates of size 6 --- looking through 105 candidates of size 7 --- looking through 365 candidates of size 8 --- tested 271 candidates -gps13 qs = foldr (+) 0 qs / fromIntegral (length qs) - -odd :: Int -> Bool --- testing 6 combinations of argument values --- pruning with 12/13 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 44 candidates of size 5 --- tested 25 candidates -odd x = 0 /= x `mod` 2 - -gps14 :: [Int] -> Int --- testing 3 combinations of argument values --- pruning with 1/1 rules --- looking through 0 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 1 candidates of size 4 --- tested 2 candidates -gps14 xs = length (filter odd xs) - -gps14 :: [Int] -> Int --- testing 3 combinations of argument values --- pruning with 39/58 rules --- looking through 3 candidates of size 1 --- looking through 9 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 27 candidates of size 4 --- looking through 30 candidates of size 5 --- looking through 258 candidates of size 6 --- looking through 474 candidates of size 7 --- tested 381 candidates -gps14 [] = 0 -gps14 (x:xs) = x + gps14 xs `mod` 2 - -gps15 :: [Int] -> [Int] -> Bool --- testing 5 combinations of argument values --- pruning with 3/7 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 4 candidates of size 4 --- tested 3 candidates -gps15 xs ys = xs == reverse ys - -gps16 :: [Char] -> [Char] -> Bool --- testing 6 combinations of argument values --- pruning with 3/3 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 2 candidates of size 5 --- tested 9 candidates -gps16 cs ds = sort cs `isSubsequenceOf` sort ds - -gps17 :: Int -> Int --- testing 4 combinations of argument values --- pruning with 27/65 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 7 candidates of size 3 --- looking through 13 candidates of size 4 --- looking through 35 candidates of size 5 --- looking through 61 candidates of size 6 --- looking through 219 candidates of size 7 --- looking through 354 candidates of size 8 --- looking through 1431 candidates of size 9 --- tested 729 candidates -gps17 0 = 0 -gps17 x = gps17 (x - 1) + x * x - -gps18 :: [Int] -> [Int] -> [Int] --- testing 3 combinations of argument values --- pruning with 2/6 rules --- looking through 3 candidates of size 1 --- looking through 7 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 37 candidates of size 4 --- looking through 98 candidates of size 5 --- looking through 106 candidates of size 6 --- looking through 440 candidates of size 7 --- looking through 428 candidates of size 8 --- looking through 1950 candidates of size 9 --- tested 2031 candidates -gps18 [] xs = xs -gps18 (x:xs) [] = xs -gps18 (x:xs) (y:ys) = x + y:gps18 xs ys - -gps18 :: [Int] -> [Int] -> [Int] --- testing 3 combinations of argument values --- pruning with 2/7 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 11 candidates of size 4 --- tested 14 candidates -gps18 xs ys = zipWith (+) xs ys - -gps19 :: Int -> [Char] -> [Char] --- testing 2 combinations of argument values --- pruning with 0/0 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- tested 1 candidates -cannot conjure - -isVowel :: Char -> Bool --- testing 12 combinations of argument values --- pruning with 0/0 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 3 candidates of size 6 --- looking through 4 candidates of size 7 --- looking through 4 candidates of size 8 --- looking through 4 candidates of size 9 --- looking through 5 candidates of size 10 --- looking through 5 candidates of size 11 --- looking through 5 candidates of size 12 --- looking through 5 candidates of size 13 --- looking through 4 candidates of size 14 --- looking through 4 candidates of size 15 --- looking through 4 candidates of size 16 --- looking through 3 candidates of size 17 --- looking through 2 candidates of size 18 --- looking through 2 candidates of size 19 --- looking through 1 candidates of size 20 --- looking through 1 candidates of size 21 --- looking through 1 candidates of size 22 --- tested 65 candidates -isVowel 'a' = True -isVowel 'e' = True -isVowel 'i' = True -isVowel 'o' = True -isVowel 'u' = True -isVowel 'y' = True -isVowel c = False - -pig1 :: [Char] -> [Char] --- pruning with 5/5 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 14 candidates of size 5 --- looking through 28 candidates of size 6 --- looking through 47 candidates of size 7 --- looking through 126 candidates of size 8 --- looking through 201 candidates of size 9 --- looking through 631 candidates of size 10 --- looking through 1069 candidates of size 11 --- looking through 3495 candidates of size 12 --- looking through 6382 candidates of size 13 --- looking through 20409 candidates of size 14 --- tested 27901 candidates -pig1 "" = "ay" -pig1 (c:cs) = if isVowel c - then (c:cs) ++ "ay" - else cs ++ (c:"ay") - -gps20c :: [Char] -> [Char] --- pruning with 1/1 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 5 candidates of size 5 --- tested 12 candidates -gps20c cs = unwords (map pig1 (words cs)) - -gps21 :: [Int] -> [Int] --- testing 4 combinations of argument values --- pruning with 4/4 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 5 candidates of size 5 --- looking through 13 candidates of size 6 --- looking through 9 candidates of size 7 --- looking through 30 candidates of size 8 --- looking through 25 candidates of size 9 --- looking through 65 candidates of size 10 --- tested 96 candidates -gps21 [] = [] -gps21 (x:xs) = (if x < 0 then 0 else x):gps21 xs - -gps22 :: [Char] -> Int --- pruning with 5/9 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 3 candidates of size 6 --- tested 5 candidates -gps22 "" = 0 -gps22 (c:cs) = gps22 cs + scrabble1 c - -gps23 :: [Char] -> ([(Int,Int)],Int,Double) --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- tested 0 candidates -cannot conjure - -gps24 :: [Char] -> Char --- testing 4 combinations of argument values --- pruning with 15/19 rules --- looking through 1 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 8 candidates of size 5 --- looking through 15 candidates of size 6 --- looking through 31 candidates of size 7 --- looking through 77 candidates of size 8 --- looking through 203 candidates of size 9 --- looking through 487 candidates of size 10 --- tested 485 candidates -gps24 cs = chr (ord ' ' + sum (map ord cs) `mod` 64) - -gps25 :: Int -> [Int] --- testing 4 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- tested 0 candidates -cannot conjure - -gps26 :: Int -> Int -> Int -> Int -> Int -> Char --- testing 5 combinations of argument values --- pruning with 4/4 rules --- looking through 5 candidates of size 1 --- looking through 0 candidates of size 2 --- tested 5 candidates -cannot conjure - -gps27 :: Int -> Int -> Int -> Int --- testing 3 combinations of argument values --- pruning with 14/18 rules --- looking through 3 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 36 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 0 candidates of size 8 --- looking through 0 candidates of size 9 --- looking through 90 candidates of size 10 --- looking through 2592 candidates of size 11 --- tested 1489 candidates -gps27 x y z = if x < y - then if y < z then y else z - else x - -gps27b :: Int -> Int -> Int -> Int --- testing 3 combinations of argument values --- pruning with 20/30 rules --- looking through 3 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 6 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 12 candidates of size 5 --- tested 15 candidates -gps27b x y z = min z (max x y) - -gps28 :: Int -> Int -> Int -> Int -> Int --- testing 5 combinations of argument values --- pruning with 6/10 rules --- looking through 4 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 6 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 12 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 36 candidates of size 7 --- tested 25 candidates -gps28 x y z x' = x `min` (y `min` (z `min` x')) - -gps29 :: [Char] -> Int --- pruning with 7/11 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 6 candidates of size 6 --- looking through 10 candidates of size 7 --- looking through 10 candidates of size 8 --- looking through 24 candidates of size 9 --- tested 40 candidates -gps29 "" = 0 -gps29 (c:cs) = gps29 cs + (if isVowel c then 1 else 0) - diff --git a/bench/gps.txt b/bench/gps.txt new file mode 100644 --- /dev/null +++ b/bench/gps.txt @@ -0,0 +1,539 @@ +gps1 :: Int -> Float -> Float +-- testing 4 combinations of argument values +-- pruning with 0/5 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- tested 4 candidates +gps1 x y = y + fromIntegral x + +gps2 :: Int -> Maybe [Char] +-- testing 6 combinations of argument values +-- pruning with 9/17 rules +-- looking through 1 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 32 candidates of size 7 +-- looking through 32 candidates of size 8 +-- looking through 48 candidates of size 9 +-- looking through 32 candidates of size 10 +-- looking through 16 candidates of size 11 +-- looking through 512 candidates of size 12 +-- looking through 1408 candidates of size 13 +-- tested 1171 candidates +gps2 x = if 2000 <= x + then Just "large" + else if x < 1000 then Just "small" else Nothing + +gps3 :: Int -> Int -> Int -> [Int] +-- testing 2 combinations of argument values +-- pruning with 11/33 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 64 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 1248 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 18672 candidates of size 8 +-- tested 12358 candidates +gps3 x y z = enumFromThenTo x (x + z) (y - 1) + +gps3 :: Int -> Int -> Int -> [Int] +-- testing 2 combinations of argument values +-- pruning with 6/18 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 15 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 81 candidates of size 7 +-- looking through 36 candidates of size 8 +-- tested 136 candidates +cannot conjure + +gps4 :: [Char] -> [Char] -> [Char] -> Bool +-- testing 9 combinations of argument values +-- pruning with 11/15 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 6 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 0 candidates of size 8 +-- looking through 102 candidates of size 9 +-- looking through 30 candidates of size 10 +-- looking through 15 candidates of size 11 +-- tested 141 candidates +gps4 cs ds es = length cs < length ds && length ds < length es + +gps5 :: [Char] -> [Char] +-- testing 5 combinations of argument values +-- pruning with 2/3 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 4 candidates of size 5 +-- looking through 13 candidates of size 6 +-- tested 28 candidates +cannot conjure + +gps6 :: Int -> Int +-- testing 9 combinations of argument values +-- pruning with 16/18 rules +-- looking through 4 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 14 candidates of size 3 +-- looking through 14 candidates of size 4 +-- looking through 186 candidates of size 5 +-- looking through 165 candidates of size 6 +-- tested 385 candidates +cannot conjure + +gps7 :: [Char] -> ([Char],Int) +-- testing 4 combinations of argument values +-- pruning with 5/10 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 7 candidates of size 6 +-- looking through 16 candidates of size 7 +-- looking through 39 candidates of size 8 +-- looking through 88 candidates of size 9 +-- looking through 201 candidates of size 10 +-- looking through 442 candidates of size 11 +-- tested 546 candidates +gps7 cs = (init (unlines (words cs)),length (filter (not . isSpace) cs)) + +gps8 :: [Char] -> [Char] -> [(Int,Char,Char)] +-- testing 3 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- tested 0 candidates +cannot conjure + +gps9 :: Int -> [Int] +-- testing 3 combinations of argument values +-- pruning with 13/14 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 4 candidates of size 4 +-- looking through 10 candidates of size 5 +-- looking through 21 candidates of size 6 +-- looking through 30 candidates of size 7 +-- looking through 77 candidates of size 8 +-- looking through 134 candidates of size 9 +-- looking through 245 candidates of size 10 +-- tested 306 candidates +gps9 x = filter even (filter (x >) (map sq [1..x])) + +wallisNext :: Ratio Integer -> Ratio Integer +-- testing 6 combinations of argument values +-- pruning with 37/64 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 15 candidates of size 4 +-- looking through 4 candidates of size 5 +-- looking through 86 candidates of size 6 +-- looking through 5 candidates of size 7 +-- looking through 537 candidates of size 8 +-- tested 588 candidates +wallisNext (x % y) = (y + 1) % (x + 1) + +wallisNext :: Ratio Integer -> Ratio Integer +-- testing 6 combinations of argument values +-- pruning with 15/26 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 16 candidates of size 4 +-- looking through 3 candidates of size 5 +-- looking through 71 candidates of size 6 +-- looking through 5 candidates of size 7 +-- looking through 393 candidates of size 8 +-- tested 451 candidates +wallisNext (x % y) = (y + 1) % (x + 1) + +gps10 :: Int -> Ratio Integer +-- testing 6 combinations of argument values +-- pruning with 3/4 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 8 candidates of size 7 +-- looking through 13 candidates of size 8 +-- tested 33 candidates +gps10 x = product (take x (iterate wallisNext (2 % 3))) + +gps11 :: [[Char]] -> [Int] +-- testing 4 combinations of argument values +-- pruning with 1/1 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- tested 2 candidates +gps11 css = reverse (map length css) + +gps11 :: [[Char]] -> [Int] +-- testing 4 combinations of argument values +-- pruning with 4/4 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 1 candidates of size 5 +-- looking through 2 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 2 candidates of size 8 +-- tested 5 candidates +gps11 [] = [] +gps11 (cs:css) = gps11 css ++ [length cs] + +gps12 :: [Int] -> Int +-- testing 6 combinations of argument values +-- pruning with 13/27 rules +-- looking through 2 candidates of size 1 +-- looking through 5 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 9 candidates of size 4 +-- looking through 22 candidates of size 5 +-- looking through 41 candidates of size 6 +-- looking through 125 candidates of size 7 +-- looking through 262 candidates of size 8 +-- looking through 816 candidates of size 9 +-- looking through 1996 candidates of size 10 +-- looking through 5925 candidates of size 11 +-- tested 6320 candidates +gps12 xs = (length xs - fromJust (findIndex (0 ==) (reverse xs))) - 1 + +gps13 :: [Ratio Integer] -> Ratio Integer +-- testing 3 combinations of argument values +-- pruning with 4/8 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 13 candidates of size 5 +-- looking through 51 candidates of size 6 +-- looking through 103 candidates of size 7 +-- looking through 365 candidates of size 8 +-- tested 267 candidates +gps13 qs = foldr (+) 0 qs / fromIntegral (length qs) + +odd :: Int -> Bool +-- testing 6 combinations of argument values +-- pruning with 12/13 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 39 candidates of size 5 +-- tested 20 candidates +odd x = 0 /= x `mod` 2 + +gps14 :: [Int] -> Int +-- testing 3 combinations of argument values +-- pruning with 1/1 rules +-- looking through 0 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- tested 2 candidates +gps14 xs = length (filter odd xs) + +gps14 :: [Int] -> Int +-- testing 3 combinations of argument values +-- pruning with 39/58 rules +-- looking through 3 candidates of size 1 +-- looking through 9 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 27 candidates of size 4 +-- looking through 30 candidates of size 5 +-- looking through 258 candidates of size 6 +-- looking through 474 candidates of size 7 +-- tested 378 candidates +gps14 [] = 0 +gps14 (x:xs) = x + gps14 xs `mod` 2 + +gps15 :: [Int] -> [Int] -> Bool +-- testing 5 combinations of argument values +-- pruning with 3/7 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 4 candidates of size 4 +-- tested 3 candidates +gps15 xs ys = xs == reverse ys + +gps16 :: [Char] -> [Char] -> Bool +-- testing 6 combinations of argument values +-- pruning with 3/3 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 2 candidates of size 5 +-- tested 9 candidates +gps16 cs ds = sort cs `isSubsequenceOf` sort ds + +gps17 :: Int -> Int +-- testing 4 combinations of argument values +-- pruning with 27/65 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 7 candidates of size 3 +-- looking through 8 candidates of size 4 +-- looking through 28 candidates of size 5 +-- looking through 35 candidates of size 6 +-- looking through 179 candidates of size 7 +-- looking through 217 candidates of size 8 +-- looking through 1196 candidates of size 9 +-- tested 492 candidates +gps17 0 = 0 +gps17 x = gps17 (x - 1) + x * x + +gps18 :: [Int] -> [Int] -> [Int] +-- testing 3 combinations of argument values +-- pruning with 2/6 rules +-- looking through 3 candidates of size 1 +-- looking through 8 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 23 candidates of size 4 +-- looking through 86 candidates of size 5 +-- looking through 84 candidates of size 6 +-- looking through 354 candidates of size 7 +-- looking through 353 candidates of size 8 +-- looking through 1528 candidates of size 9 +-- tested 1409 candidates +gps18 [] xs = xs +gps18 (x:xs) [] = xs +gps18 (x:xs) (y:ys) = x + y:gps18 xs ys + +gps18 :: [Int] -> [Int] -> [Int] +-- testing 3 combinations of argument values +-- pruning with 2/7 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 9 candidates of size 4 +-- tested 13 candidates +gps18 xs ys = zipWith (+) xs ys + +gps19 :: Int -> [Char] -> [Char] +-- testing 2 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 1 candidates +cannot conjure + +isVowel :: Char -> Bool +-- testing 12 combinations of argument values +-- pruning with 0/0 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 3 candidates of size 6 +-- looking through 4 candidates of size 7 +-- looking through 4 candidates of size 8 +-- looking through 4 candidates of size 9 +-- looking through 5 candidates of size 10 +-- looking through 5 candidates of size 11 +-- looking through 5 candidates of size 12 +-- looking through 5 candidates of size 13 +-- looking through 4 candidates of size 14 +-- looking through 4 candidates of size 15 +-- looking through 4 candidates of size 16 +-- looking through 3 candidates of size 17 +-- looking through 2 candidates of size 18 +-- looking through 2 candidates of size 19 +-- looking through 1 candidates of size 20 +-- looking through 1 candidates of size 21 +-- looking through 1 candidates of size 22 +-- tested 65 candidates +isVowel 'a' = True +isVowel 'e' = True +isVowel 'i' = True +isVowel 'o' = True +isVowel 'u' = True +isVowel 'y' = True +isVowel c = False + +pig1 :: [Char] -> [Char] +-- pruning with 5/5 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 8 candidates of size 4 +-- looking through 13 candidates of size 5 +-- looking through 28 candidates of size 6 +-- looking through 46 candidates of size 7 +-- looking through 126 candidates of size 8 +-- looking through 200 candidates of size 9 +-- looking through 631 candidates of size 10 +-- looking through 1068 candidates of size 11 +-- looking through 3495 candidates of size 12 +-- looking through 6381 candidates of size 13 +-- looking through 20409 candidates of size 14 +-- tested 27895 candidates +pig1 "" = "ay" +pig1 (c:cs) = if isVowel c + then (c:cs) ++ "ay" + else cs ++ (c:"ay") + +gps20c :: [Char] -> [Char] +-- pruning with 1/1 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 5 candidates of size 5 +-- tested 12 candidates +gps20c cs = unwords (map pig1 (words cs)) + +gps21 :: [Int] -> [Int] +-- testing 4 combinations of argument values +-- pruning with 4/4 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 4 candidates of size 5 +-- looking through 13 candidates of size 6 +-- looking through 8 candidates of size 7 +-- looking through 30 candidates of size 8 +-- looking through 24 candidates of size 9 +-- looking through 65 candidates of size 10 +-- tested 92 candidates +gps21 [] = [] +gps21 (x:xs) = (if x < 0 then 0 else x):gps21 xs + +gps22 :: [Char] -> Int +-- pruning with 5/9 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 3 candidates of size 6 +-- tested 4 candidates +gps22 "" = 0 +gps22 (c:cs) = gps22 cs + scrabble1 c + +gps23 :: [Char] -> ([(Int,Int)],Int,Double) +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 0 candidates +cannot conjure + +gps24 :: [Char] -> Char +-- testing 4 combinations of argument values +-- pruning with 15/19 rules +-- looking through 1 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 8 candidates of size 5 +-- looking through 13 candidates of size 6 +-- looking through 30 candidates of size 7 +-- looking through 75 candidates of size 8 +-- looking through 195 candidates of size 9 +-- looking through 474 candidates of size 10 +-- tested 457 candidates +gps24 cs = chr (ord ' ' + sum (map ord cs) `mod` 64) + +gps25 :: Int -> [Int] +-- testing 4 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- tested 0 candidates +cannot conjure + +gps26 :: Int -> Int -> Int -> Int -> Int -> Char +-- testing 5 combinations of argument values +-- pruning with 4/4 rules +-- looking through 5 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 5 candidates +cannot conjure + +gps27 :: Int -> Int -> Int -> Int +-- testing 3 combinations of argument values +-- pruning with 14/18 rules +-- looking through 3 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 36 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 0 candidates of size 8 +-- looking through 0 candidates of size 9 +-- looking through 90 candidates of size 10 +-- looking through 2592 candidates of size 11 +-- tested 1489 candidates +gps27 x y z = if x < y + then if y < z then y else z + else x + +gps27b :: Int -> Int -> Int -> Int +-- testing 3 combinations of argument values +-- pruning with 20/30 rules +-- looking through 3 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 6 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 12 candidates of size 5 +-- tested 15 candidates +gps27b x y z = min z (max x y) + +gps28 :: Int -> Int -> Int -> Int -> Int +-- testing 5 combinations of argument values +-- pruning with 6/10 rules +-- looking through 4 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 6 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 12 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 36 candidates of size 7 +-- tested 25 candidates +gps28 x y z x' = x `min` (y `min` (z `min` x')) + +gps29 :: [Char] -> Int +-- pruning with 7/11 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 6 candidates of size 6 +-- looking through 10 candidates of size 7 +-- looking through 10 candidates of size 8 +-- looking through 24 candidates of size 9 +-- tested 38 candidates +gps29 "" = 0 +gps29 (c:cs) = gps29 cs + (if isVowel c then 1 else 0) + diff --git a/bench/gps2.hs b/bench/gps2.hs --- a/bench/gps2.hs +++ b/bench/gps2.hs @@ -1,6 +1,6 @@ -- gps2.hs: General Program Synthesis Benchmark Suite II -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# LANGUAGE CPP, TemplateHaskell #-} #if __GLASGOW_HASKELL__ <= 710 diff --git a/bench/gps2.out b/bench/gps2.out deleted file mode 100644 --- a/bench/gps2.out +++ /dev/null @@ -1,388 +0,0 @@ -gps1 :: [Int] -> Maybe Int --- testing 4 combinations of argument values --- pruning with 11/21 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 1 candidates of size 7 --- looking through 0 candidates of size 8 --- looking through 1 candidates of size 9 --- looking through 2 candidates of size 10 --- tested 5 candidates -gps1 xs = findIndex (0 >) (map (foldr (+) 0) (tail (inits xs))) - -gps1 :: [Int] -> Maybe Int --- testing 4 combinations of argument values --- pruning with 11/21 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 1 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 1 candidates of size 7 --- looking through 4 candidates of size 8 --- tested 6 candidates -gps1 xs = findIndex (0 >) (map sum (tail (inits xs))) - -gps1 :: Int -> [Int] -> Int --- testing 6 combinations of argument values --- pruning with 8/9 rules --- looking through 4 candidates of size 1 --- looking through 24 candidates of size 2 --- looking through 75 candidates of size 3 --- looking through 234 candidates of size 4 --- tested 337 candidates -cannot conjure - -gps2 :: Double -> Double -> Int -> Double --- testing 5 combinations of argument values --- pruning with 2/6 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 17 candidates of size 3 --- looking through 62 candidates of size 4 --- looking through 266 candidates of size 5 --- looking through 1154 candidates of size 6 --- tested 1503 candidates -cannot conjure - -gps3 :: [Char] -> Int --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- tested 0 candidates -cannot conjure - -gps4 :: [Char] -> [Char] --- pruning with 13/20 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 9 candidates of size 3 --- looking through 22 candidates of size 4 --- looking through 54 candidates of size 5 --- looking through 124 candidates of size 6 --- tested 214 candidates -cannot conjure - -gps5 :: Int -> [Int] --- testing 6 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- tested 0 candidates -cannot conjure - -tell :: [Int] -> Int -> [Int] --- pruning with 0/0 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 6 candidates of size 5 --- looking through 46 candidates of size 6 --- looking through 26 candidates of size 7 --- looking through 400 candidates of size 8 --- looking through 134 candidates of size 9 --- looking through 3914 candidates of size 10 --- tested 1552 candidates -tell [] x = [] -tell (x:xs) y = y `div` x:tell xs (y `mod` x) - -gps5 :: Int -> [Int] --- testing 6 combinations of argument values --- pruning with 0/0 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 1 candidates of size 3 --- tested 2 candidates -gps5 x = tell [25,10,5,1] x - -gps5 :: Int -> [Int] --- testing 6 combinations of argument values --- pruning with 12/12 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 9 candidates of size 4 --- looking through 45 candidates of size 5 --- looking through 82 candidates of size 6 --- looking through 428 candidates of size 7 --- looking through 887 candidates of size 8 --- looking through 4354 candidates of size 9 --- looking through 9260 candidates of size 10 --- looking through 43875 candidates of size 11 --- tested 32327 candidates -gps5 x = tell [25,10,5,1] x - -gps6 :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- tested 2 candidates -cannot conjure - -gps7 :: Integer -> Integer -> Ratio Integer --- testing 6 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- tested 0 candidates -cannot conjure - -gps8 :: Int -> [Int] -> (Int,Int) --- testing 3 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- tested 0 candidates -cannot conjure - -gps9 :: Int -> [Char] --- testing 7 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- tested 0 candidates -cannot conjure - -gps10 :: [Int] -> Int --- testing 7 combinations of argument values --- pruning with 67/100 rules --- looking through 4 candidates of size 1 --- looking through 16 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 68 candidates of size 4 --- looking through 80 candidates of size 5 --- looking through 1084 candidates of size 6 --- looking through 1556 candidates of size 7 --- looking through 20600 candidates of size 8 --- looking through 35632 candidates of size 9 --- tested 29542 candidates -gps10 [] = 0 -gps10 (x:xs) = gps10 xs + (x `div` 3 - 2) - -gcd :: Int -> Int -> Int --- testing 11 combinations of argument values --- pruning with 0/0 rules --- looking through 3 candidates of size 1 --- looking through 5 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 50 candidates of size 4 --- looking through 98 candidates of size 5 --- looking through 359 candidates of size 6 --- tested 171 candidates -gcd x 0 = x -gcd x y = gcd y (x `mod` y) - -gps12 :: [Char] -> [Char] -> [Int] --- testing 5 combinations of argument values --- pruning with 1/2 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 4 candidates of size 5 --- tested 3 candidates -gps12 cs ds = findIndices (ds `isPrefixOf`) (tails cs) - -gps13_leaders :: [Int] -> [Int] --- testing 4 combinations of argument values --- pruning with 5/5 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 1 candidates of size 5 --- looking through 2 candidates of size 6 --- looking through 1 candidates of size 7 --- looking through 4 candidates of size 8 --- looking through 7 candidates of size 9 --- looking through 21 candidates of size 10 --- looking through 34 candidates of size 11 --- looking through 67 candidates of size 12 --- tested 83 candidates -gps13_leaders [] = [] -gps13_leaders (x:xs) = if all (x >) xs - then x:gps13_leaders xs - else gps13_leaders xs - -gps14_luhn :: [Int] -> Int --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- tested 0 candidates -cannot conjure - -gps15_mastermind :: () -> () --- pruning with 0/1 rules --- looking through 1 candidates of size 1 --- tested 1 candidates -gps15_mastermind u = u - -gps16_middle :: [Char] -> [Char] --- testing 7 combinations of argument values --- pruning with 10/11 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 7 candidates of size 3 --- looking through 12 candidates of size 4 --- looking through 21 candidates of size 5 --- looking through 34 candidates of size 6 --- looking through 61 candidates of size 7 --- looking through 126 candidates of size 8 --- looking through 307 candidates of size 9 --- looking through 824 candidates of size 10 --- looking through 2282 candidates of size 11 --- looking through 6293 candidates of size 12 --- tested 3977 candidates -gps16_middle "" = "" -gps16_middle (c:cs) = if length cs <= 1 - then c:cs - else gps16_middle (init cs) - -gps17_pds :: [Int] -> Int --- testing 5 combinations of argument values --- pruning with 29/40 rules --- looking through 1 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 3 candidates of size 5 --- tested 9 candidates -cannot conjure - -gps18_price :: [Double] -> [Double] -> Double --- testing 4 combinations of argument values --- pruning with 26/35 rules --- looking through 2 candidates of size 1 --- looking through 8 candidates of size 2 --- looking through 32 candidates of size 3 --- looking through 86 candidates of size 4 --- looking through 412 candidates of size 5 --- looking through 1072 candidates of size 6 --- tested 1612 candidates -cannot conjure - -gps19_snowday :: Int -> Double -> Double -> Double -> Double --- testing 7 combinations of argument values --- pruning with 6/19 rules --- looking through 3 candidates of size 1 --- looking through 4 candidates of size 2 --- looking through 22 candidates of size 3 --- looking through 118 candidates of size 4 --- looking through 318 candidates of size 5 --- looking through 1936 candidates of size 6 --- tested 2401 candidates -cannot conjure - -gps20 :: [Char] -> Bool --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- tested 0 candidates -cannot conjure - -spin :: [Char] -> [Char] --- pruning with 6/6 rules --- reasoning produced 1 incorrect properties, please re-run with more tests for faster results --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 4 candidates of size 8 --- tested 3 candidates -spin cs = if length cs >= 5 - then reverse cs - else cs - -gps21_spinwords :: [Char] -> [Char] --- pruning with 16/16 rules --- reasoning produced 2 incorrect properties, please re-run with more tests for faster results --- looking through 1 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 5 candidates of size 5 --- tested 12 candidates -gps21_spinwords cs = unwords (map spin (words cs)) - -digits :: Int -> [Int] --- testing 5 combinations of argument values --- pruning with 7/7 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 14 candidates of size 5 --- looking through 13 candidates of size 6 --- looking through 94 candidates of size 7 --- looking through 104 candidates of size 8 --- looking through 856 candidates of size 9 --- looking through 929 candidates of size 10 --- looking through 8914 candidates of size 11 --- looking through 9686 candidates of size 12 --- tested 20616 candidates -cannot conjure - -gps22 :: Int -> [Char] --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- tested 0 candidates -cannot conjure - -gps23 :: [Char] -> [Char] -> [Char] -> [Char] --- pruning with 0/0 rules --- looking through 3 candidates of size 1 --- looking through 9 candidates of size 2 --- looking through 31 candidates of size 3 --- looking through 36 candidates of size 4 --- looking through 187 candidates of size 5 --- looking through 627 candidates of size 6 --- looking through 944 candidates of size 7 --- looking through 863 candidates of size 8 --- looking through 951 candidates of size 9 --- looking through 3902 candidates of size 10 --- looking through 6758 candidates of size 11 --- looking through 3276 candidates of size 12 --- tested 17587 candidates -cannot conjure - -gps24 :: [Char] -> Twitter --- pruning with 4/8 rules --- reasoning produced 4 incorrect properties, please re-run with more tests for faster results --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 8 candidates of size 3 --- looking through 7 candidates of size 4 --- looking through 4 candidates of size 5 --- looking through 5 candidates of size 6 --- looking through 10 candidates of size 7 --- looking through 48 candidates of size 8 --- looking through 138 candidates of size 9 --- looking through 232 candidates of size 10 --- looking through 322 candidates of size 11 --- looking through 483 candidates of size 12 --- tested 936 candidates -gps24 "" = Empty -gps24 (c:cs) = if 140 > length cs - then Tweet (length (c:cs)) - else TooMany - -gps25 :: [Double] -> [Double] -> Double --- testing 6 combinations of argument values --- pruning with 31/59 rules --- looking through 2 candidates of size 1 --- looking through 9 candidates of size 2 --- looking through 49 candidates of size 3 --- looking through 211 candidates of size 4 --- looking through 1063 candidates of size 5 --- looking through 4717 candidates of size 6 --- tested 6051 candidates -cannot conjure - diff --git a/bench/gps2.txt b/bench/gps2.txt new file mode 100644 --- /dev/null +++ b/bench/gps2.txt @@ -0,0 +1,387 @@ +gps1 :: [Int] -> Maybe Int +-- testing 4 combinations of argument values +-- pruning with 11/21 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 1 candidates of size 7 +-- looking through 0 candidates of size 8 +-- looking through 1 candidates of size 9 +-- looking through 2 candidates of size 10 +-- tested 5 candidates +gps1 xs = findIndex (0 >) (map (foldr (+) 0) (tail (inits xs))) + +gps1 :: [Int] -> Maybe Int +-- testing 4 combinations of argument values +-- pruning with 11/21 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 1 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 1 candidates of size 7 +-- looking through 4 candidates of size 8 +-- tested 6 candidates +gps1 xs = findIndex (0 >) (map sum (tail (inits xs))) + +gps1 :: Int -> [Int] -> Int +-- testing 6 combinations of argument values +-- pruning with 8/9 rules +-- looking through 4 candidates of size 1 +-- looking through 24 candidates of size 2 +-- looking through 75 candidates of size 3 +-- looking through 216 candidates of size 4 +-- tested 319 candidates +cannot conjure + +gps2 :: Double -> Double -> Int -> Double +-- testing 5 combinations of argument values +-- pruning with 2/6 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 17 candidates of size 3 +-- looking through 62 candidates of size 4 +-- looking through 266 candidates of size 5 +-- looking through 1154 candidates of size 6 +-- tested 1503 candidates +cannot conjure + +gps3 :: [Char] -> Int +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 0 candidates +cannot conjure + +gps4 :: [Char] -> [Char] +-- pruning with 13/20 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 8 candidates of size 3 +-- looking through 20 candidates of size 4 +-- looking through 51 candidates of size 5 +-- looking through 119 candidates of size 6 +-- tested 203 candidates +cannot conjure + +gps5 :: Int -> [Int] +-- testing 6 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- tested 0 candidates +cannot conjure + +tell :: [Int] -> Int -> [Int] +-- pruning with 0/0 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 6 candidates of size 5 +-- looking through 39 candidates of size 6 +-- looking through 26 candidates of size 7 +-- looking through 328 candidates of size 8 +-- looking through 134 candidates of size 9 +-- looking through 3229 candidates of size 10 +-- tested 783 candidates +tell [] x = [] +tell (x:xs) y = y `div` x:tell xs (y `mod` x) + +gps5 :: Int -> [Int] +-- testing 6 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- tested 2 candidates +gps5 x = tell [25,10,5,1] x + +gps5 :: Int -> [Int] +-- testing 6 combinations of argument values +-- pruning with 12/12 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 5 candidates of size 3 +-- looking through 9 candidates of size 4 +-- looking through 45 candidates of size 5 +-- looking through 82 candidates of size 6 +-- looking through 428 candidates of size 7 +-- looking through 882 candidates of size 8 +-- looking through 4350 candidates of size 9 +-- looking through 9232 candidates of size 10 +-- looking through 43847 candidates of size 11 +-- tested 32290 candidates +gps5 x = tell [25,10,5,1] x + +gps6 :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 1 candidates of size 2 +-- tested 1 candidates +cannot conjure + +gps7 :: Integer -> Integer -> Ratio Integer +-- testing 6 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- tested 0 candidates +cannot conjure + +gps8 :: Int -> [Int] -> (Int,Int) +-- testing 3 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 0 candidates +cannot conjure + +gps9 :: Int -> [Char] +-- testing 7 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- tested 0 candidates +cannot conjure + +gps10 :: [Int] -> Int +-- testing 7 combinations of argument values +-- pruning with 67/100 rules +-- looking through 4 candidates of size 1 +-- looking through 16 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 68 candidates of size 4 +-- looking through 80 candidates of size 5 +-- looking through 1084 candidates of size 6 +-- looking through 1556 candidates of size 7 +-- looking through 20600 candidates of size 8 +-- looking through 35632 candidates of size 9 +-- tested 29538 candidates +gps10 [] = 0 +gps10 (x:xs) = gps10 xs + (x `div` 3 - 2) + +gcd :: Int -> Int -> Int +-- testing 11 combinations of argument values +-- pruning with 0/0 rules +-- looking through 3 candidates of size 1 +-- looking through 6 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 50 candidates of size 4 +-- looking through 98 candidates of size 5 +-- looking through 344 candidates of size 6 +-- tested 173 candidates +gcd x 0 = x +gcd x y = gcd y (x `mod` y) + +gps12 :: [Char] -> [Char] -> [Int] +-- testing 5 combinations of argument values +-- pruning with 1/2 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 4 candidates of size 5 +-- tested 3 candidates +gps12 cs ds = findIndices (ds `isPrefixOf`) (tails cs) + +gps13_leaders :: [Int] -> [Int] +-- testing 4 combinations of argument values +-- pruning with 5/5 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 1 candidates of size 5 +-- looking through 2 candidates of size 6 +-- looking through 1 candidates of size 7 +-- looking through 4 candidates of size 8 +-- looking through 7 candidates of size 9 +-- looking through 21 candidates of size 10 +-- looking through 34 candidates of size 11 +-- looking through 67 candidates of size 12 +-- tested 82 candidates +gps13_leaders [] = [] +gps13_leaders (x:xs) = if all (x >) xs + then x:gps13_leaders xs + else gps13_leaders xs + +gps14_luhn :: [Int] -> Int +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 0 candidates +cannot conjure + +gps15_mastermind :: () -> () +-- pruning with 0/1 rules +-- looking through 1 candidates of size 1 +-- tested 1 candidates +gps15_mastermind u = u + +gps16_middle :: [Char] -> [Char] +-- testing 7 combinations of argument values +-- pruning with 10/11 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 6 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 19 candidates of size 5 +-- looking through 32 candidates of size 6 +-- looking through 59 candidates of size 7 +-- looking through 124 candidates of size 8 +-- looking through 305 candidates of size 9 +-- looking through 822 candidates of size 10 +-- looking through 2276 candidates of size 11 +-- looking through 6273 candidates of size 12 +-- tested 3956 candidates +gps16_middle "" = "" +gps16_middle (c:cs) = if length cs <= 1 + then c:cs + else gps16_middle (init cs) + +gps17_pds :: [Int] -> Int +-- testing 5 combinations of argument values +-- pruning with 29/40 rules +-- looking through 1 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 3 candidates of size 5 +-- tested 8 candidates +cannot conjure + +gps18_price :: [Double] -> [Double] -> Double +-- testing 4 combinations of argument values +-- pruning with 26/35 rules +-- looking through 2 candidates of size 1 +-- looking through 8 candidates of size 2 +-- looking through 32 candidates of size 3 +-- looking through 70 candidates of size 4 +-- looking through 396 candidates of size 5 +-- looking through 1016 candidates of size 6 +-- tested 1524 candidates +cannot conjure + +gps19_snowday :: Int -> Double -> Double -> Double -> Double +-- testing 7 combinations of argument values +-- pruning with 6/19 rules +-- looking through 3 candidates of size 1 +-- looking through 6 candidates of size 2 +-- looking through 24 candidates of size 3 +-- looking through 120 candidates of size 4 +-- looking through 318 candidates of size 5 +-- looking through 1944 candidates of size 6 +-- tested 2415 candidates +cannot conjure + +gps20 :: [Char] -> Bool +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 0 candidates +cannot conjure + +spin :: [Char] -> [Char] +-- pruning with 6/6 rules +-- reasoning produced 1 incorrect properties, please re-run with more tests for faster results +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 4 candidates of size 8 +-- tested 3 candidates +spin cs = if length cs >= 5 + then reverse cs + else cs + +gps21_spinwords :: [Char] -> [Char] +-- pruning with 16/16 rules +-- reasoning produced 2 incorrect properties, please re-run with more tests for faster results +-- looking through 1 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 5 candidates of size 5 +-- tested 12 candidates +gps21_spinwords cs = unwords (map spin (words cs)) + +digits :: Int -> [Int] +-- testing 5 combinations of argument values +-- pruning with 7/7 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 11 candidates of size 5 +-- looking through 13 candidates of size 6 +-- looking through 91 candidates of size 7 +-- looking through 104 candidates of size 8 +-- looking through 850 candidates of size 9 +-- looking through 923 candidates of size 10 +-- looking through 8902 candidates of size 11 +-- looking through 9662 candidates of size 12 +-- tested 20562 candidates +cannot conjure + +gps22 :: Int -> [Char] +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- tested 0 candidates +cannot conjure + +gps23 :: [Char] -> [Char] -> [Char] -> [Char] +-- pruning with 0/0 rules +-- looking through 3 candidates of size 1 +-- looking through 12 candidates of size 2 +-- looking through 33 candidates of size 3 +-- looking through 36 candidates of size 4 +-- looking through 127 candidates of size 5 +-- looking through 507 candidates of size 6 +-- looking through 839 candidates of size 7 +-- looking through 784 candidates of size 8 +-- looking through 600 candidates of size 9 +-- looking through 2722 candidates of size 10 +-- looking through 5292 candidates of size 11 +-- looking through 2832 candidates of size 12 +-- tested 13787 candidates +cannot conjure + +gps24 :: [Char] -> Twitter +-- pruning with 4/8 rules +-- reasoning produced 4 incorrect properties, please re-run with more tests for faster results +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 6 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 3 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 10 candidates of size 7 +-- looking through 48 candidates of size 8 +-- looking through 134 candidates of size 9 +-- looking through 224 candidates of size 10 +-- looking through 314 candidates of size 11 +-- looking through 479 candidates of size 12 +-- tested 908 candidates +gps24 "" = Empty +gps24 (c:cs) = if 140 > length cs + then Tweet (length (c:cs)) + else TooMany + +gps25 :: [Double] -> [Double] -> Double +-- testing 6 combinations of argument values +-- pruning with 31/59 rules +-- looking through 2 candidates of size 1 +-- looking through 9 candidates of size 2 +-- looking through 49 candidates of size 3 +-- looking through 195 candidates of size 4 +-- looking through 1035 candidates of size 5 +-- looking through 4596 candidates of size 6 +-- tested 5886 candidates +cannot conjure + diff --git a/bench/ill-hit.out b/bench/ill-hit.out deleted file mode 100644 --- a/bench/ill-hit.out +++ /dev/null @@ -1,23 +0,0 @@ -sum :: [Int] -> Int --- testing 4 combinations of argument values --- pruning with 14/25 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 7 candidates of size 4 --- looking through 11 candidates of size 5 --- tested 16 candidates -sum [] = 0 -sum (x:xs) = x + sum xs - -sum :: [Int] -> Int --- pruning with 14/25 rules --- looking through 2 candidates of size 1 --- looking through 5 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 12 candidates of size 4 --- looking through 18 candidates of size 5 --- tested 25 candidates -sum [] = 0 -sum (x:xs) = x + sum xs - diff --git a/bench/ill-hit.txt b/bench/ill-hit.txt new file mode 100644 --- /dev/null +++ b/bench/ill-hit.txt @@ -0,0 +1,23 @@ +sum :: [Int] -> Int +-- testing 4 combinations of argument values +-- pruning with 14/25 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 11 candidates of size 5 +-- tested 14 candidates +sum [] = 0 +sum (x:xs) = x + sum xs + +sum :: [Int] -> Int +-- pruning with 14/25 rules +-- looking through 2 candidates of size 1 +-- looking through 5 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 18 candidates of size 5 +-- tested 21 candidates +sum [] = 0 +sum (x:xs) = x + sum xs + diff --git a/bench/longshot.hs b/bench/longshot.hs --- a/bench/longshot.hs +++ b/bench/longshot.hs @@ -1,6 +1,6 @@ -- longshot.hs: miscellaneous longshots -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/bench/longshot.out b/bench/longshot.out deleted file mode 100644 --- a/bench/longshot.out +++ /dev/null diff --git a/bench/longshot.txt b/bench/longshot.txt new file mode 100644 --- /dev/null +++ b/bench/longshot.txt diff --git a/bench/lowtests.hs b/bench/lowtests.hs --- a/bench/lowtests.hs +++ b/bench/lowtests.hs @@ -1,6 +1,6 @@ -- lowtests.hs: conjuring with a low number of tests -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). -- -- With a low number of tests Conjure may not be able to find the actual diff --git a/bench/lowtests.out b/bench/lowtests.out deleted file mode 100644 --- a/bench/lowtests.out +++ /dev/null @@ -1,89 +0,0 @@ -subset :: [Int] -> [Int] -> Bool --- testing 44 combinations of argument values --- pruning with 3/3 rules -{- -rules: -xs `isSubsequenceOf` xs == True -sort (sort xs) == sort xs -sort xs `isSubsequenceOf` ys == xs `isSubsequenceOf` sort ys - --} --- reasoning produced 1 incorrect properties, please re-run with more tests for faster results -{- -invalid: -xs `isSubsequenceOf` sort xs == True --} --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 12 candidates of size 7 --- looking through 21 candidates of size 8 --- looking through 8 candidates of size 9 --- looking through 6 candidates of size 10 --- looking through 30 candidates of size 11 --- looking through 45 candidates of size 12 --- tested 128 candidates -cannot conjure - -subset :: [Int] -> [Int] -> Bool --- testing 44 combinations of argument values --- pruning with 3/3 rules -{- -rules: -xs `isSubsequenceOf` xs == True -sort (sort xs) == sort xs -sort xs `isSubsequenceOf` xs == xs `isSubsequenceOf` sort xs - --} --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 2 candidates of size 5 --- tested 9 candidates -subset xs ys = sort xs `isSubsequenceOf` sort ys - -replicates :: [Char] -> Int -> [Char] --- testing 60 combinations of argument values --- pruning with 2/2 rules -{- -rules: -concat (transpose xss) == concat xss -transpose (transpose (transpose xss)) == transpose xss - --} --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 1 candidates of size 7 --- looking through 0 candidates of size 8 --- looking through 0 candidates of size 9 --- looking through 1 candidates of size 10 --- looking through 0 candidates of size 11 --- looking through 0 candidates of size 12 --- tested 4 candidates -cannot conjure - -replicates :: [Char] -> Int -> [Char] --- testing 360 combinations of argument values --- pruning with 2/2 rules -{- -rules: -transpose (transpose (transpose xss)) == transpose xss -replicate x (concat (transpose xss)) == replicate x (concat xss) - --} --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 1 candidates of size 5 --- tested 3 candidates -replicates cs x = concat (transpose (replicate x cs)) - diff --git a/bench/lowtests.txt b/bench/lowtests.txt new file mode 100644 --- /dev/null +++ b/bench/lowtests.txt @@ -0,0 +1,89 @@ +subset :: [Int] -> [Int] -> Bool +-- testing 44 combinations of argument values +-- pruning with 3/3 rules +{- +rules: +xs `isSubsequenceOf` xs == True +sort (sort xs) == sort xs +sort xs `isSubsequenceOf` ys == xs `isSubsequenceOf` sort ys + +-} +-- reasoning produced 1 incorrect properties, please re-run with more tests for faster results +{- +invalid: +xs `isSubsequenceOf` sort xs == True +-} +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 4 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 10 candidates of size 7 +-- looking through 10 candidates of size 8 +-- looking through 0 candidates of size 9 +-- looking through 6 candidates of size 10 +-- looking through 20 candidates of size 11 +-- looking through 15 candidates of size 12 +-- tested 67 candidates +cannot conjure + +subset :: [Int] -> [Int] -> Bool +-- testing 44 combinations of argument values +-- pruning with 3/3 rules +{- +rules: +xs `isSubsequenceOf` xs == True +sort (sort xs) == sort xs +sort xs `isSubsequenceOf` xs == xs `isSubsequenceOf` sort xs + +-} +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 2 candidates of size 5 +-- tested 9 candidates +subset xs ys = sort xs `isSubsequenceOf` sort ys + +replicates :: [Char] -> Int -> [Char] +-- testing 60 combinations of argument values +-- pruning with 2/2 rules +{- +rules: +concat (transpose xss) == concat xss +transpose (transpose (transpose xss)) == transpose xss + +-} +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 1 candidates of size 7 +-- looking through 0 candidates of size 8 +-- looking through 0 candidates of size 9 +-- looking through 1 candidates of size 10 +-- looking through 0 candidates of size 11 +-- looking through 0 candidates of size 12 +-- tested 4 candidates +cannot conjure + +replicates :: [Char] -> Int -> [Char] +-- testing 360 combinations of argument values +-- pruning with 2/2 rules +{- +rules: +transpose (transpose (transpose xss)) == transpose xss +replicate x (concat (transpose xss)) == replicate x (concat xss) + +-} +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 1 candidates of size 5 +-- tested 3 candidates +replicates cs x = concat (transpose (replicate x cs)) + diff --git a/bench/p12.hs b/bench/p12.hs --- a/bench/p12.hs +++ b/bench/p12.hs @@ -1,6 +1,6 @@ -- 12 background primitives -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure import System.Environment diff --git a/bench/p12.out b/bench/p12.out deleted file mode 100644 --- a/bench/p12.out +++ /dev/null @@ -1,14 +0,0 @@ -running with 13 primitives -factorial :: Int -> Int --- testing 6 combinations of argument values --- pruning with 67/100 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 6 candidates of size 3 --- looking through 15 candidates of size 4 --- looking through 43 candidates of size 5 --- looking through 152 candidates of size 6 --- tested 77 candidates -factorial 0 = 1 -factorial x = x * factorial (dec x) - diff --git a/bench/p12.txt b/bench/p12.txt new file mode 100644 --- /dev/null +++ b/bench/p12.txt @@ -0,0 +1,14 @@ +running with 13 primitives +factorial :: Int -> Int +-- testing 6 combinations of argument values +-- pruning with 67/100 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 6 candidates of size 3 +-- looking through 13 candidates of size 4 +-- looking through 40 candidates of size 5 +-- looking through 138 candidates of size 6 +-- tested 69 candidates +factorial 0 = 1 +factorial x = x * factorial (dec x) + diff --git a/bench/p30.hs b/bench/p30.hs --- a/bench/p30.hs +++ b/bench/p30.hs @@ -1,6 +1,6 @@ -- 30 background primitives, does Conjure scale? -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure import System.Environment diff --git a/bench/p30.out b/bench/p30.out deleted file mode 100644 --- a/bench/p30.out +++ /dev/null @@ -1,2 +0,0 @@ -running with 26 primitives -usage: p30 [t] diff --git a/bench/p30.txt b/bench/p30.txt new file mode 100644 --- /dev/null +++ b/bench/p30.txt @@ -0,0 +1,2 @@ +running with 26 primitives +usage: p30 [t] diff --git a/bench/redundants.hs b/bench/redundants.hs --- a/bench/redundants.hs +++ b/bench/redundants.hs @@ -1,12 +1,14 @@ -- Print redundant candidates -- --- Copyright (C) 2023 Rudy Matela +-- Copyright (C) 2023-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure -- This script needs some internal utilities of Conjure: import Conjure.Engine import Conjure.Defn +import Conjure.Defn.Redundancy +import Conjure.Defn.Test import Conjure.Utils import Test.LeanCheck.Tiers (discardT) @@ -41,8 +43,8 @@ (css', thy) = candidateDefnsC args nm f ps -- Conjure uses this for listing candidates nRules = length (rules thy) nREs = length (equations thy) + nRules - maxTests = 360 -- a hardcoded value probably will not hurt in this simple benchmark - maxEvalRecursions = 60 + maxTests = 60 -- a hardcoded value probably will not hurt in this simple benchmark + maxEvalRecursions = 30 -- shows a class of candidates showClass :: [Defn] -> String @@ -56,8 +58,8 @@ -- This N value limits the maximum size of candidates, -- increase it to print redundant candidates of bigger size. - let n = 5 - -- With n = 5, this should run in a few seconds. + let n = 6 + -- With n = 6, this should run in a few seconds. -- With n = 7 and -O2 optimization, -- this should take a few minutes to run and generate a ~300K text file. -- We can also customize the n per-function below: diff --git a/bench/redundants.out b/bench/redundants.out deleted file mode 100644 --- a/bench/redundants.out +++ /dev/null @@ -1,953 +0,0 @@ -Redundant candidates for: foo :: Int -> Int - pruning with 15/35 rules - [3,3,8,13,29] candidates - 46/56 unique candidates - 10/56 redundant candidates - -rules: -x * y == x + y -x * y == y + x -x - x == 0 -x + 0 == x -0 + x == x -x - 0 == x -(x + y) + z == x + (y + z) -(x + y) + z == y + (x + z) -x - (y - z) == z + (x - y) -(x - y) - z == x - (y + z) -(x - y) - z == x - (z + y) -(x + y) - z == x + (y - z) -(x + y) - z == y + (x - z) -x + (y - x) == y -(x - y) + y == x -equations: -y + x == x + y -y + (x + z) == x + (y + z) -z + (x + y) == x + (y + z) -z + (y + x) == x + (y + z) -y + (x - z) == x + (y - z) -(x - z) + y == x + (y - z) -(z - y) + x == (x - y) + z -y - (x + y) == 0 - x -y - (y + x) == 0 - x -z - (y + z) == x - (x + y) -z - (y + z) == x - (y + x) -z - (z + y) == x - (x + y) -z - (z + y) == x - (y + x) -x + (0 - y) == x - y -(0 - y) + x == x - y -x - (x + 1) == 0 - 1 -x - (1 + x) == 0 - 1 -y - (y + 1) == x - (x + 1) -y - (y + 1) == x - (1 + x) -y - (1 + y) == x - (1 + x) - -class of 2 equivalent candidates: - - foo x = x + x - - foo 0 = 0 - foo x = x + x - - -class of 2 equivalent candidates: - - foo x = x + 1 - - foo 0 = 1 - foo x = x + 1 - - -class of 2 equivalent candidates: - - foo x = x - 1 - - foo 1 = 0 - foo x = x - 1 - - -class of 4 equivalent candidates: - - foo x = 0 - x - - foo 0 = 0 - foo x = 0 - x - - foo x = x - (x + x) - - foo x = 1 - (x + 1) - - -class of 4 equivalent candidates: - - foo x = 1 - x - - foo 0 = 1 - foo x = 1 - x - - foo x = 1 + (0 - x) - - foo 1 = 0 - foo x = 1 - x - - -class of 2 equivalent candidates: - - foo x = x + (x + 1) - - foo x = 1 + (x + x) - - - -Redundant candidates for: ? :: Int -> Int -> Int - pruning with 10/23 rules - [3,7,22,53,129] candidates - 192/214 unique candidates - 22/214 redundant candidates - -rules: -x * y == x + y -x * y == y + x -x + 0 == x -0 + x == x -dec (x + y) == x + dec y -dec (x + y) == y + dec x -dec (x + y) == dec x + y -dec (x + y) == dec y + x -(x + y) + z == x + (y + z) -(x + y) + z == y + (x + z) -equations: -y + x == x + y -y + dec x == x + dec y -dec x + y == x + dec y -dec y + x == dec x + y -x + dec 0 == dec x -dec 0 + x == dec x -y + (x + z) == x + (y + z) -z + (x + y) == x + (y + z) -z + (y + x) == x + (y + z) -y + dec (dec x) == x + dec (dec y) -dec (dec x) + y == x + dec (dec y) -x + dec (dec 0) == dec (dec x) -dec (dec 0) + x == dec (dec x) - -class of 2 equivalent candidates: - - x ? y = x + x - - 0 ? x = 0 - x ? y = x + x - - -class of 4 equivalent candidates: - - x ? y = x + y - - x ? 0 = x - x ? y = x + y - - 0 ? x = x - x ? y = x + y - - 0 ? x = x - x ? 0 = x - x ? y = x + y - - -class of 2 equivalent candidates: - - x ? y = y + y - - x ? 0 = 0 - x ? y = y + y - - -class of 2 equivalent candidates: - - x ? y = x + dec y - - x ? y = y + dec x - - -class of 2 equivalent candidates: - - x ? 0 = x - x ? y = x + x - - 0 ? x = 0 - x ? 0 = x - x ? y = x + x - - -class of 2 equivalent candidates: - - x ? 0 = 0 - x ? y = x + x - - 0 ? x = 0 - x ? 0 = 0 - x ? y = x + x - - -class of 2 equivalent candidates: - - x ? 0 = 0 - x ? y = x + y - - 0 ? x = x - x ? 0 = 0 - x ? y = x + y - - -class of 2 equivalent candidates: - - 0 ? x = x - x ? y = y + y - - 0 ? x = x - x ? 0 = 0 - x ? y = y + y - - -class of 2 equivalent candidates: - - 0 ? x = 0 - x ? y = x + y - - 0 ? x = 0 - x ? 0 = x - x ? y = x + y - - -class of 2 equivalent candidates: - - 0 ? x = 0 - x ? y = y + y - - 0 ? x = 0 - x ? 0 = 0 - x ? y = y + y - - -class of 2 equivalent candidates: - - x ? y = x + (x + y) - - x ? y = y + (x + x) - - -class of 2 equivalent candidates: - - x ? y = x + (y + y) - - x ? y = y + (x + y) - - -class of 2 equivalent candidates: - - x ? y = x + dec (dec x) - - x ? y = dec x + dec x - - -class of 3 equivalent candidates: - - x ? y = x + dec (dec y) - - x ? y = y + dec (dec x) - - x ? y = dec x + dec y - - -class of 2 equivalent candidates: - - x ? y = y + dec (dec y) - - x ? y = dec y + dec y - - -class of 2 equivalent candidates: - - x ? 0 = x - x ? y = x + dec y - - x ? 0 = x - x ? y = y + dec x - - -class of 2 equivalent candidates: - - x ? 0 = 0 - x ? y = x + dec y - - x ? 0 = 0 - x ? y = y + dec x - - -class of 2 equivalent candidates: - - 0 ? x = x - x ? y = x + dec y - - 0 ? x = x - x ? y = y + dec x - - -class of 2 equivalent candidates: - - 0 ? x = 0 - x ? y = x + dec y - - 0 ? x = 0 - x ? y = y + dec x - - - -Redundant candidates for: goo :: [Int] -> [Int] - pruning with 4/4 rules - [2,1,2,2,4] candidates - 9/11 unique candidates - 2/11 redundant candidates - -rules: -xs ++ [] == xs -[] ++ xs == xs -(xs ++ ys) ++ zs == xs ++ (ys ++ zs) -(x:xs) ++ ys == x:(xs ++ ys) - -class of 2 equivalent candidates: - - goo xs = xs - - goo [] = [] - goo (x:xs) = x:goo xs - - -class of 2 equivalent candidates: - - goo xs = [] - - goo [] = [] - goo (x:xs) = goo xs - - - -Redundant candidates for: ?? :: [Int] -> [Int] -> [Int] - pruning with 4/4 rules - [3,7,15,57,134] candidates - 160/216 unique candidates - 56/216 redundant candidates - -rules: -xs ++ [] == xs -[] ++ xs == xs -(xs ++ ys) ++ zs == xs ++ (ys ++ zs) -(x:xs) ++ ys == x:(xs ++ ys) - -class of 2 equivalent candidates: - - xs ?? ys = xs - - xs ?? [] = xs - xs ?? (x:ys) = xs ?? ys - - -class of 2 equivalent candidates: - - xs ?? ys = ys - - [] ?? xs = xs - (x:xs) ?? ys = xs ?? ys - - -class of 22 equivalent candidates: - - xs ?? ys = [] - - xs ?? [] = [] - xs ?? (x:ys) = xs ?? ys - - xs ?? [] = [] - xs ?? (x:ys) = ys ?? xs - - xs ?? [] = [] - xs ?? (x:ys) = ys ?? ys - - xs ?? [] = [] - xs ?? (x:ys) = [] ?? xs - - xs ?? [] = [] - xs ?? (x:ys) = [] ?? ys - - [] ?? xs = [] - (x:xs) ?? ys = xs ?? xs - - [] ?? xs = [] - (x:xs) ?? ys = xs ?? ys - - [] ?? xs = [] - (x:xs) ?? ys = xs ?? [] - - [] ?? xs = [] - (x:xs) ?? ys = ys ?? xs - - [] ?? xs = [] - (x:xs) ?? ys = ys ?? [] - - [] ?? xs = [] - (x:xs) ?? [] = xs ?? xs - (x:xs) ?? (y:ys) = [] - - [] ?? xs = [] - (x:xs) ?? [] = xs ?? [] - (x:xs) ?? (y:ys) = [] - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = xs ?? xs - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = xs ?? ys - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = xs ?? [] - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = ys ?? xs - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = ys ?? ys - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = ys ?? [] - - [] ?? [] = [] - [] ?? (x:xs) = xs ?? xs - (x:xs) ?? ys = [] - - [] ?? [] = [] - [] ?? (x:xs) = xs ?? [] - (x:xs) ?? ys = [] - - [] ?? [] = [] - [] ?? (x:xs) = [] ?? xs - (x:xs) ?? ys = [] - - -class of 5 equivalent candidates: - - xs ?? [] = xs - xs ?? (x:ys) = [] - - xs ?? [] = xs - xs ?? (x:ys) = ys ?? ys - - xs ?? [] = xs - xs ?? (x:ys) = [] ?? xs - - xs ?? [] = xs - xs ?? (x:ys) = [] ?? ys - - [] ?? xs = [] - (x:xs) ?? [] = x:xs - (x:xs) ?? (y:ys) = [] - - -class of 2 equivalent candidates: - - xs ?? [] = [] - xs ?? (x:ys) = xs - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = x:xs - - -class of 3 equivalent candidates: - - xs ?? [] = [] - xs ?? (x:ys) = ys - - [] ?? [] = [] - [] ?? (x:xs) = xs - (x:xs) ?? ys = xs ?? ys - - [] ?? [] = [] - [] ?? (x:xs) = xs - (x:xs) ?? ys = [] ?? ys - - -class of 10 equivalent candidates: - - [] ?? xs = xs - (x:xs) ?? ys = [] - - [] ?? xs = xs - (x:xs) ?? ys = xs ?? xs - - [] ?? xs = xs - (x:xs) ?? ys = xs ?? [] - - [] ?? xs = xs - (x:xs) ?? ys = ys ?? [] - - [] ?? xs = xs - (x:xs) ?? [] = xs ?? xs - (x:xs) ?? (y:ys) = [] - - [] ?? xs = xs - (x:xs) ?? [] = xs ?? [] - (x:xs) ?? (y:ys) = [] - - [] ?? xs = xs - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = xs ?? xs - - [] ?? xs = xs - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = xs ?? [] - - [] ?? xs = xs - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = ys ?? ys - - [] ?? xs = xs - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = ys ?? [] - - -class of 2 equivalent candidates: - - [] ?? xs = [] - (x:xs) ?? ys = xs - - [] ?? [] = [] - [] ?? (x:xs) = [] ?? xs - (x:xs) ?? ys = xs - - -class of 3 equivalent candidates: - - [] ?? xs = [] - (x:xs) ?? ys = ys - - [] ?? [] = [] - [] ?? (x:xs) = xs ?? [] - (x:xs) ?? ys = ys - - [] ?? [] = [] - [] ?? (x:xs) = [] ?? xs - (x:xs) ?? ys = ys - - -class of 3 equivalent candidates: - - [] ?? xs = xs - (x:xs) ?? [] = xs - (x:xs) ?? (y:ys) = [] - - [] ?? xs = xs - (x:xs) ?? [] = xs - (x:xs) ?? (y:ys) = xs ?? xs - - [] ?? xs = xs - (x:xs) ?? [] = xs - (x:xs) ?? (y:ys) = ys ?? ys - - -class of 2 equivalent candidates: - - [] ?? xs = xs - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = xs - - [] ?? xs = xs - (x:xs) ?? [] = xs ?? [] - (x:xs) ?? (y:ys) = xs - - -class of 2 equivalent candidates: - - [] ?? xs = xs - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = ys - - [] ?? xs = xs - (x:xs) ?? [] = xs ?? [] - (x:xs) ?? (y:ys) = ys - - -class of 3 equivalent candidates: - - [] ?? xs = [] - (x:xs) ?? [] = xs - (x:xs) ?? (y:ys) = [] - - [] ?? xs = [] - (x:xs) ?? [] = xs - (x:xs) ?? (y:ys) = xs ?? xs - - [] ?? xs = [] - (x:xs) ?? [] = xs - (x:xs) ?? (y:ys) = ys ?? ys - - -class of 2 equivalent candidates: - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = xs - - [] ?? xs = [] - (x:xs) ?? [] = xs ?? [] - (x:xs) ?? (y:ys) = xs - - -class of 2 equivalent candidates: - - [] ?? xs = [] - (x:xs) ?? [] = [] - (x:xs) ?? (y:ys) = ys - - [] ?? xs = [] - (x:xs) ?? [] = xs ?? [] - (x:xs) ?? (y:ys) = ys - - -class of 2 equivalent candidates: - - [] ?? [] = [] - [] ?? (x:xs) = xs - (x:xs) ?? ys = ys - - [] ?? [] = [] - [] ?? (x:xs) = xs ?? xs - (x:xs) ?? ys = ys - - -class of 4 equivalent candidates: - - [] ?? [] = [] - [] ?? (x:xs) = xs - (x:xs) ?? ys = [] - - [] ?? [] = [] - [] ?? (x:xs) = xs - (x:xs) ?? ys = xs ?? xs - - [] ?? [] = [] - [] ?? (x:xs) = xs - (x:xs) ?? ys = xs ?? [] - - [] ?? [] = [] - [] ?? (x:xs) = xs - (x:xs) ?? ys = ys ?? [] - - -class of 2 equivalent candidates: - - [] ?? xs = xs - (x:xs) ?? ys = ys ?? xs - - [] ?? xs = xs - (x:xs) ?? [] = xs - (x:xs) ?? (y:ys) = xs ?? ys - - -class of 2 equivalent candidates: - - [] ?? [] = [] - [] ?? (x:xs) = xs ?? xs - (x:xs) ?? ys = xs - - [] ?? [] = [] - [] ?? (x:xs) = xs ?? [] - (x:xs) ?? ys = xs - - - -Redundant candidates for: ton :: Bool -> Bool - pruning with 39/49 rules - [3,2,0,0,0] candidates - 4/5 unique candidates - 1/5 redundant candidates - -rules: -not False == True -not True == False -p && p == p -p || p == p -not (not p) == p -p && False == False -p && True == p -False && p == False -True && p == p -p || False == p -p || True == True -False || p == p -True || p == True -not (p && q) == not p || not q -not (p && q) == not q || not p -not (p || q) == not p && not q -not (p || q) == not q && not p -p && not p == False -not p && p == False -p || not p == True -not p || p == True -(p && q) && r == p && (q && r) -(p && q) && r == q && (p && r) -(p || q) || r == p || (q || r) -(p || q) || r == q || (p || r) -p && (p && q) == p && q -p && (q && p) == p && q -p && (q && p) == q && p -p || (p || q) == p || q -p || (q || p) == p || q -p || (q || p) == q || p -p && (p || q) == p -p && (q || p) == p -(p || q) && p == p -(p || q) && q == q -p || p && q == p -p || q && p == p -p && q || p == p -p && q || q == q -equations: -q && p == p && q -q || p == p || q -q && (p && r) == p && (q && r) -r && (p && q) == p && (q && r) -r && (q && p) == p && (q && r) -q || (p || r) == p || (q || r) -r || (p || q) == p || (q || r) -r || (q || p) == p || (q || r) -(r || q) && p == p && (q || r) -r && q || p == p || q && r - -class of 2 equivalent candidates: - - ton p = not p - - ton False = True - ton True = False - - - -Redundant candidates for: &| :: Bool -> Bool -> Bool - pruning with 39/49 rules - [4,12,20,6,2] candidates - 16/44 unique candidates - 28/44 redundant candidates - -rules: -not False == True -not True == False -p && p == p -p || p == p -not (not p) == p -p && False == False -p && True == p -False && p == False -True && p == p -p || False == p -p || True == True -False || p == p -True || p == True -not (p && q) == not p || not q -not (p && q) == not q || not p -not (p || q) == not p && not q -not (p || q) == not q && not p -p && not p == False -not p && p == False -p || not p == True -not p || p == True -(p && q) && r == p && (q && r) -(p && q) && r == q && (p && r) -(p || q) || r == p || (q || r) -(p || q) || r == q || (p || r) -p && (p && q) == p && q -p && (q && p) == p && q -p && (q && p) == q && p -p || (p || q) == p || q -p || (q || p) == p || q -p || (q || p) == q || p -p && (p || q) == p -p && (q || p) == p -(p || q) && p == p -(p || q) && q == q -p || p && q == p -p || q && p == p -p && q || p == p -p && q || q == q -equations: -q && p == p && q -q || p == p || q -q && (p && r) == p && (q && r) -r && (p && q) == p && (q && r) -r && (q && p) == p && (q && r) -q || (p || r) == p || (q || r) -r || (p || q) == p || (q || r) -r || (q || p) == p || (q || r) -(r || q) && p == p && (q || r) -r && q || p == p || q && r - -class of 2 equivalent candidates: - - p &| q = not p - - False &| p = True - True &| p = False - - -class of 4 equivalent candidates: - - p &| q = not q - - p &| False = True - p &| True = False - - False &| p = not p - True &| False = True - True &| True = False - - False &| False = True - False &| True = False - True &| p = not p - - -class of 4 equivalent candidates: - - p &| False = p - p &| True = False - - False &| p = False - True &| p = not p - - False &| p = False - True &| False = True - True &| True = False - - p &| q = p && not q - - -class of 3 equivalent candidates: - - p &| False = p - p &| True = True - - False &| p = p - True &| p = True - - p &| q = p || q - - -class of 3 equivalent candidates: - - p &| False = False - p &| True = p - - False &| p = False - True &| p = p - - p &| q = p && q - - -class of 4 equivalent candidates: - - p &| False = True - p &| True = p - - False &| p = not p - True &| p = True - - False &| False = True - False &| True = False - True &| p = True - - p &| q = p || not q - - -class of 3 equivalent candidates: - - False &| p = p - True &| p = False - - p &| False = False - p &| True = not p - - p &| q = q && not p - - -class of 3 equivalent candidates: - - False &| p = True - True &| p = p - - p &| False = not p - p &| True = True - - p &| q = q || not p - - -class of 3 equivalent candidates: - - p &| False = p - p &| True = not p - - False &| p = p - True &| p = not p - - False &| p = p - True &| False = True - True &| True = False - - -class of 4 equivalent candidates: - - p &| False = True - p &| True = not p - - False &| p = True - True &| p = not p - - False &| p = True - True &| False = True - True &| True = False - - p &| q = not p || not q - - -class of 3 equivalent candidates: - - p &| False = not p - p &| True = p - - False &| p = not p - True &| p = p - - False &| False = True - False &| True = False - True &| p = p - - -class of 4 equivalent candidates: - - p &| False = not p - p &| True = False - - False &| p = not p - True &| p = False - - False &| False = True - False &| True = False - True &| p = False - - p &| q = not p && not q - - - diff --git a/bench/redundants.txt b/bench/redundants.txt new file mode 100644 --- /dev/null +++ b/bench/redundants.txt @@ -0,0 +1,1990 @@ +Redundant candidates for: foo :: Int -> Int + pruning with 15/35 rules + [3,3,8,9,21,27] candidates + 63/71 unique candidates + 8/71 redundant candidates + +rules: +x * y == x + y +x * y == y + x +x - x == 0 +x + 0 == x +0 + x == x +x - 0 == x +(x + y) + z == x + (y + z) +(x + y) + z == y + (x + z) +x - (y - z) == z + (x - y) +(x - y) - z == x - (y + z) +(x - y) - z == x - (z + y) +(x + y) - z == x + (y - z) +(x + y) - z == y + (x - z) +x + (y - x) == y +(x - y) + y == x +equations: +y + x == x + y +y + (x + z) == x + (y + z) +z + (x + y) == x + (y + z) +z + (y + x) == x + (y + z) +y + (x - z) == x + (y - z) +(x - z) + y == x + (y - z) +(z - y) + x == (x - y) + z +y - (x + y) == 0 - x +y - (y + x) == 0 - x +z - (y + z) == x - (x + y) +z - (y + z) == x - (y + x) +z - (z + y) == x - (x + y) +z - (z + y) == x - (y + x) +x + (0 - y) == x - y +(0 - y) + x == x - y +x - (x + 1) == 0 - 1 +x - (1 + x) == 0 - 1 +y - (y + 1) == x - (x + 1) +y - (y + 1) == x - (1 + x) +y - (1 + y) == x - (1 + x) + +class of 3 equivalent candidates: + + foo x = 0 - x + + foo x = x - (x + x) + + foo x = 1 - (x + 1) + + +class of 2 equivalent candidates: + + foo x = 1 - x + + foo x = 1 + (0 - x) + + +class of 2 equivalent candidates: + + foo 0 = 0 + foo x = 1 - x + + foo 0 = 0 + foo x = 1 + (0 - x) + + +class of 3 equivalent candidates: + + foo 0 = 1 + foo x = 0 - x + + foo 0 = 1 + foo x = x - (x + x) + + foo 0 = 1 + foo x = 1 - (x + 1) + + +class of 2 equivalent candidates: + + foo x = x + (x + 1) + + foo x = 1 + (x + x) + + +class of 2 equivalent candidates: + + foo 0 = 0 + foo x = x + (x + 1) + + foo 0 = 0 + foo x = 1 + (x + x) + + + +Redundant candidates for: ? :: Int -> Int -> Int + pruning with 10/23 rules + [3,8,22,50,116,302] candidates + 410/501 unique candidates + 91/501 redundant candidates + +rules: +x * y == x + y +x * y == y + x +x + 0 == x +0 + x == x +dec (x + y) == x + dec y +dec (x + y) == y + dec x +dec (x + y) == dec x + y +dec (x + y) == dec y + x +(x + y) + z == x + (y + z) +(x + y) + z == y + (x + z) +equations: +y + x == x + y +y + dec x == x + dec y +dec x + y == x + dec y +dec y + x == dec x + y +x + dec 0 == dec x +dec 0 + x == dec x +y + (x + z) == x + (y + z) +z + (x + y) == x + (y + z) +z + (y + x) == x + (y + z) +y + dec (dec x) == x + dec (dec y) +dec (dec x) + y == x + dec (dec y) +x + dec (dec 0) == dec (dec x) +dec (dec 0) + x == dec (dec x) + +class of 3 equivalent candidates: + + x ? y = x + + x ? 0 = x + x ? y = x ? dec y + + 0 ? x = 0 + x ? 0 = x + x ? y = x ? dec y + + +class of 3 equivalent candidates: + + x ? y = y + + 0 ? x = x + x ? y = dec x ? y + + 0 ? x = x + x ? 0 = 0 + x ? y = dec x ? y + + +class of 2 equivalent candidates: + + x ? y = dec x + + x ? 0 = dec x + x ? y = x ? dec y + + +class of 2 equivalent candidates: + + x ? y = dec y + + 0 ? x = dec x + x ? y = dec x ? y + + +class of 2 equivalent candidates: + + x ? 0 = x + x ? y = y + + 0 ? x = x + x ? 0 = x + x ? y = dec x ? y + + +class of 6 equivalent candidates: + + x ? 0 = x + x ? y = 0 + + x ? 0 = x + x ? y = 0 ? dec y + + x ? 0 = x + x ? y = dec y ? dec y + + 0 ? x = 0 + x ? 0 = x + x ? y = dec x ? x + + 0 ? x = 0 + x ? 0 = x + x ? y = dec x ? y + + 0 ? x = 0 + x ? 0 = x + x ? y = dec y ? x + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? y = x + + 0 ? x = x + x ? 0 = x + x ? y = x ? dec y + + +class of 6 equivalent candidates: + + 0 ? x = x + x ? y = 0 + + 0 ? x = x + x ? y = dec x ? 0 + + 0 ? x = x + x ? y = dec x ? dec x + + 0 ? x = x + x ? 0 = 0 + x ? y = x ? dec y + + 0 ? x = x + x ? 0 = 0 + x ? y = y ? dec x + + 0 ? x = x + x ? 0 = 0 + x ? y = y ? dec y + + +class of 2 equivalent candidates: + + x ? 0 = dec x + x ? y = 0 + + x ? 0 = dec x + x ? y = y ? dec y + + +class of 2 equivalent candidates: + + 0 ? x = dec x + x ? y = 0 + + 0 ? x = dec x + x ? y = dec x ? x + + +class of 4 equivalent candidates: + + x ? y = x + dec y + + x ? y = y + dec x + + x ? 0 = dec x + x ? y = x + dec y + + 0 ? x = dec x + x ? y = y + dec x + + +class of 3 equivalent candidates: + + x ? 0 = x + x ? y = dec x ? y + + x ? 0 = x + x ? y = dec (dec x) ? y + + x ? 0 = x + x ? y = dec (dec x ? y) + + +class of 3 equivalent candidates: + + 0 ? x = x + x ? y = x ? dec y + + 0 ? x = x + x ? y = x ? dec (dec y) + + 0 ? x = x + x ? y = dec (x ? dec y) + + +class of 2 equivalent candidates: + + x ? y = x + (x + y) + + x ? y = y + (x + x) + + +class of 2 equivalent candidates: + + x ? y = x + (y + y) + + x ? y = y + (x + y) + + +class of 2 equivalent candidates: + + x ? y = x + dec (dec x) + + x ? y = dec x + dec x + + +class of 3 equivalent candidates: + + x ? y = x + dec (dec y) + + x ? y = y + dec (dec x) + + x ? y = dec x + dec y + + +class of 2 equivalent candidates: + + x ? y = y + dec (dec y) + + x ? y = dec y + dec y + + +class of 2 equivalent candidates: + + x ? 0 = x + x ? y = x + dec y + + x ? 0 = x + x ? y = y + dec x + + +class of 2 equivalent candidates: + + x ? 0 = 0 + x ? y = x + dec y + + x ? 0 = 0 + x ? y = y + dec x + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? y = x + dec y + + 0 ? x = x + x ? y = y + dec x + + +class of 2 equivalent candidates: + + 0 ? x = 0 + x ? y = x + dec y + + 0 ? x = 0 + x ? y = y + dec x + + +class of 2 equivalent candidates: + + x ? 0 = x + x ? y = dec x ? dec y + + x ? 0 = x + x ? y = dec (x ? dec y) + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? y = dec x ? dec y + + 0 ? x = x + x ? y = dec (dec x ? y) + + +class of 3 equivalent candidates: + + x ? 0 = 0 + x ? y = dec (x ? dec y) + + x ? 0 = 0 + x ? y = dec (y ? dec y) + + x ? 0 = 0 + x ? y = dec (0 ? dec y) + + +class of 3 equivalent candidates: + + 0 ? x = 0 + x ? y = dec (dec x ? x) + + 0 ? x = 0 + x ? y = dec (dec x ? y) + + 0 ? x = 0 + x ? y = dec (dec x ? 0) + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? 0 = x + x ? y = y ? dec y + + 0 ? x = x + x ? 0 = x + x ? y = dec x ? x + + +class of 2 equivalent candidates: + + x ? y = x + dec (dec (dec x)) + + x ? y = dec x + dec (dec x) + + +class of 4 equivalent candidates: + + x ? y = x + dec (dec (dec y)) + + x ? y = y + dec (dec (dec x)) + + x ? y = dec x + dec (dec y) + + x ? y = dec y + dec (dec x) + + +class of 2 equivalent candidates: + + x ? y = x + (x + dec x) + + x ? y = dec x + (x + x) + + +class of 5 equivalent candidates: + + x ? y = x + (x + dec y) + + x ? y = x + (y + dec x) + + x ? y = y + (x + dec x) + + x ? y = dec x + (x + y) + + x ? y = dec y + (x + x) + + +class of 5 equivalent candidates: + + x ? y = x + (y + dec y) + + x ? y = y + (x + dec y) + + x ? y = y + (y + dec x) + + x ? y = dec x + (y + y) + + x ? y = dec y + (x + y) + + +class of 2 equivalent candidates: + + x ? y = y + dec (dec (dec y)) + + x ? y = dec y + dec (dec y) + + +class of 2 equivalent candidates: + + x ? y = y + (y + dec y) + + x ? y = dec y + (y + y) + + +class of 2 equivalent candidates: + + x ? 0 = x + x ? y = x + (x + y) + + x ? 0 = x + x ? y = y + (x + x) + + +class of 2 equivalent candidates: + + x ? 0 = x + x ? y = x + dec (dec x) + + x ? 0 = x + x ? y = dec x + dec x + + +class of 3 equivalent candidates: + + x ? 0 = x + x ? y = x + dec (dec y) + + x ? 0 = x + x ? y = y + dec (dec x) + + x ? 0 = x + x ? y = dec x + dec y + + +class of 2 equivalent candidates: + + x ? 0 = x + x ? y = y + dec (dec y) + + x ? 0 = x + x ? y = dec y + dec y + + +class of 2 equivalent candidates: + + x ? 0 = 0 + x ? y = x + (x + y) + + x ? 0 = 0 + x ? y = y + (x + x) + + +class of 2 equivalent candidates: + + x ? 0 = 0 + x ? y = x + (y + y) + + x ? 0 = 0 + x ? y = y + (x + y) + + +class of 2 equivalent candidates: + + x ? 0 = 0 + x ? y = x + dec (dec x) + + x ? 0 = 0 + x ? y = dec x + dec x + + +class of 3 equivalent candidates: + + x ? 0 = 0 + x ? y = x + dec (dec y) + + x ? 0 = 0 + x ? y = y + dec (dec x) + + x ? 0 = 0 + x ? y = dec x + dec y + + +class of 2 equivalent candidates: + + x ? 0 = 0 + x ? y = y + dec (dec y) + + x ? 0 = 0 + x ? y = dec y + dec y + + +class of 2 equivalent candidates: + + x ? 0 = x + dec (dec x) + x ? y = x + + x ? 0 = dec x + dec x + x ? y = x + + +class of 2 equivalent candidates: + + x ? 0 = x + dec (dec x) + x ? y = y + + x ? 0 = dec x + dec x + x ? y = y + + +class of 2 equivalent candidates: + + x ? 0 = x + dec (dec x) + x ? y = 0 + + x ? 0 = dec x + dec x + x ? y = 0 + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? y = x + (y + y) + + 0 ? x = x + x ? y = y + (x + y) + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? y = x + dec (dec x) + + 0 ? x = x + x ? y = dec x + dec x + + +class of 3 equivalent candidates: + + 0 ? x = x + x ? y = x + dec (dec y) + + 0 ? x = x + x ? y = y + dec (dec x) + + 0 ? x = x + x ? y = dec x + dec y + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? y = y + dec (dec y) + + 0 ? x = x + x ? y = dec y + dec y + + +class of 2 equivalent candidates: + + 0 ? x = 0 + x ? y = x + (x + y) + + 0 ? x = 0 + x ? y = y + (x + x) + + +class of 2 equivalent candidates: + + 0 ? x = 0 + x ? y = x + (y + y) + + 0 ? x = 0 + x ? y = y + (x + y) + + +class of 2 equivalent candidates: + + 0 ? x = 0 + x ? y = x + dec (dec x) + + 0 ? x = 0 + x ? y = dec x + dec x + + +class of 3 equivalent candidates: + + 0 ? x = 0 + x ? y = x + dec (dec y) + + 0 ? x = 0 + x ? y = y + dec (dec x) + + 0 ? x = 0 + x ? y = dec x + dec y + + +class of 2 equivalent candidates: + + 0 ? x = 0 + x ? y = y + dec (dec y) + + 0 ? x = 0 + x ? y = dec y + dec y + + +class of 2 equivalent candidates: + + 0 ? x = x + dec (dec x) + x ? y = x + + 0 ? x = dec x + dec x + x ? y = x + + +class of 2 equivalent candidates: + + 0 ? x = x + dec (dec x) + x ? y = y + + 0 ? x = dec x + dec x + x ? y = y + + +class of 2 equivalent candidates: + + 0 ? x = x + dec (dec x) + x ? y = 0 + + 0 ? x = dec x + dec x + x ? y = 0 + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? 0 = x + x ? y = x + dec y + + 0 ? x = x + x ? 0 = x + x ? y = y + dec x + + +class of 2 equivalent candidates: + + 0 ? x = x + x ? 0 = 0 + x ? y = x + dec y + + 0 ? x = x + x ? 0 = 0 + x ? y = y + dec x + + +class of 2 equivalent candidates: + + 0 ? x = 0 + x ? 0 = x + x ? y = x + dec y + + 0 ? x = 0 + x ? 0 = x + x ? y = y + dec x + + +class of 2 equivalent candidates: + + 0 ? x = 0 + x ? 0 = 0 + x ? y = x + dec y + + 0 ? x = 0 + x ? 0 = 0 + x ? y = y + dec x + + + +Redundant candidates for: goo :: [Int] -> [Int] + pruning with 4/4 rules + [2,1,1,2,4,7] candidates + 15/17 unique candidates + 2/17 redundant candidates + +rules: +xs ++ [] == xs +[] ++ xs == xs +(xs ++ ys) ++ zs == xs ++ (ys ++ zs) +(x:xs) ++ ys == x:(xs ++ ys) + +class of 2 equivalent candidates: + + goo xs = xs + + goo [] = [] + goo (x:xs) = x:goo xs + + +class of 2 equivalent candidates: + + goo xs = [] + + goo [] = [] + goo (x:xs) = goo xs ++ goo xs + + + +Redundant candidates for: ?? :: [Int] -> [Int] -> [Int] + pruning with 4/4 rules + [3,8,15,43,122,264] candidates + 325/455 unique candidates + 130/455 redundant candidates + +rules: +xs ++ [] == xs +[] ++ xs == xs +(xs ++ ys) ++ zs == xs ++ (ys ++ zs) +(x:xs) ++ ys == x:(xs ++ ys) + +class of 9 equivalent candidates: + + xs ?? ys = xs + + xs ?? [] = xs + xs ?? (x:ys) = xs ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = xs ++ [] ?? xs + + xs ?? [] = xs + xs ?? (x:ys) = xs ++ [] ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = [] ?? xs ++ xs + + xs ?? [] = xs + xs ?? (x:ys) = [] ?? ys ++ xs + + [] ?? xs = [] + (x:xs) ?? ys = x:xs ?? xs + + [] ?? xs = [] + (x:xs) ?? ys = x:xs ?? ys + + [] ?? xs = [] + (x:xs) ?? ys = x:xs ?? [] + + +class of 9 equivalent candidates: + + xs ?? ys = ys + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? ys + + xs ?? [] = [] + xs ?? (x:ys) = x:xs ?? ys + + xs ?? [] = [] + xs ?? (x:ys) = x:ys ?? ys + + xs ?? [] = [] + xs ?? (x:ys) = x:[] ?? ys + + [] ?? xs = xs + (x:xs) ?? ys = ys ++ xs ?? [] + + [] ?? xs = xs + (x:xs) ?? ys = ys ++ ys ?? [] + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? [] ++ ys + + [] ?? xs = xs + (x:xs) ?? ys = ys ?? [] ++ ys + + +class of 6 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = [] + + xs ?? [] = xs + xs ?? (x:ys) = ys ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = [] ?? xs + + xs ?? [] = xs + xs ?? (x:ys) = [] ?? ys + + [] ?? xs = [] + (x:xs) ?? [] = x:xs + (x:xs) ?? (y:ys) = [] + + xs ?? [] = xs + xs ?? (x:ys) = (ys ++ ys) ?? ys + + +class of 6 equivalent candidates: + + xs ?? [] = [] + xs ?? (x:ys) = xs + + [] ?? xs = [] + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = x:xs + + xs ?? [] = [] + xs ?? (x:ys) = xs ++ [] ?? xs + + xs ?? [] = [] + xs ?? (x:ys) = xs ++ [] ?? ys + + xs ?? [] = [] + xs ?? (x:ys) = [] ?? xs ++ xs + + xs ?? [] = [] + xs ?? (x:ys) = [] ?? ys ++ xs + + +class of 3 equivalent candidates: + + xs ?? [] = [] + xs ?? (x:ys) = ys + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? ys = xs ?? ys + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? ys = [] ?? ys + + +class of 11 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = [] + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? xs + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? [] + + [] ?? xs = xs + (x:xs) ?? ys = ys ?? [] + + [] ?? xs = xs + (x:xs) ?? [] = xs ?? xs + (x:xs) ?? (y:ys) = [] + + [] ?? xs = xs + (x:xs) ?? [] = xs ?? [] + (x:xs) ?? (y:ys) = [] + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = xs ?? xs + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = xs ?? [] + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = ys ?? ys + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = ys ?? [] + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? (xs ++ xs) + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? ys = xs + + [] ?? [] = [] + [] ?? (x:xs) = [] ?? xs + (x:xs) ?? ys = xs + + +class of 7 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? ys = ys + + [] ?? [] = [] + [] ?? (x:xs) = xs ?? [] + (x:xs) ?? ys = ys + + [] ?? [] = [] + [] ?? (x:xs) = [] ?? xs + (x:xs) ?? ys = ys + + [] ?? xs = [] + (x:xs) ?? ys = ys ++ xs ?? [] + + [] ?? xs = [] + (x:xs) ?? ys = ys ++ ys ?? [] + + [] ?? xs = [] + (x:xs) ?? ys = xs ?? [] ++ ys + + [] ?? xs = [] + (x:xs) ?? ys = ys ?? [] ++ ys + + +class of 2 equivalent candidates: + + xs ?? ys = xs ++ xs + + xs ?? [] = xs ++ xs + xs ?? (x:ys) = xs ?? ys + + +class of 4 equivalent candidates: + + xs ?? ys = xs ++ ys + + [] ?? xs = xs + (x:xs) ?? ys = x:xs ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = xs ++ (x:ys) + + [] ?? xs = xs + (x:xs) ?? ys = x:(xs ++ ys) + + +class of 4 equivalent candidates: + + xs ?? ys = ys ++ xs + + xs ?? [] = xs + xs ?? (x:ys) = x:xs ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = x:(ys ++ xs) + + [] ?? xs = xs + (x:xs) ?? ys = ys ++ (x:xs) + + +class of 2 equivalent candidates: + + xs ?? ys = ys ++ ys + + [] ?? xs = xs ++ xs + (x:xs) ?? ys = xs ?? ys + + +class of 3 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = [] + + [] ?? xs = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? xs + + [] ?? xs = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ?? ys + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = xs + + [] ?? xs = xs + (x:xs) ?? [] = xs ?? [] + (x:xs) ?? (y:ys) = xs + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = ys + + [] ?? xs = xs + (x:xs) ?? [] = xs ?? [] + (x:xs) ?? (y:ys) = ys + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys + + [] ?? [] = [] + [] ?? (x:xs) = [] ?? xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys + + +class of 5 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = [] + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? xs + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ?? ys + + [] ?? [] = [] + [] ?? (x:xs) = xs ?? xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = [] + + [] ?? [] = [] + [] ?? (x:xs) = [] ?? xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = [] + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = xs + + [] ?? xs = [] + (x:xs) ?? [] = xs ?? [] + (x:xs) ?? (y:ys) = xs + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = ys + + [] ?? xs = [] + (x:xs) ?? [] = xs ?? [] + (x:xs) ?? (y:ys) = ys + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? ys = ys + + [] ?? [] = [] + [] ?? (x:xs) = xs ?? xs + (x:xs) ?? ys = ys + + +class of 6 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? ys = [] + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? ys = xs ?? xs + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? ys = xs ?? [] + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? ys = ys ?? [] + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs ?? xs + (x:xs) ?? (y:ys) = [] + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs ?? [] + (x:xs) ?? (y:ys) = [] + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = ys ?? xs + + [] ?? xs = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? ys + + +class of 3 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = x:ys + + xs ?? [] = xs + xs ?? (x:ys) = x:ys ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = x:[] ?? ys + + +class of 4 equivalent candidates: + + xs ?? [] = xs ++ xs + xs ?? (x:ys) = [] + + xs ?? [] = xs ++ xs + xs ?? (x:ys) = ys ?? ys + + xs ?? [] = xs ++ xs + xs ?? (x:ys) = [] ?? xs + + xs ?? [] = xs ++ xs + xs ?? (x:ys) = [] ?? ys + + +class of 3 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = x:xs + + [] ?? xs = xs + (x:xs) ?? ys = x:xs ?? xs + + [] ?? xs = xs + (x:xs) ?? ys = x:xs ?? [] + + +class of 4 equivalent candidates: + + [] ?? xs = xs ++ xs + (x:xs) ?? ys = [] + + [] ?? xs = xs ++ xs + (x:xs) ?? ys = xs ?? xs + + [] ?? xs = xs ++ xs + (x:xs) ?? ys = xs ?? [] + + [] ?? xs = xs ++ xs + (x:xs) ?? ys = ys ?? [] + + +class of 3 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = [] + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? xs + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ?? ys + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? ys + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? [] + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ?? xs + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ?? [] + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs ?? xs + (x:xs) ?? ys = xs + + [] ?? [] = [] + [] ?? (x:xs) = xs ?? [] + (x:xs) ?? ys = xs + + +class of 4 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ++ ys + + [] ?? xs = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ++ xs + + [] ?? xs = xs + (x:xs) ?? ys = xs ++ ys ?? [] + + [] ?? xs = xs + (x:xs) ?? ys = ys ?? [] ++ xs + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = xs ++ ys + + [] ?? xs = xs + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = ys ++ xs + + +class of 4 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ++ ys + + [] ?? xs = [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ++ xs + + [] ?? xs = [] + (x:xs) ?? ys = xs ++ ys ?? [] + + [] ?? xs = [] + (x:xs) ?? ys = ys ?? [] ++ xs + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = xs ++ ys + + [] ?? xs = [] + (x:xs) ?? [] = [] + (x:xs) ?? (y:ys) = ys ++ xs + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = (x:ys) ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = [x] ?? ys + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = (xs ++ ys) ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = xs ++ ys ?? ys + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = (ys ++ xs) ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = ys ?? ys ++ xs + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? (x:xs) + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? [x] + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? (xs ++ ys) + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? xs ++ ys + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? (ys ++ xs) + + [] ?? xs = xs + (x:xs) ?? ys = ys ++ xs ?? xs + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = x:ys ?? xs + + xs ?? [] = xs + xs ?? (x:ys) = x:(xs ++ ys) + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = xs ++ xs ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = xs ?? ys ++ xs + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = ys ++ ys ?? xs + + xs ?? [] = xs + xs ?? (x:ys) = ys ?? xs ++ ys + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = ys ++ ys ?? ys + + xs ?? [] = xs + xs ?? (x:ys) = ys ++ [] ?? ys + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = ys ++ [] ?? xs + + xs ?? [] = xs + xs ?? (x:ys) = [] ?? xs ++ ys + + +class of 2 equivalent candidates: + + xs ?? [] = xs + xs ?? (x:ys) = ys ?? ys ++ ys + + xs ?? [] = xs + xs ?? (x:ys) = [] ?? ys ++ ys + + +class of 2 equivalent candidates: + + xs ?? [] = [] + xs ?? (x:ys) = xs ++ xs ?? ys + + xs ?? [] = [] + xs ?? (x:ys) = xs ?? ys ++ xs + + +class of 3 equivalent candidates: + + xs ?? [] = [] + xs ?? (x:ys) = ys ++ xs ?? ys + + xs ?? [] = [] + xs ?? (x:ys) = ys ++ ys ?? ys + + xs ?? [] = [] + xs ?? (x:ys) = ys ++ [] ?? ys + + +class of 2 equivalent candidates: + + xs ?? [] = [] + xs ?? (x:ys) = ys ++ ys ?? xs + + xs ?? [] = [] + xs ?? (x:ys) = ys ?? xs ++ ys + + +class of 2 equivalent candidates: + + xs ?? [] = [] + xs ?? (x:ys) = ys ++ [] ?? xs + + xs ?? [] = [] + xs ?? (x:ys) = [] ?? xs ++ ys + + +class of 3 equivalent candidates: + + xs ?? [] = [] + xs ?? (x:ys) = xs ?? ys ++ ys + + xs ?? [] = [] + xs ?? (x:ys) = ys ?? ys ++ ys + + xs ?? [] = [] + xs ?? (x:ys) = [] ?? ys ++ ys + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = x:ys ?? xs + + [] ?? xs = xs + (x:xs) ?? ys = x:(ys ++ xs) + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = xs ++ xs ?? xs + + [] ?? xs = xs + (x:xs) ?? ys = xs ++ xs ?? [] + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = xs ++ ys ?? xs + + [] ?? xs = xs + (x:xs) ?? ys = ys ?? xs ++ xs + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = ys ++ xs ?? ys + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? ys ++ ys + + +class of 2 equivalent candidates: + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? xs ++ xs + + [] ?? xs = xs + (x:xs) ?? ys = xs ?? [] ++ xs + + +class of 3 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? ys = xs ++ xs ?? xs + + [] ?? xs = [] + (x:xs) ?? ys = xs ++ xs ?? ys + + [] ?? xs = [] + (x:xs) ?? ys = xs ++ xs ?? [] + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? ys = xs ++ ys ?? xs + + [] ?? xs = [] + (x:xs) ?? ys = ys ?? xs ++ xs + + +class of 2 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? ys = ys ++ xs ?? ys + + [] ?? xs = [] + (x:xs) ?? ys = xs ?? ys ++ ys + + +class of 3 equivalent candidates: + + [] ?? xs = [] + (x:xs) ?? ys = xs ?? xs ++ xs + + [] ?? xs = [] + (x:xs) ?? ys = xs ?? ys ++ xs + + [] ?? xs = [] + (x:xs) ?? ys = xs ?? [] ++ xs + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? ys + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ?? xs + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ?? [] + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = [] ?? xs + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ?? [] + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = [] ?? ys + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs ?? xs + (x:xs) ?? (y:ys) = xs + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = [] ?? xs + (x:xs) ?? (y:ys) = xs + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs ?? xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys + + [] ?? [] = [] + [] ?? (x:xs) = xs ?? [] + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys + + +class of 2 equivalent candidates: + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = xs ++ ys + + [] ?? [] = [] + [] ?? (x:xs) = xs + (x:xs) ?? [] = xs + (x:xs) ?? (y:ys) = ys ++ xs + + + +Redundant candidates for: ton :: Bool -> Bool + pruning with 39/49 rules + [3,2,0,0,0,0] candidates + 4/5 unique candidates + 1/5 redundant candidates + +rules: +not False == True +not True == False +p && p == p +p || p == p +not (not p) == p +p && False == False +p && True == p +False && p == False +True && p == p +p || False == p +p || True == True +False || p == p +True || p == True +not (p && q) == not p || not q +not (p && q) == not q || not p +not (p || q) == not p && not q +not (p || q) == not q && not p +p && not p == False +not p && p == False +p || not p == True +not p || p == True +(p && q) && r == p && (q && r) +(p && q) && r == q && (p && r) +(p || q) || r == p || (q || r) +(p || q) || r == q || (p || r) +p && (p && q) == p && q +p && (q && p) == p && q +p && (q && p) == q && p +p || (p || q) == p || q +p || (q || p) == p || q +p || (q || p) == q || p +p && (p || q) == p +p && (q || p) == p +(p || q) && p == p +(p || q) && q == q +p || p && q == p +p || q && p == p +p && q || p == p +p && q || q == q +equations: +q && p == p && q +q || p == p || q +q && (p && r) == p && (q && r) +r && (p && q) == p && (q && r) +r && (q && p) == p && (q && r) +q || (p || r) == p || (q || r) +r || (p || q) == p || (q || r) +r || (q || p) == p || (q || r) +(r || q) && p == p && (q || r) +r && q || p == p || q && r + +class of 2 equivalent candidates: + + ton p = not p + + ton False = True + ton True = False + + + +Redundant candidates for: &| :: Bool -> Bool -> Bool + pruning with 39/49 rules + [4,12,20,6,2,16] candidates + 16/60 unique candidates + 44/60 redundant candidates + +rules: +not False == True +not True == False +p && p == p +p || p == p +not (not p) == p +p && False == False +p && True == p +False && p == False +True && p == p +p || False == p +p || True == True +False || p == p +True || p == True +not (p && q) == not p || not q +not (p && q) == not q || not p +not (p || q) == not p && not q +not (p || q) == not q && not p +p && not p == False +not p && p == False +p || not p == True +not p || p == True +(p && q) && r == p && (q && r) +(p && q) && r == q && (p && r) +(p || q) || r == p || (q || r) +(p || q) || r == q || (p || r) +p && (p && q) == p && q +p && (q && p) == p && q +p && (q && p) == q && p +p || (p || q) == p || q +p || (q || p) == p || q +p || (q || p) == q || p +p && (p || q) == p +p && (q || p) == p +(p || q) && p == p +(p || q) && q == q +p || p && q == p +p || q && p == p +p && q || p == p +p && q || q == q +equations: +q && p == p && q +q || p == p || q +q && (p && r) == p && (q && r) +r && (p && q) == p && (q && r) +r && (q && p) == p && (q && r) +q || (p || r) == p || (q || r) +r || (p || q) == p || (q || r) +r || (q || p) == p || (q || r) +(r || q) && p == p && (q || r) +r && q || p == p || q && r + +class of 5 equivalent candidates: + + p &| q = False + + p &| q = p && (q && not p) + + p &| q = q && (p && not q) + + p &| q = not p && (p && q) + + p &| q = not q && (p && q) + + +class of 5 equivalent candidates: + + p &| q = True + + p &| q = p || (q || not p) + + p &| q = q || (p || not q) + + p &| q = not p || (p || q) + + p &| q = not q || (p || q) + + +class of 2 equivalent candidates: + + p &| q = not p + + False &| p = True + True &| p = False + + +class of 4 equivalent candidates: + + p &| q = not q + + p &| False = True + p &| True = False + + False &| p = not p + True &| False = True + True &| True = False + + False &| False = True + False &| True = False + True &| p = not p + + +class of 5 equivalent candidates: + + p &| False = p + p &| True = False + + False &| p = False + True &| p = not p + + False &| p = False + True &| False = True + True &| True = False + + p &| q = p && not q + + p &| q = not q && (p || q) + + +class of 5 equivalent candidates: + + p &| False = p + p &| True = True + + False &| p = p + True &| p = True + + p &| q = p || q + + p &| q = p || q && not p + + p &| q = q || p && not q + + +class of 5 equivalent candidates: + + p &| False = False + p &| True = p + + False &| p = False + True &| p = p + + p &| q = p && q + + p &| q = p && (q || not p) + + p &| q = q && (p || not q) + + +class of 5 equivalent candidates: + + p &| False = True + p &| True = p + + False &| p = not p + True &| p = True + + False &| False = True + False &| True = False + True &| p = True + + p &| q = p || not q + + p &| q = not q || p && q + + +class of 4 equivalent candidates: + + False &| p = p + True &| p = False + + p &| False = False + p &| True = not p + + p &| q = q && not p + + p &| q = not p && (p || q) + + +class of 4 equivalent candidates: + + False &| p = True + True &| p = p + + p &| False = not p + p &| True = True + + p &| q = q || not p + + p &| q = not p || p && q + + +class of 3 equivalent candidates: + + p &| False = p + p &| True = not p + + False &| p = p + True &| p = not p + + False &| p = p + True &| False = True + True &| True = False + + +class of 4 equivalent candidates: + + p &| False = True + p &| True = not p + + False &| p = True + True &| p = not p + + False &| p = True + True &| False = True + True &| True = False + + p &| q = not p || not q + + +class of 3 equivalent candidates: + + p &| False = not p + p &| True = p + + False &| p = not p + True &| p = p + + False &| False = True + False &| True = False + True &| p = p + + +class of 4 equivalent candidates: + + p &| False = not p + p &| True = False + + False &| p = not p + True &| p = False + + False &| False = True + False &| True = False + True &| p = False + + p &| q = not p && not q + + + diff --git a/bench/runtime/lapmatrud/bench/candidates.runtime b/bench/runtime/lapmatrud/bench/candidates.runtime --- a/bench/runtime/lapmatrud/bench/candidates.runtime +++ b/bench/runtime/lapmatrud/bench/candidates.runtime @@ -1,1 +1,1 @@ -8.0 +5.5 diff --git a/bench/runtime/lapmatrud/bench/gps.runtime b/bench/runtime/lapmatrud/bench/gps.runtime --- a/bench/runtime/lapmatrud/bench/gps.runtime +++ b/bench/runtime/lapmatrud/bench/gps.runtime @@ -1,1 +1,1 @@ -15.1 +15.8 diff --git a/bench/runtime/lapmatrud/bench/gps2.runtime b/bench/runtime/lapmatrud/bench/gps2.runtime --- a/bench/runtime/lapmatrud/bench/gps2.runtime +++ b/bench/runtime/lapmatrud/bench/gps2.runtime @@ -1,1 +1,1 @@ -12.3 +13.1 diff --git a/bench/runtime/lapmatrud/bench/ill-hit.runtime b/bench/runtime/lapmatrud/bench/ill-hit.runtime --- a/bench/runtime/lapmatrud/bench/ill-hit.runtime +++ b/bench/runtime/lapmatrud/bench/ill-hit.runtime @@ -1,1 +1,1 @@ -0.5 +0.4 diff --git a/bench/runtime/lapmatrud/bench/redundants.runtime b/bench/runtime/lapmatrud/bench/redundants.runtime --- a/bench/runtime/lapmatrud/bench/redundants.runtime +++ b/bench/runtime/lapmatrud/bench/redundants.runtime @@ -1,1 +1,1 @@ -1.9 +3.9 diff --git a/bench/runtime/lapmatrud/bench/terpret.runtime b/bench/runtime/lapmatrud/bench/terpret.runtime --- a/bench/runtime/lapmatrud/bench/terpret.runtime +++ b/bench/runtime/lapmatrud/bench/terpret.runtime @@ -1,1 +1,1 @@ -7.2 +8.3 diff --git a/bench/runtime/lapmatrud/bench/weird.runtime b/bench/runtime/lapmatrud/bench/weird.runtime --- a/bench/runtime/lapmatrud/bench/weird.runtime +++ b/bench/runtime/lapmatrud/bench/weird.runtime @@ -1,1 +1,1 @@ -2.8 +3.1 diff --git a/bench/runtime/lapmatrud/eg/bools.runtime b/bench/runtime/lapmatrud/eg/bools.runtime --- a/bench/runtime/lapmatrud/eg/bools.runtime +++ b/bench/runtime/lapmatrud/eg/bools.runtime @@ -1,1 +1,1 @@ -1.8 +1.6 diff --git a/bench/runtime/lapmatrud/eg/count.runtime b/bench/runtime/lapmatrud/eg/count.runtime --- a/bench/runtime/lapmatrud/eg/count.runtime +++ b/bench/runtime/lapmatrud/eg/count.runtime @@ -1,1 +1,1 @@ -0.5 +0.3 diff --git a/bench/runtime/lapmatrud/eg/dupos.runtime b/bench/runtime/lapmatrud/eg/dupos.runtime --- a/bench/runtime/lapmatrud/eg/dupos.runtime +++ b/bench/runtime/lapmatrud/eg/dupos.runtime @@ -1,1 +1,1 @@ -3.6 +3.3 diff --git a/bench/runtime/lapmatrud/eg/factorial.runtime b/bench/runtime/lapmatrud/eg/factorial.runtime --- a/bench/runtime/lapmatrud/eg/factorial.runtime +++ b/bench/runtime/lapmatrud/eg/factorial.runtime @@ -1,1 +1,1 @@ -1.3 +1.2 diff --git a/bench/runtime/lapmatrud/eg/fib01.runtime b/bench/runtime/lapmatrud/eg/fib01.runtime --- a/bench/runtime/lapmatrud/eg/fib01.runtime +++ b/bench/runtime/lapmatrud/eg/fib01.runtime @@ -1,1 +1,1 @@ -2.4 +1.2 diff --git a/bench/runtime/lapmatrud/eg/fibonacci.runtime b/bench/runtime/lapmatrud/eg/fibonacci.runtime --- a/bench/runtime/lapmatrud/eg/fibonacci.runtime +++ b/bench/runtime/lapmatrud/eg/fibonacci.runtime @@ -1,1 +1,1 @@ -3.7 +4.2 diff --git a/bench/runtime/lapmatrud/eg/pow.runtime b/bench/runtime/lapmatrud/eg/pow.runtime --- a/bench/runtime/lapmatrud/eg/pow.runtime +++ b/bench/runtime/lapmatrud/eg/pow.runtime @@ -1,1 +1,1 @@ -4.7 +3.8 diff --git a/bench/runtime/lapmatrud/eg/sort.runtime b/bench/runtime/lapmatrud/eg/sort.runtime --- a/bench/runtime/lapmatrud/eg/sort.runtime +++ b/bench/runtime/lapmatrud/eg/sort.runtime @@ -1,1 +1,1 @@ -1.1 +1.2 diff --git a/bench/runtime/lapmatrud/eg/spec.runtime b/bench/runtime/lapmatrud/eg/spec.runtime --- a/bench/runtime/lapmatrud/eg/spec.runtime +++ b/bench/runtime/lapmatrud/eg/spec.runtime @@ -1,1 +1,1 @@ -0.6 +0.5 diff --git a/bench/runtime/lapmatrud/eg/subset.runtime b/bench/runtime/lapmatrud/eg/subset.runtime --- a/bench/runtime/lapmatrud/eg/subset.runtime +++ b/bench/runtime/lapmatrud/eg/subset.runtime @@ -1,1 +1,1 @@ -0.5 +0.4 diff --git a/bench/runtime/lapmatrud/eg/tree.runtime b/bench/runtime/lapmatrud/eg/tree.runtime --- a/bench/runtime/lapmatrud/eg/tree.runtime +++ b/bench/runtime/lapmatrud/eg/tree.runtime @@ -1,1 +1,1 @@ -1.2 +1.5 diff --git a/bench/runtime/lapmatrud/versions b/bench/runtime/lapmatrud/versions --- a/bench/runtime/lapmatrud/versions +++ b/bench/runtime/lapmatrud/versions @@ -1,4 +1,4 @@ GHC 9.0.2 -leancheck-1.0.0 -express-1.0.12 +leancheck-1.0.2 +express-1.0.14 speculate-0.4.14 diff --git a/bench/runtime/zero/bench/candidates.runtime b/bench/runtime/zero/bench/candidates.runtime --- a/bench/runtime/zero/bench/candidates.runtime +++ b/bench/runtime/zero/bench/candidates.runtime @@ -1,1 +1,1 @@ -10.0 +9.7 diff --git a/bench/runtime/zero/bench/erroneous.runtime b/bench/runtime/zero/bench/erroneous.runtime new file mode 100644 --- /dev/null +++ b/bench/runtime/zero/bench/erroneous.runtime @@ -0,0 +1,1 @@ +3.7 diff --git a/bench/runtime/zero/bench/gps.runtime b/bench/runtime/zero/bench/gps.runtime --- a/bench/runtime/zero/bench/gps.runtime +++ b/bench/runtime/zero/bench/gps.runtime @@ -1,1 +1,1 @@ -28.4 +28.5 diff --git a/bench/runtime/zero/bench/gps2.runtime b/bench/runtime/zero/bench/gps2.runtime --- a/bench/runtime/zero/bench/gps2.runtime +++ b/bench/runtime/zero/bench/gps2.runtime @@ -1,1 +1,1 @@ -22.6 +26.1 diff --git a/bench/runtime/zero/bench/p12.runtime b/bench/runtime/zero/bench/p12.runtime --- a/bench/runtime/zero/bench/p12.runtime +++ b/bench/runtime/zero/bench/p12.runtime @@ -1,1 +1,1 @@ -3.1 +3.8 diff --git a/bench/runtime/zero/bench/redundants.runtime b/bench/runtime/zero/bench/redundants.runtime --- a/bench/runtime/zero/bench/redundants.runtime +++ b/bench/runtime/zero/bench/redundants.runtime @@ -1,1 +1,1 @@ -2.7 +14.9 diff --git a/bench/runtime/zero/bench/terpret.runtime b/bench/runtime/zero/bench/terpret.runtime --- a/bench/runtime/zero/bench/terpret.runtime +++ b/bench/runtime/zero/bench/terpret.runtime @@ -1,1 +1,1 @@ -15.1 +14.8 diff --git a/bench/runtime/zero/bench/weird.runtime b/bench/runtime/zero/bench/weird.runtime --- a/bench/runtime/zero/bench/weird.runtime +++ b/bench/runtime/zero/bench/weird.runtime @@ -1,1 +1,1 @@ -5.1 +5.4 diff --git a/bench/runtime/zero/eg/bools.runtime b/bench/runtime/zero/eg/bools.runtime --- a/bench/runtime/zero/eg/bools.runtime +++ b/bench/runtime/zero/eg/bools.runtime @@ -1,1 +1,1 @@ -3.1 +3.2 diff --git a/bench/runtime/zero/eg/bst.runtime b/bench/runtime/zero/eg/bst.runtime --- a/bench/runtime/zero/eg/bst.runtime +++ b/bench/runtime/zero/eg/bst.runtime @@ -1,1 +1,1 @@ -13.9 +13.8 diff --git a/bench/runtime/zero/eg/count.runtime b/bench/runtime/zero/eg/count.runtime --- a/bench/runtime/zero/eg/count.runtime +++ b/bench/runtime/zero/eg/count.runtime @@ -1,1 +1,1 @@ -0.7 +0.6 diff --git a/bench/runtime/zero/eg/dupos.runtime b/bench/runtime/zero/eg/dupos.runtime --- a/bench/runtime/zero/eg/dupos.runtime +++ b/bench/runtime/zero/eg/dupos.runtime @@ -1,1 +1,1 @@ -7.4 +6.5 diff --git a/bench/runtime/zero/eg/either.runtime b/bench/runtime/zero/eg/either.runtime new file mode 100644 --- /dev/null +++ b/bench/runtime/zero/eg/either.runtime @@ -0,0 +1,1 @@ +0.2 diff --git a/bench/runtime/zero/eg/fib01.runtime b/bench/runtime/zero/eg/fib01.runtime --- a/bench/runtime/zero/eg/fib01.runtime +++ b/bench/runtime/zero/eg/fib01.runtime @@ -1,1 +1,1 @@ -2.3 +2.6 diff --git a/bench/runtime/zero/eg/fibonacci.runtime b/bench/runtime/zero/eg/fibonacci.runtime --- a/bench/runtime/zero/eg/fibonacci.runtime +++ b/bench/runtime/zero/eg/fibonacci.runtime @@ -1,1 +1,1 @@ -8.2 +9.1 diff --git a/bench/runtime/zero/eg/higher.runtime b/bench/runtime/zero/eg/higher.runtime --- a/bench/runtime/zero/eg/higher.runtime +++ b/bench/runtime/zero/eg/higher.runtime @@ -1,1 +1,1 @@ -1.2 +1.1 diff --git a/bench/runtime/zero/eg/maybe.runtime b/bench/runtime/zero/eg/maybe.runtime new file mode 100644 --- /dev/null +++ b/bench/runtime/zero/eg/maybe.runtime @@ -0,0 +1,1 @@ +0.5 diff --git a/bench/runtime/zero/eg/oddeven.runtime b/bench/runtime/zero/eg/oddeven.runtime new file mode 100644 --- /dev/null +++ b/bench/runtime/zero/eg/oddeven.runtime @@ -0,0 +1,1 @@ +2.8 diff --git a/bench/runtime/zero/eg/pow.runtime b/bench/runtime/zero/eg/pow.runtime --- a/bench/runtime/zero/eg/pow.runtime +++ b/bench/runtime/zero/eg/pow.runtime @@ -1,1 +1,1 @@ -6.9 +7.4 diff --git a/bench/runtime/zero/eg/sort.runtime b/bench/runtime/zero/eg/sort.runtime --- a/bench/runtime/zero/eg/sort.runtime +++ b/bench/runtime/zero/eg/sort.runtime @@ -1,1 +1,1 @@ -2.5 +2.7 diff --git a/bench/runtime/zero/eg/spec.runtime b/bench/runtime/zero/eg/spec.runtime --- a/bench/runtime/zero/eg/spec.runtime +++ b/bench/runtime/zero/eg/spec.runtime @@ -1,1 +1,1 @@ -1.2 +1.1 diff --git a/bench/runtime/zero/versions b/bench/runtime/zero/versions --- a/bench/runtime/zero/versions +++ b/bench/runtime/zero/versions @@ -1,4 +1,4 @@ GHC 9.0.2 -leancheck-1.0.0 -express-1.0.12 +leancheck-1.0.2 +express-1.0.16 speculate-0.4.14 diff --git a/bench/self.hs b/bench/self.hs --- a/bench/self.hs +++ b/bench/self.hs @@ -1,6 +1,6 @@ -- self.hs: conjuring functions through themselves -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/bench/self.out b/bench/self.out deleted file mode 100644 --- a/bench/self.out +++ /dev/null @@ -1,36 +0,0 @@ -(?) :: Int -> Int -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 4 candidates of size 1 --- looking through 15 candidates of size 2 --- looking through 55 candidates of size 3 --- tested 21 candidates -x ? y = x + y - -(?) :: Int -> Int -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 4 candidates of size 1 --- looking through 15 candidates of size 2 --- looking through 55 candidates of size 3 --- tested 33 candidates -x ? y = x * y - -i :: Int -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 3 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 13 candidates of size 3 --- tested 8 candidates -i x = x + 1 - -d :: Int -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 12 candidates of size 3 --- tested 18 candidates -cannot conjure - diff --git a/bench/self.txt b/bench/self.txt new file mode 100644 --- /dev/null +++ b/bench/self.txt @@ -0,0 +1,36 @@ +(?) :: Int -> Int -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 4 candidates of size 1 +-- looking through 16 candidates of size 2 +-- looking through 56 candidates of size 3 +-- tested 22 candidates +x ? y = x + y + +(?) :: Int -> Int -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 4 candidates of size 1 +-- looking through 16 candidates of size 2 +-- looking through 56 candidates of size 3 +-- tested 34 candidates +x ? y = x * y + +i :: Int -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 3 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 13 candidates of size 3 +-- tested 8 candidates +i x = x + 1 + +d :: Int -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 12 candidates of size 3 +-- tested 18 candidates +cannot conjure + diff --git a/bench/take-drop.out b/bench/take-drop.out deleted file mode 100644 --- a/bench/take-drop.out +++ /dev/null @@ -1,32 +0,0 @@ -drop :: Int -> [A] -> [A] --- testing 360 combinations of argument values --- pruning with 4/7 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 9 candidates of size 4 --- looking through 10 candidates of size 5 --- looking through 28 candidates of size 6 --- looking through 50 candidates of size 7 --- tested 63 candidates -drop 0 xs = xs -drop x [] = [] -drop x (y:xs) = drop (x - 1) xs - -take :: Int -> [A] -> [A] --- testing 143 combinations of argument values --- pruning with 14/21 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 9 candidates of size 4 --- looking through 10 candidates of size 5 --- looking through 28 candidates of size 6 --- looking through 50 candidates of size 7 --- looking through 83 candidates of size 8 --- looking through 133 candidates of size 9 --- tested 249 candidates -take 0 xs = [] -take x [] = [] -take x (y:xs) = y:take (x - 1) xs - diff --git a/bench/take-drop.txt b/bench/take-drop.txt new file mode 100644 --- /dev/null +++ b/bench/take-drop.txt @@ -0,0 +1,32 @@ +drop :: Int -> [A] -> [A] +-- testing 360 combinations of argument values +-- pruning with 4/7 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 8 candidates of size 5 +-- looking through 13 candidates of size 6 +-- looking through 24 candidates of size 7 +-- tested 39 candidates +drop 0 xs = xs +drop x [] = [] +drop x (y:xs) = drop (x - 1) xs + +take :: Int -> [A] -> [A] +-- testing 143 combinations of argument values +-- pruning with 14/21 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 8 candidates of size 5 +-- looking through 13 candidates of size 6 +-- looking through 24 candidates of size 7 +-- looking through 31 candidates of size 8 +-- looking through 59 candidates of size 9 +-- tested 111 candidates +take 0 xs = [] +take x [] = [] +take x (y:xs) = y:take (x - 1) xs + diff --git a/bench/terpret.hs b/bench/terpret.hs --- a/bench/terpret.hs +++ b/bench/terpret.hs @@ -1,6 +1,6 @@ -- terpret.hs: Benchmark execution-model problems from TerpreT -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). -- -- You can find the description of these exercises on: diff --git a/bench/terpret.out b/bench/terpret.out deleted file mode 100644 --- a/bench/terpret.out +++ /dev/null @@ -1,172 +0,0 @@ -TerpreT benchmark #1: invert - -invert :: [Bool] -> [Bool] --- testing 4 combinations of argument values --- pruning with 41/51 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 10 candidates of size 4 --- looking through 17 candidates of size 5 --- looking through 41 candidates of size 6 --- tested 36 candidates -invert [] = [] -invert (p:ps) = not p:invert ps - -TerpreT benchmark #2: prepend zero - -prependZero :: [Bool] -> [Bool] --- testing 3 combinations of argument values --- pruning with 41/51 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 5 candidates of size 3 --- tested 5 candidates -prependZero ps = False:ps - -TerpreT benchmark #3: binary decrement - -decrement :: [Bool] -> [Bool] --- testing 3 combinations of argument values --- pruning with 41/51 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 10 candidates of size 4 --- looking through 17 candidates of size 5 --- looking through 41 candidates of size 6 --- looking through 86 candidates of size 7 --- looking through 202 candidates of size 8 --- looking through 487 candidates of size 9 --- tested 418 candidates -decrement [] = [] -decrement (p:ps) = not p:(if p then ps else decrement ps) - -TerpreT benchmark #4: controlled shift - -cshift :: (Bool,Bool,Bool) -> (Bool,Bool,Bool) --- testing 4 combinations of argument values --- pruning with 41/51 rules --- reasoning produced 2 incorrect properties, please re-run with more tests for faster results --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 10 candidates of size 4 --- looking through 125 candidates of size 5 --- looking through 225 candidates of size 6 --- looking through 625 candidates of size 7 --- looking through 1242 candidates of size 8 --- looking through 3087 candidates of size 9 --- looking through 8937 candidates of size 10 --- looking through 102875 candidates of size 11 --- tested 40385 candidates -cshift (p,q,r) = if p - then (p,r,q) - else (p,q,r) - -cshift :: Bool -> Bool -> Bool -> (Bool,Bool,Bool) --- testing 4 combinations of argument values --- pruning with 41/51 rules --- reasoning produced 2 incorrect properties, please re-run with more tests for faster results --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 125 candidates of size 4 --- looking through 225 candidates of size 5 --- looking through 585 candidates of size 6 --- looking through 1242 candidates of size 7 --- looking through 15183 candidates of size 8 --- tested 15459 candidates -cshift False p q = (False,p,q) -cshift True p q = (True,q,p) - -TerpreT benchmark #5: full adder - -fadder :: Bool -> Bool -> Bool -> (Bool,Bool) --- testing 8 combinations of argument values --- pruning with 18/22 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 9 candidates of size 3 --- looking through 18 candidates of size 4 --- looking through 27 candidates of size 5 --- looking through 72 candidates of size 6 --- looking through 245 candidates of size 7 --- looking through 663 candidates of size 8 --- tested 1034 candidates -fadder False False False = (False,False) -fadder False False True = (False,True) -fadder False True False = (False,True) -fadder False True True = (True,False) -fadder True False False = (False,True) -fadder True False True = (True,False) -fadder True True False = (True,False) -fadder True True True = (True,True) - -TerpreT benchmark #6: 2-bit adder - -adder2 :: (Bool,Bool) -> (Bool,Bool) -> (Bool,Bool,Bool) --- testing 5 combinations of argument values --- pruning with 74/92 rules --- reasoning produced 2 incorrect properties, please re-run with more tests for faster results --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 128 candidates of size 5 --- looking through 408 candidates of size 6 --- tested 544 candidates -cannot conjure - -TerpreT benchmark #7: access - -access :: [A] -> Int -> A --- testing 5 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 1 candidates of size 3 --- tested 1 candidates -xs `access` x = xs !! x - -access :: [A] -> Int -> A --- testing 5 combinations of argument values --- pruning with 4/7 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 9 candidates of size 5 --- looking through 17 candidates of size 6 --- looking through 46 candidates of size 7 --- tested 46 candidates -[] `access` x = undefined -(x:xs) `access` 0 = x -(x:xs) `access` y = xs `access` (y - 1) - -TerpreT benchmark #8: decrement elements - -decrelements :: [Int] -> [Int] --- testing 3 combinations of argument values --- pruning with 3/23 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 7 candidates of size 4 --- looking through 9 candidates of size 5 --- looking through 29 candidates of size 6 --- looking through 41 candidates of size 7 --- tested 53 candidates -decrelements [] = [] -decrelements (x:xs) = x - 1:decrelements xs - -decrelements :: [Int] -> [Int] --- testing 3 combinations of argument values --- pruning with 5/26 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 8 candidates of size 4 --- tested 8 candidates -decrelements xs = map (subtract 1) xs - diff --git a/bench/terpret.txt b/bench/terpret.txt new file mode 100644 --- /dev/null +++ b/bench/terpret.txt @@ -0,0 +1,172 @@ +TerpreT benchmark #1: invert + +invert :: [Bool] -> [Bool] +-- testing 4 combinations of argument values +-- pruning with 41/51 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 15 candidates of size 5 +-- looking through 41 candidates of size 6 +-- tested 33 candidates +invert [] = [] +invert (p:ps) = not p:invert ps + +TerpreT benchmark #2: prepend zero + +prependZero :: [Bool] -> [Bool] +-- testing 3 combinations of argument values +-- pruning with 41/51 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 4 candidates of size 3 +-- tested 4 candidates +prependZero ps = False:ps + +TerpreT benchmark #3: binary decrement + +decrement :: [Bool] -> [Bool] +-- testing 3 combinations of argument values +-- pruning with 41/51 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 15 candidates of size 5 +-- looking through 41 candidates of size 6 +-- looking through 82 candidates of size 7 +-- looking through 202 candidates of size 8 +-- looking through 479 candidates of size 9 +-- tested 411 candidates +decrement [] = [] +decrement (p:ps) = not p:(if p then ps else decrement ps) + +TerpreT benchmark #4: controlled shift + +cshift :: (Bool,Bool,Bool) -> (Bool,Bool,Bool) +-- testing 4 combinations of argument values +-- pruning with 41/51 rules +-- reasoning produced 2 incorrect properties, please re-run with more tests for faster results +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 125 candidates of size 5 +-- looking through 225 candidates of size 6 +-- looking through 625 candidates of size 7 +-- looking through 1242 candidates of size 8 +-- looking through 3087 candidates of size 9 +-- looking through 8937 candidates of size 10 +-- looking through 102875 candidates of size 11 +-- tested 40385 candidates +cshift (p,q,r) = if p + then (p,r,q) + else (p,q,r) + +cshift :: Bool -> Bool -> Bool -> (Bool,Bool,Bool) +-- testing 4 combinations of argument values +-- pruning with 41/51 rules +-- reasoning produced 2 incorrect properties, please re-run with more tests for faster results +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 125 candidates of size 4 +-- looking through 225 candidates of size 5 +-- looking through 585 candidates of size 6 +-- looking through 1242 candidates of size 7 +-- looking through 15183 candidates of size 8 +-- tested 15459 candidates +cshift False p q = (False,p,q) +cshift True p q = (True,q,p) + +TerpreT benchmark #5: full adder + +fadder :: Bool -> Bool -> Bool -> (Bool,Bool) +-- testing 8 combinations of argument values +-- pruning with 18/22 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 9 candidates of size 3 +-- looking through 18 candidates of size 4 +-- looking through 27 candidates of size 5 +-- looking through 72 candidates of size 6 +-- looking through 245 candidates of size 7 +-- looking through 663 candidates of size 8 +-- tested 1034 candidates +fadder False False False = (False,False) +fadder False False True = (False,True) +fadder False True False = (False,True) +fadder False True True = (True,False) +fadder True False False = (False,True) +fadder True False True = (True,False) +fadder True True False = (True,False) +fadder True True True = (True,True) + +TerpreT benchmark #6: 2-bit adder + +adder2 :: (Bool,Bool) -> (Bool,Bool) -> (Bool,Bool,Bool) +-- testing 5 combinations of argument values +-- pruning with 74/92 rules +-- reasoning produced 2 incorrect properties, please re-run with more tests for faster results +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 8 candidates of size 4 +-- looking through 128 candidates of size 5 +-- looking through 408 candidates of size 6 +-- tested 544 candidates +cannot conjure + +TerpreT benchmark #7: access + +access :: [A] -> Int -> A +-- testing 5 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- tested 1 candidates +xs `access` x = xs !! x + +access :: [A] -> Int -> A +-- testing 5 combinations of argument values +-- pruning with 4/7 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 6 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 19 candidates of size 7 +-- tested 18 candidates +[] `access` x = undefined +(x:xs) `access` 0 = x +(x:xs) `access` y = xs `access` (y - 1) + +TerpreT benchmark #8: decrement elements + +decrelements :: [Int] -> [Int] +-- testing 3 combinations of argument values +-- pruning with 3/23 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 7 candidates of size 4 +-- looking through 8 candidates of size 5 +-- looking through 29 candidates of size 6 +-- looking through 39 candidates of size 7 +-- tested 51 candidates +decrelements [] = [] +decrelements (x:xs) = x - 1:decrelements xs + +decrelements :: [Int] -> [Int] +-- testing 3 combinations of argument values +-- pruning with 5/26 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 8 candidates of size 4 +-- tested 7 candidates +decrelements xs = map (subtract 1) xs + diff --git a/bench/time b/bench/time --- a/bench/time +++ b/bench/time @@ -2,7 +2,7 @@ # # bench/time: runs a program, discards stdout and print name and runtime # -# Copyright (C) 2021 Rudy Matela +# Copyright (C) 2021-2024 Rudy Matela # Distributed under the 3-Clause BSD licence (see the file LICENSE). printf "%-14s " "$*" diff --git a/bench/versions b/bench/versions --- a/bench/versions +++ b/bench/versions @@ -2,7 +2,7 @@ # # bench/versions: print versions of installed dependencies # -# Copyright (C) 2021 Rudy Matela +# Copyright (C) 2021-2024 Rudy Matela # Distributed under the 3-Clause BSD licence (see the file LICENSE). get-ghc-v() { ghc --version | sed -e "s/.* version/GHC/" diff --git a/bench/weird.out b/bench/weird.out deleted file mode 100644 --- a/bench/weird.out +++ /dev/null @@ -1,29 +0,0 @@ -(^^^) :: Int -> Int -> Int --- testing 360 combinations of argument values --- pruning with 56/91 rules --- looking through 4 candidates of size 1 --- looking through 15 candidates of size 2 --- looking through 39 candidates of size 3 --- tested 36 candidates -0 ^^^ x = x -x ^^^ 0 = x -x ^^^ y = 0 - -(^^^) :: Int -> Int -> Int --- testing 360 combinations of argument values --- pruning with 56/91 rules --- looking through 4 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 9 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 39 candidates of size 5 --- looking through 60 candidates of size 6 --- looking through 225 candidates of size 7 --- looking through 1056 candidates of size 8 --- looking through 1488 candidates of size 9 --- looking through 13020 candidates of size 10 --- tested 7148 candidates -x ^^^ y = if 0 == x * y - then x + y - else 0 - diff --git a/bench/weird.txt b/bench/weird.txt new file mode 100644 --- /dev/null +++ b/bench/weird.txt @@ -0,0 +1,29 @@ +(^^^) :: Int -> Int -> Int +-- testing 360 combinations of argument values +-- pruning with 56/91 rules +-- looking through 4 candidates of size 1 +-- looking through 16 candidates of size 2 +-- looking through 40 candidates of size 3 +-- tested 37 candidates +0 ^^^ x = x +x ^^^ 0 = x +x ^^^ y = 0 + +(^^^) :: Int -> Int -> Int +-- testing 360 combinations of argument values +-- pruning with 56/91 rules +-- looking through 4 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 9 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 39 candidates of size 5 +-- looking through 60 candidates of size 6 +-- looking through 225 candidates of size 7 +-- looking through 1056 candidates of size 8 +-- looking through 1488 candidates of size 9 +-- looking through 13020 candidates of size 10 +-- tested 7148 candidates +x ^^^ y = if 0 == x * y + then x + y + else 0 + diff --git a/changelog.md b/changelog.md --- a/changelog.md +++ b/changelog.md @@ -2,9 +2,27 @@ ============================ -v0.5.8 ------- +v0.5.10 (February 2024) +----------------------- +* improve pruning of candidate functions; +* `Conjure`: un-export experimental `equalModuloTesting` +* `Conjure.Conjurable`: add `conjureListFor`, `conjureSizeFor` & `conjureGrounds`; +* Reorganize internal modules +* Add `Conjure.Defn.Redundancy` module for redundant candidates; +* Add `Conjure.Defn.Test` module testing candidate definitions; +* Add `Conjure.Reason` module for term-rewriting-based reasoning; +* Add `Conjure.Red` module for recursive descent; +* `Conjure.Expr`: add a few auxiliary functions +* Move functions out of `Conjure.Engine` into new modules +* add more examples and benchmarks; +* improved testing of Conjure itself; +* and several other improvements and fixes. + + +v0.5.8 (January 2024) +--------------------- + * prune redundant mutants using a few new rules * rework numeric recursion criteria * improve pretty-printing @@ -14,8 +32,8 @@ * bump Express requirement to v1.0.14 (bugfix) -v0.5.6 ------- +v0.5.6 (November 2023) +---------------------- * `Conjure` module: no main API changes * `Conjure.Engine`: add `equalModuloTesting` @@ -23,8 +41,8 @@ * add `bench/redundants` that reports groups of redundant candidates -v0.5.4 ------- +v0.5.4 (November 2023) +---------------------- This has been the "dev" version after v0.5.2 for almost a couple of years: @@ -36,8 +54,8 @@ * add (but not use) `conjureSize` to `Conjurable` -v0.5.2 ------- +v0.5.2 (March 2022) +------------------- * show number of tested candidates * complete `Conjurable` derivation functions @@ -46,8 +64,8 @@ to allow computing the near upper/lower limit on pruning -v0.5.0 ------- +v0.5.0 (September 2021) +----------------------- * allow synthesizing/conjuring from properties with `conjureFromSpec`; * complete Haddock documentation; @@ -56,8 +74,8 @@ * Makefile: add targets to run GPS(2) and TerpreT benches. -v0.4.4 ------- +v0.4.4 (September 2021) +----------------------- * remove need for explicit deconstructions: - use `-` and `1` instead of `dec`; @@ -68,8 +86,8 @@ * minor fixes in the README. -v0.4.2 ------- +v0.4.2 (August 2021) +-------------------- * default to using top-level patterns on generated functions; * memoize function evaluation; @@ -81,8 +99,8 @@ * improve tests and benchmarks. -v0.4.0 ------- +v0.4.0 (July 2021) +------------------ * background primitives are now provided with `pr` and `prim`. * report number of rules used in pruning @@ -94,8 +112,8 @@ * cleanup unused code -v0.3.6 ------- +v0.3.6 (June 2021) +------------------ * add switch for descending recursions to allow generation of `gcd` @@ -105,8 +123,8 @@ at this point, the old names were misnomers. -v0.3.4 ------- +v0.3.4 (June 2021) +------------------ * reallow recursions under `&&` and `||` (simplifies the generated `or`, `and`, `set` and `elem` functions) @@ -117,8 +135,8 @@ * add 4 new benchmarks: `count`, `gcd`, `tree` and `setelem` -v0.3.2 ------- +v0.3.2 (June 2021) +------------------ * significant runtime reduction in several benchmarks, e.g.: - take is now reachable in about 5 seconds @@ -136,30 +154,30 @@ - add stub `Conjure.Constructors` module -v0.3.0 ------- +v0.3.0 (May 2021) +----------------- * only automatically include an `if` for the return type of the given function * add the `take-drop` benchmark * make bottom-up enumeration more type directed -v0.2.8 ------- +v0.2.8 (May 2021) +----------------- * export the `A`, `B`, `C`, `D`, `E` and `F` helper types -v0.2.6 ------- +v0.2.6 (May 2021) +----------------- * require Express v0.1.10 due to `hasHole` being now exported there * require Eq result on `conjure1`, `conjure2` and `conjure3` * code cleanup and more tests -v0.2.4 ------- +v0.2.4 (May 2021) +----------------- * allow conjuring from specifications in addition to partial definitions (`conjure1`, `conjure2`, `conjure3` and related functions) @@ -170,21 +188,21 @@ * add code-optional candidate nubbing and debug functions -v0.2.2 ------- +v0.2.2 (May 2021) +----------------- * by default, search for 60 argument combinations among 100000 enumerated combinations -v0.2.0 ------- +v0.2.0 (May 2021) +----------------- * search until 100% match is found and exit * other misc changes -v0.1.2 ------- +v0.1.2 (April 2021) +------------------- For the changelog of earlier versions, check the git commit history. diff --git a/code-conjure.cabal b/code-conjure.cabal --- a/code-conjure.cabal +++ b/code-conjure.cabal @@ -1,9 +1,9 @@ -- Cabal file for the Conjure program generation library. -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). name: code-conjure -version: 0.5.8 +version: 0.5.10 synopsis: synthesize Haskell functions out of partial definitions description: Conjure is a tool that synthesizes Haskell functions out of partial definitions. @@ -26,11 +26,11 @@ , Makefile , bench/bench , bench/*.hs - , bench/*.out + , bench/*.txt , eg/*.hs - , eg/*.out + , eg/*.txt , proto/*.hs - , proto/*.out + , proto/*.txt , mk/All.hs , mk/Toplibs.hs , mk/depend.mk @@ -49,6 +49,7 @@ , bench/runtime/lapmatrud/versions , bench/versions , bench/time + , test/mk , test/sdist tested-with: GHC==9.4 , GHC==9.2 @@ -64,7 +65,7 @@ source-repository this type: git location: https://github.com/rudymatela/conjure - tag: v0.5.8 + tag: v0.5.10 library exposed-modules: Conjure @@ -75,12 +76,16 @@ , Conjure.Prim , Conjure.Utils , Conjure.Defn + , Conjure.Defn.Redundancy + , Conjure.Defn.Test + , Conjure.Red + , Conjure.Reason other-extensions: TemplateHaskell, CPP build-depends: base >= 4 && < 5 , leancheck >= 1.0.0 , template-haskell , speculate >= 0.4.14 - , express >= 1.0.14 + , express >= 1.0.16 hs-source-dirs: src default-language: Haskell2010 @@ -119,6 +124,14 @@ test-suite derive type: exitcode-stdio-1.0 main-is: derive.hs + other-modules: Test, Test.ListableExpr + hs-source-dirs: test + build-depends: base >= 4 && < 5, leancheck, express, speculate, code-conjure + default-language: Haskell2010 + +test-suite red + type: exitcode-stdio-1.0 + main-is: red.hs other-modules: Test, Test.ListableExpr hs-source-dirs: test build-depends: base >= 4 && < 5, leancheck, express, speculate, code-conjure diff --git a/eg/arith.hs b/eg/arith.hs --- a/eg/arith.hs +++ b/eg/arith.hs @@ -1,6 +1,6 @@ -- arith.hs: conjuring simple non-recursive numeric functions -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/eg/arith.out b/eg/arith.out deleted file mode 100644 --- a/eg/arith.out +++ /dev/null @@ -1,62 +0,0 @@ -double :: Int -> Int --- testing 4 combinations of argument values --- pruning with 14/25 rules --- looking through 3 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 6 candidates of size 3 --- tested 5 candidates -double x = x + x - -triple :: Int -> Int --- testing 4 combinations of argument values --- pruning with 14/25 rules --- looking through 3 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 6 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 11 candidates of size 5 --- tested 15 candidates -triple x = x + (x + x) - -add :: Int -> Int -> Int --- testing 4 combinations of argument values --- pruning with 14/25 rules --- looking through 4 candidates of size 1 --- looking through 15 candidates of size 2 --- looking through 39 candidates of size 3 --- tested 21 candidates -add x y = x + y - -square :: Int -> Int --- testing 3 combinations of argument values --- pruning with 14/25 rules --- looking through 3 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 4 candidates of size 3 --- tested 7 candidates -square x = x * x - -cube :: Int -> Int --- testing 3 combinations of argument values --- pruning with 14/25 rules --- looking through 3 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 4 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 11 candidates of size 5 --- tested 19 candidates -cube x = x * (x * x) - -tnpo :: Int -> Int --- testing 3 combinations of argument values --- pruning with 14/25 rules --- looking through 3 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 6 candidates of size 3 --- looking through 5 candidates of size 4 --- looking through 11 candidates of size 5 --- looking through 11 candidates of size 6 --- looking through 35 candidates of size 7 --- tested 40 candidates -tnpo x = x + (x + (x + 1)) - diff --git a/eg/arith.txt b/eg/arith.txt new file mode 100644 --- /dev/null +++ b/eg/arith.txt @@ -0,0 +1,62 @@ +double :: Int -> Int +-- testing 4 combinations of argument values +-- pruning with 14/25 rules +-- looking through 3 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 6 candidates of size 3 +-- tested 5 candidates +double x = x + x + +triple :: Int -> Int +-- testing 4 combinations of argument values +-- pruning with 14/25 rules +-- looking through 3 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 6 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 11 candidates of size 5 +-- tested 13 candidates +triple x = x + (x + x) + +add :: Int -> Int -> Int +-- testing 4 combinations of argument values +-- pruning with 14/25 rules +-- looking through 4 candidates of size 1 +-- looking through 16 candidates of size 2 +-- looking through 40 candidates of size 3 +-- tested 22 candidates +add x y = x + y + +square :: Int -> Int +-- testing 3 combinations of argument values +-- pruning with 14/25 rules +-- looking through 3 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 4 candidates of size 3 +-- tested 7 candidates +square x = x * x + +cube :: Int -> Int +-- testing 3 combinations of argument values +-- pruning with 14/25 rules +-- looking through 3 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 10 candidates of size 5 +-- tested 17 candidates +cube x = x * (x * x) + +tnpo :: Int -> Int +-- testing 3 combinations of argument values +-- pruning with 14/25 rules +-- looking through 3 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 6 candidates of size 3 +-- looking through 4 candidates of size 4 +-- looking through 11 candidates of size 5 +-- looking through 7 candidates of size 6 +-- looking through 35 candidates of size 7 +-- tested 35 candidates +tnpo x = x + (x + (x + 1)) + diff --git a/eg/bools.hs b/eg/bools.hs --- a/eg/bools.hs +++ b/eg/bools.hs @@ -1,6 +1,6 @@ -- bools.hs: simple recursive functions over boolean lists -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/eg/bools.out b/eg/bools.out deleted file mode 100644 --- a/eg/bools.out +++ /dev/null @@ -1,44 +0,0 @@ -and :: [Bool] -> Bool --- testing 14 combinations of argument values --- pruning with 37/47 rules --- looking through 2 candidates of size 1 --- looking through 6 candidates of size 2 --- looking through 12 candidates of size 3 --- looking through 16 candidates of size 4 --- looking through 28 candidates of size 5 --- tested 42 candidates -and [] = True -and (p:ps) = p && and ps - -or :: [Bool] -> Bool --- testing 14 combinations of argument values --- pruning with 37/47 rules --- looking through 2 candidates of size 1 --- looking through 6 candidates of size 2 --- looking through 12 candidates of size 3 --- looking through 16 candidates of size 4 --- looking through 28 candidates of size 5 --- tested 39 candidates -or [] = False -or (p:ps) = p || or ps - -and :: [Bool] -> Bool --- testing 14 combinations of argument values --- pruning with 40/50 rules --- looking through 2 candidates of size 1 --- looking through 6 candidates of size 2 --- looking through 12 candidates of size 3 --- looking through 18 candidates of size 4 --- tested 28 candidates -and ps = foldr (&&) True ps - -or :: [Bool] -> Bool --- testing 14 combinations of argument values --- pruning with 40/50 rules --- looking through 2 candidates of size 1 --- looking through 6 candidates of size 2 --- looking through 12 candidates of size 3 --- looking through 18 candidates of size 4 --- tested 27 candidates -or ps = foldr (||) False ps - diff --git a/eg/bools.txt b/eg/bools.txt new file mode 100644 --- /dev/null +++ b/eg/bools.txt @@ -0,0 +1,44 @@ +and :: [Bool] -> Bool +-- testing 14 combinations of argument values +-- pruning with 37/47 rules +-- looking through 2 candidates of size 1 +-- looking through 6 candidates of size 2 +-- looking through 10 candidates of size 3 +-- looking through 14 candidates of size 4 +-- looking through 28 candidates of size 5 +-- tested 38 candidates +and [] = True +and (p:ps) = p && and ps + +or :: [Bool] -> Bool +-- testing 14 combinations of argument values +-- pruning with 37/47 rules +-- looking through 2 candidates of size 1 +-- looking through 6 candidates of size 2 +-- looking through 10 candidates of size 3 +-- looking through 14 candidates of size 4 +-- looking through 28 candidates of size 5 +-- tested 35 candidates +or [] = False +or (p:ps) = p || or ps + +and :: [Bool] -> Bool +-- testing 14 combinations of argument values +-- pruning with 40/50 rules +-- looking through 2 candidates of size 1 +-- looking through 6 candidates of size 2 +-- looking through 10 candidates of size 3 +-- looking through 16 candidates of size 4 +-- tested 24 candidates +and ps = foldr (&&) True ps + +or :: [Bool] -> Bool +-- testing 14 combinations of argument values +-- pruning with 40/50 rules +-- looking through 2 candidates of size 1 +-- looking through 6 candidates of size 2 +-- looking through 10 candidates of size 3 +-- looking through 16 candidates of size 4 +-- tested 23 candidates +or ps = foldr (||) False ps + diff --git a/eg/bst.hs b/eg/bst.hs --- a/eg/bst.hs +++ b/eg/bst.hs @@ -1,6 +1,6 @@ -- bst.hs: conjuring functions over binary search trees (BSTs) -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# LANGUAGE CPP, TemplateHaskell #-} diff --git a/eg/bst.out b/eg/bst.out deleted file mode 100644 --- a/eg/bst.out +++ /dev/null @@ -1,122 +0,0 @@ -mem :: Int -> Tree -> Bool --- testing 360 combinations of argument values --- pruning with 20/30 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 7 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 31 candidates of size 8 --- looking through 92 candidates of size 9 --- looking through 0 candidates of size 10 --- looking through 304 candidates of size 11 --- looking through 199 candidates of size 12 --- tested 501 candidates -mem x Leaf = False -mem x (Node t1 y t2) = mem x t1 || (mem x t2 || x == y) - -mem :: Int -> Tree -> Bool --- testing 360 combinations of argument values --- pruning with 1/2 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 6 candidates of size 7 --- looking through 24 candidates of size 8 --- looking through 0 candidates of size 9 --- looking through 192 candidates of size 10 --- looking through 0 candidates of size 11 --- looking through 384 candidates of size 12 --- tested 375 candidates -mem x Leaf = False -mem x (Node t1 y t2) = case x `compare` y of LT -> mem x t1; EQ -> True; GT -> mem x t2 - -insert :: Int -> Tree -> Tree --- testing 360 combinations of argument values --- pruning with 6/7 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 21 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 86 candidates of size 7 --- looking through 239 candidates of size 8 --- looking through 104 candidates of size 9 --- looking through 1558 candidates of size 10 --- looking through 3555 candidates of size 11 --- looking through 4028 candidates of size 12 --- tested 9603 candidates -cannot conjure - -before :: Int -> Tree -> Tree --- pruning with 5/6 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 21 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 86 candidates of size 7 --- looking through 239 candidates of size 8 --- looking through 104 candidates of size 9 --- looking through 1558 candidates of size 10 --- looking through 3555 candidates of size 11 --- looking through 4028 candidates of size 12 --- tested 9603 candidates -cannot conjure - -before :: Int -> Tree -> Tree --- pruning with 2/4 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 21 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 68 candidates of size 7 --- looking through 287 candidates of size 8 --- looking through 32 candidates of size 9 --- looking through 1216 candidates of size 10 --- looking through 5103 candidates of size 11 --- looking through 1472 candidates of size 12 --- tested 8211 candidates -cannot conjure - -beyond :: Int -> Tree -> Tree --- pruning with 2/4 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 21 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 68 candidates of size 7 --- looking through 287 candidates of size 8 --- looking through 32 candidates of size 9 --- looking through 1216 candidates of size 10 --- looking through 5103 candidates of size 11 --- looking through 1472 candidates of size 12 --- tested 8211 candidates -cannot conjure - -union :: Tree -> Tree -> Tree --- testing 360 combinations of argument values --- pruning with 6/8 rules --- looking through 3 candidates of size 1 --- looking through 11 candidates of size 2 --- looking through 32 candidates of size 3 --- looking through 84 candidates of size 4 --- looking through 470 candidates of size 5 --- looking through 1074 candidates of size 6 --- looking through 4088 candidates of size 7 --- looking through 16373 candidates of size 8 --- looking through 41366 candidates of size 9 --- tested 63501 candidates -cannot conjure - diff --git a/eg/bst.txt b/eg/bst.txt new file mode 100644 --- /dev/null +++ b/eg/bst.txt @@ -0,0 +1,122 @@ +mem :: Int -> Tree -> Bool +-- testing 360 combinations of argument values +-- pruning with 20/30 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 31 candidates of size 8 +-- looking through 92 candidates of size 9 +-- looking through 0 candidates of size 10 +-- looking through 304 candidates of size 11 +-- looking through 199 candidates of size 12 +-- tested 497 candidates +mem x Leaf = False +mem x (Node t1 y t2) = mem x t1 || (mem x t2 || x == y) + +mem :: Int -> Tree -> Bool +-- testing 360 combinations of argument values +-- pruning with 1/2 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 6 candidates of size 7 +-- looking through 24 candidates of size 8 +-- looking through 0 candidates of size 9 +-- looking through 192 candidates of size 10 +-- looking through 0 candidates of size 11 +-- looking through 384 candidates of size 12 +-- tested 371 candidates +mem x Leaf = False +mem x (Node t1 y t2) = case x `compare` y of LT -> mem x t1; EQ -> True; GT -> mem x t2 + +insert :: Int -> Tree -> Tree +-- testing 360 combinations of argument values +-- pruning with 6/7 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 4 candidates of size 4 +-- looking through 21 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 86 candidates of size 7 +-- looking through 239 candidates of size 8 +-- looking through 104 candidates of size 9 +-- looking through 1558 candidates of size 10 +-- looking through 3555 candidates of size 11 +-- looking through 4028 candidates of size 12 +-- tested 9599 candidates +cannot conjure + +before :: Int -> Tree -> Tree +-- pruning with 5/6 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 4 candidates of size 4 +-- looking through 21 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 86 candidates of size 7 +-- looking through 239 candidates of size 8 +-- looking through 104 candidates of size 9 +-- looking through 1558 candidates of size 10 +-- looking through 3555 candidates of size 11 +-- looking through 4028 candidates of size 12 +-- tested 9599 candidates +cannot conjure + +before :: Int -> Tree -> Tree +-- pruning with 2/4 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 4 candidates of size 4 +-- looking through 21 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 68 candidates of size 7 +-- looking through 287 candidates of size 8 +-- looking through 32 candidates of size 9 +-- looking through 1216 candidates of size 10 +-- looking through 5103 candidates of size 11 +-- looking through 1472 candidates of size 12 +-- tested 8207 candidates +cannot conjure + +beyond :: Int -> Tree -> Tree +-- pruning with 2/4 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 4 candidates of size 4 +-- looking through 21 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 68 candidates of size 7 +-- looking through 287 candidates of size 8 +-- looking through 32 candidates of size 9 +-- looking through 1216 candidates of size 10 +-- looking through 5103 candidates of size 11 +-- looking through 1472 candidates of size 12 +-- tested 8207 candidates +cannot conjure + +union :: Tree -> Tree -> Tree +-- testing 360 combinations of argument values +-- pruning with 6/8 rules +-- looking through 3 candidates of size 1 +-- looking through 12 candidates of size 2 +-- looking through 32 candidates of size 3 +-- looking through 58 candidates of size 4 +-- looking through 434 candidates of size 5 +-- looking through 922 candidates of size 6 +-- looking through 3088 candidates of size 7 +-- looking through 14022 candidates of size 8 +-- looking through 31810 candidates of size 9 +-- tested 50381 candidates +cannot conjure + diff --git a/eg/count.out b/eg/count.out deleted file mode 100644 --- a/eg/count.out +++ /dev/null @@ -1,29 +0,0 @@ -count :: A -> [A] -> Int --- testing 13 combinations of argument values --- pruning with 1/2 rules --- looking through 0 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 1 candidates of size 5 --- tested 2 candidates -count x xs = length (filter (x ==) xs) - -count :: A -> [A] -> Int --- testing 13 combinations of argument values --- pruning with 8/13 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 8 candidates of size 5 --- looking through 14 candidates of size 6 --- looking through 24 candidates of size 7 --- looking through 58 candidates of size 8 --- looking through 134 candidates of size 9 --- looking through 302 candidates of size 10 --- looking through 633 candidates of size 11 --- tested 909 candidates -count x [] = 0 -count x (y:xs) = count x xs + (if x == y then 1 else 0) - diff --git a/eg/count.txt b/eg/count.txt new file mode 100644 --- /dev/null +++ b/eg/count.txt @@ -0,0 +1,29 @@ +count :: A -> [A] -> Int +-- testing 13 combinations of argument values +-- pruning with 1/2 rules +-- looking through 0 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 1 candidates of size 5 +-- tested 2 candidates +count x xs = length (filter (x ==) xs) + +count :: A -> [A] -> Int +-- testing 13 combinations of argument values +-- pruning with 8/13 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 10 candidates of size 6 +-- looking through 20 candidates of size 7 +-- looking through 54 candidates of size 8 +-- looking through 130 candidates of size 9 +-- looking through 298 candidates of size 10 +-- looking through 629 candidates of size 11 +-- tested 875 candidates +count x [] = 0 +count x (y:xs) = count x xs + (if x == y then 1 else 0) + diff --git a/eg/dupos.hs b/eg/dupos.hs --- a/eg/dupos.hs +++ b/eg/dupos.hs @@ -1,6 +1,6 @@ -- dupos.hs: duplicates and positions -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure import Test.LeanCheck -- needed for duplicatesSpec only diff --git a/eg/dupos.out b/eg/dupos.out deleted file mode 100644 --- a/eg/dupos.out +++ /dev/null @@ -1,72 +0,0 @@ -duplicates :: [Int] -> [Int] --- testing 6 combinations of argument values --- pruning with 21/26 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 1 candidates of size 5 --- looking through 2 candidates of size 6 --- looking through 3 candidates of size 7 --- looking through 8 candidates of size 8 --- looking through 16 candidates of size 9 --- looking through 25 candidates of size 10 --- looking through 36 candidates of size 11 --- looking through 63 candidates of size 12 --- looking through 133 candidates of size 13 --- looking through 299 candidates of size 14 --- looking through 602 candidates of size 15 --- looking through 1116 candidates of size 16 --- looking through 2031 candidates of size 17 --- tested 2451 candidates -duplicates [] = [] -duplicates (x:xs) = if elem x xs && not (elem x (duplicates xs)) - then x:duplicates xs - else duplicates xs - -duplicates :: [Int] -> [Int] --- pruning with 21/26 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 1 candidates of size 5 --- looking through 2 candidates of size 6 --- looking through 3 candidates of size 7 --- looking through 8 candidates of size 8 --- looking through 16 candidates of size 9 --- looking through 25 candidates of size 10 --- looking through 36 candidates of size 11 --- looking through 63 candidates of size 12 --- looking through 133 candidates of size 13 --- looking through 299 candidates of size 14 --- looking through 602 candidates of size 15 --- looking through 1116 candidates of size 16 --- looking through 2031 candidates of size 17 --- tested 2451 candidates -duplicates [] = [] -duplicates (x:xs) = if elem x xs && not (elem x (duplicates xs)) - then x:duplicates xs - else duplicates xs - -positionsFrom :: Int -> A -> [A] -> [Int] --- testing 360 combinations of argument values --- pruning with 5/10 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 5 candidates of size 4 --- looking through 13 candidates of size 5 --- looking through 18 candidates of size 6 --- looking through 47 candidates of size 7 --- looking through 77 candidates of size 8 --- looking through 193 candidates of size 9 --- looking through 293 candidates of size 10 --- looking through 738 candidates of size 11 --- looking through 1173 candidates of size 12 --- looking through 2879 candidates of size 13 --- looking through 4537 candidates of size 14 --- tested 5610 candidates -positionsFrom x y [] = [] -positionsFrom x y (z:xs) = (if y == z then (x :) else id) (positionsFrom (x + 1) y xs) - diff --git a/eg/dupos.txt b/eg/dupos.txt new file mode 100644 --- /dev/null +++ b/eg/dupos.txt @@ -0,0 +1,72 @@ +duplicates :: [Int] -> [Int] +-- testing 6 combinations of argument values +-- pruning with 21/26 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 1 candidates of size 5 +-- looking through 2 candidates of size 6 +-- looking through 3 candidates of size 7 +-- looking through 8 candidates of size 8 +-- looking through 16 candidates of size 9 +-- looking through 25 candidates of size 10 +-- looking through 36 candidates of size 11 +-- looking through 63 candidates of size 12 +-- looking through 133 candidates of size 13 +-- looking through 299 candidates of size 14 +-- looking through 602 candidates of size 15 +-- looking through 1116 candidates of size 16 +-- looking through 2031 candidates of size 17 +-- tested 2450 candidates +duplicates [] = [] +duplicates (x:xs) = if elem x xs && not (elem x (duplicates xs)) + then x:duplicates xs + else duplicates xs + +duplicates :: [Int] -> [Int] +-- pruning with 21/26 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 1 candidates of size 5 +-- looking through 2 candidates of size 6 +-- looking through 3 candidates of size 7 +-- looking through 8 candidates of size 8 +-- looking through 16 candidates of size 9 +-- looking through 25 candidates of size 10 +-- looking through 36 candidates of size 11 +-- looking through 63 candidates of size 12 +-- looking through 133 candidates of size 13 +-- looking through 299 candidates of size 14 +-- looking through 602 candidates of size 15 +-- looking through 1116 candidates of size 16 +-- looking through 2031 candidates of size 17 +-- tested 2450 candidates +duplicates [] = [] +duplicates (x:xs) = if elem x xs && not (elem x (duplicates xs)) + then x:duplicates xs + else duplicates xs + +positionsFrom :: Int -> A -> [A] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 5/10 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 5 candidates of size 4 +-- looking through 9 candidates of size 5 +-- looking through 16 candidates of size 6 +-- looking through 43 candidates of size 7 +-- looking through 73 candidates of size 8 +-- looking through 185 candidates of size 9 +-- looking through 285 candidates of size 10 +-- looking through 722 candidates of size 11 +-- looking through 1157 candidates of size 12 +-- looking through 2847 candidates of size 13 +-- looking through 4505 candidates of size 14 +-- tested 5484 candidates +positionsFrom x y [] = [] +positionsFrom x y (z:xs) = (if y == z then (x :) else id) (positionsFrom (x + 1) y xs) + diff --git a/eg/either.hs b/eg/either.hs new file mode 100644 --- /dev/null +++ b/eg/either.hs @@ -0,0 +1,67 @@ +-- either.hs: conjuring functions over either values +-- +-- Copyright (C) 2024 Rudy Matela +-- Distributed under the 3-Clause BSD licence (see the file LICENSE). +import Conjure + +isLeft' :: Either A A -> Bool +isLeft' (Left 0) = True +isLeft' (Left 1) = True +isLeft' (Right 0) = False +isLeft' (Right 1) = False + +isRight' :: Either A A -> Bool +isRight' (Left 0) = False +isRight' (Left 1) = False +isRight' (Right 0) = True +isRight' (Right 1) = True + +fromLeft' :: A -> Either A A -> A +fromLeft' 0 (Left 1) = 1 +fromLeft' 0 (Left 2) = 2 +fromLeft' 1 (Left 0) = 0 +fromLeft' 0 (Right 1) = 0 +fromLeft' 1 (Right 0) = 1 + +fromRight' :: A -> Either A A -> A +fromRight' 0 (Left 1) = 0 +fromRight' 0 (Left 2) = 0 +fromRight' 1 (Left 0) = 1 +fromRight' 0 (Right 1) = 1 +fromRight' 1 (Right 0) = 0 + +eitherSpec :: ((A -> A) -> (A -> A) -> Either A A -> A) -> Bool +eitherSpec either = and + [ either (+1) (+2) (Left 0) == 1 + , either (+1) (+2) (Right 0) == 2 + , either (*10) (*100) (Left 1) == 10 + , either (*10) (*100) (Right 2) == 200 + ] + +lefts' :: [Either A A] -> [A] +lefts' [] = [] +lefts' [Right 0] = [] +lefts' [Left 0, Right 1] = [0] +lefts' [Right 0, Left 1] = [1] +lefts' [Left 0, Left 1] = [0,1] + +main :: IO () +main = do + conjure "isLeft" isLeft' primitives + conjure "isRight" isRight' primitives + conjure "fromLeft" fromLeft' primitives + conjure "fromLeft" fromRight' primitives + conjureFromSpec "either" eitherSpec primitives + conjure "lefts" lefts' primitives + +primitives :: [Prim] +primitives = + [ prim "Left" (Left :: A -> Either A A) + , prim "Right" (Right :: A -> Either A A) + + , pr False + , pr True + + , pr ([] :: [A]) + , prim ":" ((:) :: A -> [A] -> [A]) + ] diff --git a/eg/either.txt b/eg/either.txt new file mode 100644 --- /dev/null +++ b/eg/either.txt @@ -0,0 +1,54 @@ +isLeft :: Either A A -> Bool +-- testing 4 combinations of argument values +-- pruning with 0/0 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- tested 4 candidates +isLeft (Left x) = True +isLeft (Right x) = False + +isRight :: Either A A -> Bool +-- testing 4 combinations of argument values +-- pruning with 0/0 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- tested 3 candidates +isRight (Left x) = False +isRight (Right x) = True + +fromLeft :: A -> Either A A -> A +-- testing 5 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 3 candidates of size 2 +-- tested 3 candidates +fromLeft x (Left y) = y +fromLeft x (Right y) = x + +fromLeft :: A -> Either A A -> A +-- testing 5 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 3 candidates of size 2 +-- tested 2 candidates +fromLeft x (Left y) = x +fromLeft x (Right y) = y + +either :: (A -> A) -> (A -> A) -> Either A A -> A +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 12 candidates of size 4 +-- tested 11 candidates +either f g (Left x) = f x +either f g (Right x) = g x + +lefts :: [Either A A] -> [A] +-- testing 5 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 1 candidates +cannot conjure + diff --git a/eg/factorial.hs b/eg/factorial.hs --- a/eg/factorial.hs +++ b/eg/factorial.hs @@ -1,6 +1,6 @@ -- factorial.hs: conjuring a factorial function -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/eg/factorial.out b/eg/factorial.out deleted file mode 100644 --- a/eg/factorial.out +++ /dev/null @@ -1,26 +0,0 @@ -factorial :: Int -> Int --- testing 4 combinations of argument values --- pruning with 27/65 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 7 candidates of size 3 --- looking through 13 candidates of size 4 --- looking through 35 candidates of size 5 --- looking through 61 candidates of size 6 --- looking through 219 candidates of size 7 --- tested 153 candidates -factorial 0 = 1 -factorial x = x * factorial (x - 1) - -factorial :: Int -> Int --- testing 4 combinations of argument values --- pruning with 32/72 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 7 candidates of size 3 --- looking through 13 candidates of size 4 --- looking through 35 candidates of size 5 --- looking through 101 candidates of size 6 --- tested 89 candidates -factorial x = foldr (*) 1 [1..x] - diff --git a/eg/factorial.txt b/eg/factorial.txt new file mode 100644 --- /dev/null +++ b/eg/factorial.txt @@ -0,0 +1,26 @@ +factorial :: Int -> Int +-- testing 4 combinations of argument values +-- pruning with 27/65 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 7 candidates of size 3 +-- looking through 8 candidates of size 4 +-- looking through 28 candidates of size 5 +-- looking through 35 candidates of size 6 +-- looking through 179 candidates of size 7 +-- tested 95 candidates +factorial 0 = 1 +factorial x = x * factorial (x - 1) + +factorial :: Int -> Int +-- testing 4 combinations of argument values +-- pruning with 32/72 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 7 candidates of size 3 +-- looking through 8 candidates of size 4 +-- looking through 28 candidates of size 5 +-- looking through 75 candidates of size 6 +-- tested 74 candidates +factorial x = foldr (*) 1 [1..x] + diff --git a/eg/fib01.out b/eg/fib01.out deleted file mode 100644 --- a/eg/fib01.out +++ /dev/null @@ -1,27 +0,0 @@ -fib01 :: Int -> Int -> Int -> Int --- testing 8 combinations of argument values --- pruning with 6/10 rules --- looking through 4 candidates of size 1 --- looking through 24 candidates of size 2 --- looking through 115 candidates of size 3 --- looking through 470 candidates of size 4 --- looking through 1657 candidates of size 5 --- tested 2270 candidates -cannot conjure - -fib01 :: Int -> Int -> Int -> Int --- testing 8 combinations of argument values --- pruning with 18/37 rules --- looking through 4 candidates of size 1 --- looking through 4 candidates of size 2 --- looking through 10 candidates of size 3 --- looking through 16 candidates of size 4 --- looking through 44 candidates of size 5 --- looking through 92 candidates of size 6 --- looking through 234 candidates of size 7 --- looking through 544 candidates of size 8 --- looking through 1332 candidates of size 9 --- looking through 7796 candidates of size 10 --- tested 10076 candidates -cannot conjure - diff --git a/eg/fib01.txt b/eg/fib01.txt new file mode 100644 --- /dev/null +++ b/eg/fib01.txt @@ -0,0 +1,27 @@ +fib01 :: Int -> Int -> Int -> Int +-- testing 8 combinations of argument values +-- pruning with 6/10 rules +-- looking through 4 candidates of size 1 +-- looking through 27 candidates of size 2 +-- looking through 117 candidates of size 3 +-- looking through 464 candidates of size 4 +-- looking through 1564 candidates of size 5 +-- tested 2176 candidates +cannot conjure + +fib01 :: Int -> Int -> Int -> Int +-- testing 8 combinations of argument values +-- pruning with 18/37 rules +-- looking through 4 candidates of size 1 +-- looking through 4 candidates of size 2 +-- looking through 10 candidates of size 3 +-- looking through 16 candidates of size 4 +-- looking through 44 candidates of size 5 +-- looking through 92 candidates of size 6 +-- looking through 234 candidates of size 7 +-- looking through 544 candidates of size 8 +-- looking through 1332 candidates of size 9 +-- looking through 10676 candidates of size 10 +-- tested 12956 candidates +cannot conjure + diff --git a/eg/fibonacci.out b/eg/fibonacci.out deleted file mode 100644 --- a/eg/fibonacci.out +++ /dev/null @@ -1,20 +0,0 @@ -fibonacci :: Int -> Int --- testing 7 combinations of argument values --- pruning with 21/44 rules --- looking through 4 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 9 candidates of size 3 --- looking through 11 candidates of size 4 --- looking through 34 candidates of size 5 --- looking through 41 candidates of size 6 --- looking through 187 candidates of size 7 --- looking through 204 candidates of size 8 --- looking through 957 candidates of size 9 --- looking through 1059 candidates of size 10 --- looking through 5295 candidates of size 11 --- looking through 6052 candidates of size 12 --- tested 8126 candidates -fibonacci 0 = 1 -fibonacci 1 = 1 -fibonacci x = fibonacci (x - 1) + fibonacci (x - 2) - diff --git a/eg/fibonacci.txt b/eg/fibonacci.txt new file mode 100644 --- /dev/null +++ b/eg/fibonacci.txt @@ -0,0 +1,20 @@ +fibonacci :: Int -> Int +-- testing 7 combinations of argument values +-- pruning with 21/44 rules +-- looking through 4 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 9 candidates of size 3 +-- looking through 9 candidates of size 4 +-- looking through 30 candidates of size 5 +-- looking through 30 candidates of size 6 +-- looking through 156 candidates of size 7 +-- looking through 157 candidates of size 8 +-- looking through 813 candidates of size 9 +-- looking through 797 candidates of size 10 +-- looking through 4449 candidates of size 11 +-- looking through 4438 candidates of size 12 +-- tested 6539 candidates +fibonacci 0 = 1 +fibonacci 1 = 1 +fibonacci x = fibonacci (x - 1) + fibonacci (x - 2) + diff --git a/eg/gcd.hs b/eg/gcd.hs --- a/eg/gcd.hs +++ b/eg/gcd.hs @@ -1,6 +1,6 @@ -- gcd.hs: conjuring a GCD implementation -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/eg/gcd.out b/eg/gcd.out deleted file mode 100644 --- a/eg/gcd.out +++ /dev/null @@ -1,13 +0,0 @@ -gcd :: Int -> Int -> Int --- testing 11 combinations of argument values --- pruning with 0/0 rules --- looking through 3 candidates of size 1 --- looking through 5 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 50 candidates of size 4 --- looking through 98 candidates of size 5 --- looking through 359 candidates of size 6 --- tested 171 candidates -gcd x 0 = x -gcd x y = gcd y (x `mod` y) - diff --git a/eg/gcd.txt b/eg/gcd.txt new file mode 100644 --- /dev/null +++ b/eg/gcd.txt @@ -0,0 +1,13 @@ +gcd :: Int -> Int -> Int +-- testing 11 combinations of argument values +-- pruning with 0/0 rules +-- looking through 3 candidates of size 1 +-- looking through 6 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 50 candidates of size 4 +-- looking through 98 candidates of size 5 +-- looking through 344 candidates of size 6 +-- tested 173 candidates +gcd x 0 = x +gcd x y = gcd y (x `mod` y) + diff --git a/eg/higher.hs b/eg/higher.hs --- a/eg/higher.hs +++ b/eg/higher.hs @@ -9,8 +9,6 @@ && (abs $ (-2)) == 2 && (negate $ 1) == -1 --- composeSpec :: ((Int->Int) -> (Int->Int) -> Int->Int) -> - composeSpec :: ((Int->Int) -> (Int->Int) -> Int->Int) -> Bool composeSpec (.) = ((*2) . (*3)) 1 == 6 && (abs . negate) 7 == 7 diff --git a/eg/higher.out b/eg/higher.out deleted file mode 100644 --- a/eg/higher.out +++ /dev/null @@ -1,69 +0,0 @@ -($) :: (Int -> Int) -> Int -> Int --- pruning with 3/3 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- tested 2 candidates -f $ x = f x - -(.) :: (Int -> Int) -> (Int -> Int) -> Int -> Int --- pruning with 3/3 rules --- looking through 1 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 4 candidates of size 3 --- tested 5 candidates -(f . g) x = f (g x) - -flip :: (Int -> Int -> Int) -> Int -> Int -> Int --- pruning with 3/3 rules --- looking through 2 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 4 candidates of size 3 --- tested 5 candidates -flip f x y = f y x - -map :: (Int -> Int) -> [Int] -> [Int] --- pruning with 3/3 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 6 candidates of size 6 --- looking through 9 candidates of size 7 --- tested 17 candidates -map f [] = [] -map f (x:xs) = f x:map f xs - -fold :: (Int -> Int -> Int) -> Int -> [Int] -> Int --- pruning with 3/3 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 4 candidates of size 5 --- looking through 23 candidates of size 6 --- looking through 26 candidates of size 7 --- tested 45 candidates -fold f x [] = x -fold f x (y:xs) = fold f (f x y) xs - -filter :: (Int -> Bool) -> [Int] -> [Int] --- pruning with 3/3 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 6 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 22 candidates of size 8 --- looking through 0 candidates of size 9 --- looking through 65 candidates of size 10 --- looking through 0 candidates of size 11 --- looking through 219 candidates of size 12 --- tested 166 candidates -filter f [] = [] -filter f (x:xs) = if f x - then x:filter f xs - else filter f xs - diff --git a/eg/higher.txt b/eg/higher.txt new file mode 100644 --- /dev/null +++ b/eg/higher.txt @@ -0,0 +1,69 @@ +($) :: (Int -> Int) -> Int -> Int +-- pruning with 3/3 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- tested 2 candidates +f $ x = f x + +(.) :: (Int -> Int) -> (Int -> Int) -> Int -> Int +-- pruning with 3/3 rules +-- looking through 1 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 4 candidates of size 3 +-- tested 5 candidates +(f . g) x = f (g x) + +flip :: (Int -> Int -> Int) -> Int -> Int -> Int +-- pruning with 3/3 rules +-- looking through 2 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 4 candidates of size 3 +-- tested 5 candidates +flip f x y = f y x + +map :: (Int -> Int) -> [Int] -> [Int] +-- pruning with 3/3 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 7 candidates of size 7 +-- tested 13 candidates +map f [] = [] +map f (x:xs) = f x:map f xs + +fold :: (Int -> Int -> Int) -> Int -> [Int] -> Int +-- pruning with 3/3 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 4 candidates of size 5 +-- looking through 23 candidates of size 6 +-- looking through 19 candidates of size 7 +-- tested 38 candidates +fold f x [] = x +fold f x (y:xs) = fold f (f x y) xs + +filter :: (Int -> Bool) -> [Int] -> [Int] +-- pruning with 3/3 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 17 candidates of size 8 +-- looking through 0 candidates of size 9 +-- looking through 44 candidates of size 10 +-- looking through 0 candidates of size 11 +-- looking through 142 candidates of size 12 +-- tested 72 candidates +filter f [] = [] +filter f (x:xs) = if f x + then x:filter f xs + else filter f xs + diff --git a/eg/id.out b/eg/id.out deleted file mode 100644 --- a/eg/id.out +++ /dev/null @@ -1,14 +0,0 @@ -id :: Int -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 1 candidates of size 1 --- tested 1 candidates -id x = x - -const :: Int -> Int -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 2 candidates of size 1 --- tested 1 candidates -const x y = x - diff --git a/eg/id.txt b/eg/id.txt new file mode 100644 --- /dev/null +++ b/eg/id.txt @@ -0,0 +1,14 @@ +id :: Int -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- tested 1 candidates +id x = x + +const :: Int -> Int -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 2 candidates of size 1 +-- tested 1 candidates +const x y = x + diff --git a/eg/ints.hs b/eg/ints.hs --- a/eg/ints.hs +++ b/eg/ints.hs @@ -1,6 +1,6 @@ -- ints.hs: conjuring functions over lists of ints -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/eg/ints.out b/eg/ints.out deleted file mode 100644 --- a/eg/ints.out +++ /dev/null @@ -1,63 +0,0 @@ -second :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- tested 2 candidates -second xs = head (tail xs) - -third :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 1 candidates of size 4 --- tested 3 candidates -third xs = head (tail (tail xs)) - -sum :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 14/25 rules --- looking through 2 candidates of size 1 --- looking through 4 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 6 candidates of size 5 --- tested 15 candidates -sum [] = 0 -sum (x:xs) = x + sum xs - -product :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 14/25 rules --- looking through 2 candidates of size 1 --- looking through 4 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 6 candidates of size 5 --- tested 20 candidates -product [] = 1 -product (x:xs) = x * product xs - -sum :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 15/26 rules --- looking through 2 candidates of size 1 --- looking through 4 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 9 candidates of size 4 --- tested 9 candidates -sum xs = foldr (+) 0 xs - -product :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 15/26 rules --- looking through 2 candidates of size 1 --- looking through 4 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 9 candidates of size 4 --- tested 11 candidates -product xs = foldr (*) 1 xs - diff --git a/eg/ints.txt b/eg/ints.txt new file mode 100644 --- /dev/null +++ b/eg/ints.txt @@ -0,0 +1,63 @@ +second :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- tested 2 candidates +second xs = head (tail xs) + +third :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- tested 3 candidates +third xs = head (tail (tail xs)) + +sum :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 14/25 rules +-- looking through 2 candidates of size 1 +-- looking through 4 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 6 candidates of size 5 +-- tested 13 candidates +sum [] = 0 +sum (x:xs) = x + sum xs + +product :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 14/25 rules +-- looking through 2 candidates of size 1 +-- looking through 4 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 6 candidates of size 5 +-- tested 18 candidates +product [] = 1 +product (x:xs) = x * product xs + +sum :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 15/26 rules +-- looking through 2 candidates of size 1 +-- looking through 4 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 9 candidates of size 4 +-- tested 7 candidates +sum xs = foldr (+) 0 xs + +product :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 15/26 rules +-- looking through 2 candidates of size 1 +-- looking through 4 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 9 candidates of size 4 +-- tested 9 candidates +product xs = foldr (*) 1 xs + diff --git a/eg/list.hs b/eg/list.hs --- a/eg/list.hs +++ b/eg/list.hs @@ -1,6 +1,6 @@ -- list.hs: conjuring functions over lists (of ints) -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure @@ -58,6 +58,11 @@ zip' [x,y] [a,b] = [(x,a),(y,b)] zip' [x,y,z] [a,b,c] = [(x,a),(y,b),(z,c)] +last' :: [Int] -> Int +last' [x] = x +last' [x,y] = y +last' [x,y,z] = z + main :: IO () main = do conjure "length" length' @@ -81,6 +86,14 @@ [ pr ([] :: [Int]) , prim ":" ((:) :: Int -> [Int] -> [Int]) , prim "foldr" (foldr :: (Int -> [Int] -> [Int]) -> [Int] -> [Int] -> [Int]) + ] + + conjure "last" last' + [ pr ([] :: [Int]) + , prim ":" ((:) :: Int -> [Int] -> [Int]) + , prim "null" (null :: [Int] -> Bool) + , prif (undefined :: Int) + , prim "undefined" (undefined :: Int) ] conjure "zip" (zip') diff --git a/eg/list.out b/eg/list.out deleted file mode 100644 --- a/eg/list.out +++ /dev/null @@ -1,115 +0,0 @@ -length :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 4/8 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 2 candidates of size 5 --- tested 9 candidates -length [] = 0 -length (x:xs) = length xs + 1 - -reverse :: [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 4/4 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 4 candidates of size 5 --- looking through 7 candidates of size 6 --- looking through 10 candidates of size 7 --- tested 27 candidates -reverse [] = [] -reverse (x:xs) = reverse xs ++ [x] - -(++) :: [Int] -> [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 3 candidates of size 1 --- looking through 7 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 37 candidates of size 4 --- looking through 98 candidates of size 5 --- looking through 94 candidates of size 6 --- tested 194 candidates -[] ++ xs = xs -(x:xs) ++ ys = x:(xs ++ ys) - -(++) :: [Int] -> [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 2/2 rules --- looking through 3 candidates of size 1 --- looking through 7 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 41 candidates of size 4 --- tested 48 candidates -xs ++ ys = foldr (:) ys xs - -zip :: [Int] -> [Int] -> [(Int,Int)] --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 8 candidates of size 4 --- looking through 6 candidates of size 5 --- looking through 2 candidates of size 6 --- looking through 14 candidates of size 7 --- looking through 9 candidates of size 8 --- looking through 31 candidates of size 9 --- tested 50 candidates -zip [] xs = [] -zip (x:xs) [] = [] -zip (x:xs) (y:ys) = (x,y):zip xs ys - -(\/) :: [Int] -> [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 3 candidates of size 1 --- looking through 7 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 37 candidates of size 4 --- looking through 98 candidates of size 5 --- looking through 94 candidates of size 6 --- tested 196 candidates -[] \/ xs = xs -(x:xs) \/ ys = x:ys \/ xs - -ordered :: [Int] -> Bool --- testing 360 combinations of argument values --- pruning with 29/39 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 4 candidates of size 5 --- looking through 12 candidates of size 6 --- looking through 20 candidates of size 7 --- looking through 30 candidates of size 8 --- looking through 56 candidates of size 9 --- looking through 114 candidates of size 10 --- looking through 216 candidates of size 11 --- tested 333 candidates -ordered [] = True -ordered (x:xs) = ordered xs && (null xs || x <= head xs) - -merge :: [Int] -> [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 1/2 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 12 candidates of size 4 --- looking through 22 candidates of size 5 --- looking through 32 candidates of size 6 --- looking through 75 candidates of size 7 --- looking through 108 candidates of size 8 --- looking through 256 candidates of size 9 --- looking through 520 candidates of size 10 --- looking through 1329 candidates of size 11 --- looking through 2632 candidates of size 12 --- tested 4992 candidates -cannot conjure - diff --git a/eg/list.txt b/eg/list.txt new file mode 100644 --- /dev/null +++ b/eg/list.txt @@ -0,0 +1,131 @@ +length :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 4/8 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 2 candidates of size 5 +-- tested 8 candidates +length [] = 0 +length (x:xs) = length xs + 1 + +reverse :: [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 4/4 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 4 candidates of size 5 +-- looking through 7 candidates of size 6 +-- looking through 10 candidates of size 7 +-- tested 26 candidates +reverse [] = [] +reverse (x:xs) = reverse xs ++ [x] + +(++) :: [Int] -> [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 3 candidates of size 1 +-- looking through 8 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 23 candidates of size 4 +-- looking through 86 candidates of size 5 +-- looking through 72 candidates of size 6 +-- tested 149 candidates +[] ++ xs = xs +(x:xs) ++ ys = x:(xs ++ ys) + +(++) :: [Int] -> [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 2/2 rules +-- looking through 3 candidates of size 1 +-- looking through 8 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 27 candidates of size 4 +-- tested 35 candidates +xs ++ ys = foldr (:) ys xs + +last :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 5/5 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 2 candidates of size 6 +-- looking through 4 candidates of size 7 +-- tested 5 candidates +last [] = undefined +last (x:xs) = if null xs + then x + else last xs + +zip :: [Int] -> [Int] -> [(Int,Int)] +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 2 candidates of size 6 +-- looking through 6 candidates of size 7 +-- looking through 6 candidates of size 8 +-- looking through 30 candidates of size 9 +-- tested 25 candidates +zip [] xs = [] +zip (x:xs) [] = [] +zip (x:xs) (y:ys) = (x,y):zip xs ys + +(\/) :: [Int] -> [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 3 candidates of size 1 +-- looking through 8 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 23 candidates of size 4 +-- looking through 86 candidates of size 5 +-- looking through 72 candidates of size 6 +-- tested 151 candidates +[] \/ xs = xs +(x:xs) \/ ys = x:ys \/ xs + +ordered :: [Int] -> Bool +-- testing 360 combinations of argument values +-- pruning with 29/39 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 4 candidates of size 5 +-- looking through 12 candidates of size 6 +-- looking through 20 candidates of size 7 +-- looking through 30 candidates of size 8 +-- looking through 56 candidates of size 9 +-- looking through 114 candidates of size 10 +-- looking through 216 candidates of size 11 +-- tested 331 candidates +ordered [] = True +ordered (x:xs) = ordered xs && (null xs || x <= head xs) + +merge :: [Int] -> [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 1/2 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 21 candidates of size 5 +-- looking through 26 candidates of size 6 +-- looking through 61 candidates of size 7 +-- looking through 92 candidates of size 8 +-- looking through 203 candidates of size 9 +-- looking through 430 candidates of size 10 +-- looking through 1086 candidates of size 11 +-- looking through 2068 candidates of size 12 +-- tested 4004 candidates +cannot conjure + diff --git a/eg/maybe.hs b/eg/maybe.hs new file mode 100644 --- /dev/null +++ b/eg/maybe.hs @@ -0,0 +1,84 @@ +-- maybe.hs: conjuring functions over maybe values +-- +-- Copyright (C) 2024 Rudy Matela +-- Distributed under the 3-Clause BSD licence (see the file LICENSE). +import Conjure + +isNothing' :: Maybe A -> Bool +isNothing' Nothing = True +isNothing' (Just 0) = False +isNothing' (Just 1) = False + +isJust' :: Maybe A -> Bool +isJust' Nothing = False +isJust' (Just 0) = True +isJust' (Just 1) = True + +fromMaybe' :: A -> Maybe A -> A +fromMaybe' 0 Nothing = 0 +fromMaybe' 1 Nothing = 1 +fromMaybe' 0 (Just 1) = 1 +fromMaybe' 1 (Just 2) = 2 + +maybeSpec :: (A -> (A -> A) -> Maybe A -> A) -> Bool +maybeSpec maybe = and + [ maybe 0 undefined Nothing == 0 + , maybe 1 undefined Nothing == 1 + , maybe undefined (+1) (Just 1) == 2 + , maybe undefined (*2) (Just 3) == 6 + ] + +listToMaybe' :: [A] -> Maybe A +listToMaybe' [] = Nothing +listToMaybe' [2] = Just 2 +listToMaybe' [0,1] = Just 0 +listToMaybe' [1,0] = Just 1 + +maybeToList' :: Maybe A -> [A] +maybeToList' Nothing = [] +maybeToList' (Just 0) = [0] +maybeToList' (Just 1) = [1] +maybeToList' (Just 2) = [2] + +catMaybes' :: [Maybe A] -> [A] +catMaybes' [] = [] +catMaybes' [Nothing] = [] +catMaybes' [Just x] = [x] +catMaybes' [Just x, Nothing, Just y] = [x,y] + +main :: IO () +main = do + conjure "isNothing" isNothing' primitives + conjure "isJust" isJust' primitives + conjure "fromMaybe" fromMaybe' primitives + conjureFromSpec "maybe" maybeSpec primitives + conjure "listToMaybe" listToMaybe' primitives + conjure "maybeToList" maybeToList' primitives + + -- only top-level break downs, so would need morePrimitives + conjure "catMaybes" catMaybes' primitives + -- conjure "mapMaybe" mapMaybe' primitives -- same + +primitives :: [Prim] +primitives = + [ pr (Nothing :: Maybe A) + , prim "Just" (Just :: A -> Maybe A) + + , pr False + , pr True + + , pr ([] :: [A]) + , prim ":" ((:) :: A -> [A] -> [A]) + ] + +{- +morePrimitives :: [Prim] +morePrimitives = primitives ++ + [ prim "isNothing" (isNothing :: Maybe A -> Bool) + , prim "isJust" (isJust :: Maybe A -> Bool) + , prim "fromJust" (fromJust :: Maybe A -> A) + , prif (undefined :: A) + , prif (undefined :: Maybe A) + , prif (undefined :: [A]) + ] +-} diff --git a/eg/maybe.txt b/eg/maybe.txt new file mode 100644 --- /dev/null +++ b/eg/maybe.txt @@ -0,0 +1,65 @@ +isNothing :: Maybe A -> Bool +-- testing 3 combinations of argument values +-- pruning with 0/0 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- tested 3 candidates +isNothing Nothing = True +isNothing (Just x) = False + +isJust :: Maybe A -> Bool +-- testing 3 combinations of argument values +-- pruning with 0/0 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- tested 3 candidates +isJust Nothing = False +isJust (Just x) = True + +fromMaybe :: A -> Maybe A -> A +-- testing 4 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- tested 2 candidates +fromMaybe x Nothing = x +fromMaybe x (Just y) = y + +maybe :: A -> (A -> A) -> Maybe A -> A +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 5 candidates of size 3 +-- tested 6 candidates +maybe x f Nothing = x +maybe x f (Just y) = f y + +listToMaybe :: [A] -> Maybe A +-- testing 4 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- tested 2 candidates +listToMaybe [] = Nothing +listToMaybe (x:xs) = Just x + +maybeToList :: Maybe A -> [A] +-- testing 4 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- tested 2 candidates +maybeToList Nothing = [] +maybeToList (Just x) = [x] + +catMaybes :: [Maybe A] -> [A] +-- testing 44 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- tested 1 candidates +cannot conjure + diff --git a/eg/oddeven.hs b/eg/oddeven.hs new file mode 100644 --- /dev/null +++ b/eg/oddeven.hs @@ -0,0 +1,52 @@ +-- oddeven.hs: conjuring even and odd from two sets of primitives +-- +-- Copyright (C) 2024 Rudy Matela +-- Distributed under the 3-Clause BSD licence (see the file LICENSE). +import Conjure +import Prelude hiding (odd, even) + +odd :: Int -> Bool +odd 0 = False +odd 1 = True +odd 2 = False +odd 3 = True +odd 4 = False +odd 5 = True + +even :: Int -> Bool +even 0 = True +even 1 = False +even 2 = True +even 3 = False +even 4 = True +even 5 = False + +main :: IO () +main = do + conjure "odd" odd primitives1 + conjure "even" even primitives1 + conjure "odd" odd primitives2 + conjure "even" even primitives2 + +primitives1 :: [Prim] +primitives1 = + [ pr (0::Int) + , pr (1::Int) + , pr (2::Int) + , prim "+" ((+) :: Int -> Int -> Int) + + , prim "-" ((-) :: Int -> Int -> Int) + , pr False + , pr True + ] + +primitives2 :: [Prim] +primitives2 = + [ pr (0::Int) + , pr (1::Int) + , pr (2::Int) + , prim "+" ((+) :: Int -> Int -> Int) + + , prim "`mod`" (mod :: Int -> Int -> Int) + , prim "==" ((==) :: Int -> Int -> Bool) + ] diff --git a/eg/oddeven.txt b/eg/oddeven.txt new file mode 100644 --- /dev/null +++ b/eg/oddeven.txt @@ -0,0 +1,52 @@ +odd :: Int -> Bool +-- testing 6 combinations of argument values +-- pruning with 21/44 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 1 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 2 candidates of size 7 +-- tested 8 candidates +odd 0 = False +odd 1 = True +odd x = odd (x - 2) + +even :: Int -> Bool +-- testing 6 combinations of argument values +-- pruning with 21/44 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 1 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 2 candidates of size 7 +-- tested 8 candidates +even 0 = True +even 1 = False +even x = even (x - 2) + +odd :: Int -> Bool +-- testing 6 combinations of argument values +-- pruning with 36/55 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 50 candidates of size 5 +-- tested 35 candidates +odd x = 1 == x `mod` 2 + +even :: Int -> Bool +-- testing 6 combinations of argument values +-- pruning with 36/55 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 49 candidates of size 5 +-- tested 26 candidates +even x = 0 == x `mod` 2 + diff --git a/eg/pow.hs b/eg/pow.hs --- a/eg/pow.hs +++ b/eg/pow.hs @@ -1,6 +1,6 @@ -- pow.hs: conjuring exponentiation -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure diff --git a/eg/pow.out b/eg/pow.out deleted file mode 100644 --- a/eg/pow.out +++ /dev/null @@ -1,27 +0,0 @@ -pow :: Int -> Int -> Int --- testing 5 combinations of argument values --- pruning with 14/30 rules --- looking through 4 candidates of size 1 --- looking through 15 candidates of size 2 --- looking through 45 candidates of size 3 --- looking through 168 candidates of size 4 --- looking through 491 candidates of size 5 --- looking through 1729 candidates of size 6 --- looking through 5420 candidates of size 7 --- looking through 17952 candidates of size 8 --- tested 8593 candidates -pow x 0 = 1 -pow x y = x * pow x (y - 1) - -pow :: Int -> Int -> Int --- testing 5 combinations of argument values --- pruning with 15/19 rules --- looking through 4 candidates of size 1 --- looking through 17 candidates of size 2 --- looking through 59 candidates of size 3 --- looking through 190 candidates of size 4 --- looking through 594 candidates of size 5 --- looking through 1784 candidates of size 6 --- tested 2648 candidates -cannot conjure - diff --git a/eg/pow.txt b/eg/pow.txt new file mode 100644 --- /dev/null +++ b/eg/pow.txt @@ -0,0 +1,27 @@ +pow :: Int -> Int -> Int +-- testing 5 combinations of argument values +-- pruning with 14/30 rules +-- looking through 4 candidates of size 1 +-- looking through 16 candidates of size 2 +-- looking through 46 candidates of size 3 +-- looking through 159 candidates of size 4 +-- looking through 433 candidates of size 5 +-- looking through 1382 candidates of size 6 +-- looking through 4156 candidates of size 7 +-- looking through 13406 candidates of size 8 +-- tested 6403 candidates +pow x 0 = 1 +pow x y = x * pow x (y - 1) + +pow :: Int -> Int -> Int +-- testing 5 combinations of argument values +-- pruning with 15/19 rules +-- looking through 4 candidates of size 1 +-- looking through 18 candidates of size 2 +-- looking through 58 candidates of size 3 +-- looking through 174 candidates of size 4 +-- looking through 485 candidates of size 5 +-- looking through 1387 candidates of size 6 +-- tested 2126 candidates +cannot conjure + diff --git a/eg/replicate.hs b/eg/replicate.hs --- a/eg/replicate.hs +++ b/eg/replicate.hs @@ -1,6 +1,6 @@ -- replicate.hs: replicate and other functions -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure import Data.List (transpose) diff --git a/eg/replicate.out b/eg/replicate.out deleted file mode 100644 --- a/eg/replicate.out +++ /dev/null @@ -1,52 +0,0 @@ -replicate :: Int -> Char -> [Char] --- testing 360 combinations of argument values --- pruning with 4/7 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 4 candidates of size 5 --- looking through 6 candidates of size 6 --- looking through 8 candidates of size 7 --- looking through 19 candidates of size 8 --- tested 33 candidates -replicate 0 c = "" -replicate x c = c:replicate (x - 1) c - -replicates :: [Char] -> Int -> [Char] --- testing 360 combinations of argument values --- pruning with 2/2 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 1 candidates of size 5 --- tested 3 candidates -replicates cs x = concat (transpose (replicate x cs)) - -replicates :: [Char] -> Int -> [Char] --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 1 candidates of size 5 --- tested 2 candidates -replicates cs x = concat (map (replicate x) cs) - -replicates :: [Char] -> Int -> [Char] --- testing 360 combinations of argument values --- pruning with 9/14 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 7 candidates of size 3 --- looking through 23 candidates of size 4 --- looking through 62 candidates of size 5 --- looking through 155 candidates of size 6 --- looking through 446 candidates of size 7 --- looking through 1231 candidates of size 8 --- tested 751 candidates -replicates "" x = "" -replicates (c:cs) x = replicate x c ++ replicates cs x - diff --git a/eg/replicate.txt b/eg/replicate.txt new file mode 100644 --- /dev/null +++ b/eg/replicate.txt @@ -0,0 +1,52 @@ +replicate :: Int -> Char -> [Char] +-- testing 360 combinations of argument values +-- pruning with 4/7 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 3 candidates of size 5 +-- looking through 2 candidates of size 6 +-- looking through 3 candidates of size 7 +-- looking through 3 candidates of size 8 +-- tested 12 candidates +replicate 0 c = "" +replicate x c = c:replicate (x - 1) c + +replicates :: [Char] -> Int -> [Char] +-- testing 360 combinations of argument values +-- pruning with 2/2 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 1 candidates of size 5 +-- tested 3 candidates +replicates cs x = concat (transpose (replicate x cs)) + +replicates :: [Char] -> Int -> [Char] +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 1 candidates of size 5 +-- tested 2 candidates +replicates cs x = concat (map (replicate x) cs) + +replicates :: [Char] -> Int -> [Char] +-- testing 360 combinations of argument values +-- pruning with 9/14 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 7 candidates of size 3 +-- looking through 22 candidates of size 4 +-- looking through 59 candidates of size 5 +-- looking through 152 candidates of size 6 +-- looking through 442 candidates of size 7 +-- looking through 1223 candidates of size 8 +-- tested 736 candidates +replicates "" x = "" +replicates (c:cs) x = replicate x c ++ replicates cs x + diff --git a/eg/setelem.out b/eg/setelem.out deleted file mode 100644 --- a/eg/setelem.out +++ /dev/null @@ -1,30 +0,0 @@ -elem :: Int -> [Int] -> Bool --- testing 360 combinations of argument values --- pruning with 44/57 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 20 candidates of size 4 --- looking through 48 candidates of size 5 --- looking through 75 candidates of size 6 --- looking through 149 candidates of size 7 --- looking through 368 candidates of size 8 --- tested 396 candidates -elem x [] = False -elem x (y:xs) = elem x xs || x == y - -set :: [Int] -> Bool --- testing 360 combinations of argument values --- pruning with 46/57 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 11 candidates of size 4 --- looking through 20 candidates of size 5 --- looking through 41 candidates of size 6 --- looking through 100 candidates of size 7 --- looking through 234 candidates of size 8 --- tested 200 candidates -set [] = True -set (x:xs) = set xs && not (elem x xs) - diff --git a/eg/setelem.txt b/eg/setelem.txt new file mode 100644 --- /dev/null +++ b/eg/setelem.txt @@ -0,0 +1,30 @@ +elem :: Int -> [Int] -> Bool +-- testing 360 combinations of argument values +-- pruning with 44/57 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 5 candidates of size 3 +-- looking through 16 candidates of size 4 +-- looking through 38 candidates of size 5 +-- looking through 67 candidates of size 6 +-- looking through 134 candidates of size 7 +-- looking through 345 candidates of size 8 +-- tested 340 candidates +elem x [] = False +elem x (y:xs) = elem x xs || x == y + +set :: [Int] -> Bool +-- testing 360 combinations of argument values +-- pruning with 46/57 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 20 candidates of size 5 +-- looking through 41 candidates of size 6 +-- looking through 100 candidates of size 7 +-- looking through 234 candidates of size 8 +-- tested 198 candidates +set [] = True +set (x:xs) = set xs && not (elem x xs) + diff --git a/eg/sort.hs b/eg/sort.hs --- a/eg/sort.hs +++ b/eg/sort.hs @@ -1,6 +1,6 @@ -- sort.hs: conjuring a sort function -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure import Data.List (insert, sort) diff --git a/eg/sort.out b/eg/sort.out deleted file mode 100644 --- a/eg/sort.out +++ /dev/null @@ -1,61 +0,0 @@ -sort :: [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 6/7 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 12 candidates of size 4 --- looking through 23 candidates of size 5 --- tested 24 candidates -sort [] = [] -sort (x:xs) = insert x (sort xs) - -sort :: [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 1/2 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 1 candidates of size 3 --- looking through 4 candidates of size 4 --- tested 6 candidates -sort xs = foldr insert [] xs - -qsort :: [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 8/8 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 3 candidates of size 4 --- looking through 6 candidates of size 5 --- looking through 9 candidates of size 6 --- looking through 22 candidates of size 7 --- looking through 37 candidates of size 8 --- looking through 84 candidates of size 9 --- looking through 169 candidates of size 10 --- looking through 352 candidates of size 11 --- looking through 767 candidates of size 12 --- looking through 1600 candidates of size 13 --- looking through 3499 candidates of size 14 --- tested 3668 candidates -qsort [] = [] -qsort (x:xs) = filter (x >) (qsort xs) ++ (x:filter (x <=) (qsort xs)) - -merge :: [Int] -> [Int] -> [Int] --- testing 360 combinations of argument values --- pruning with 4/4 rules --- looking through 3 candidates of size 1 --- looking through 7 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 37 candidates of size 4 --- looking through 98 candidates of size 5 --- looking through 94 candidates of size 6 --- looking through 383 candidates of size 7 --- looking through 375 candidates of size 8 --- looking through 1263 candidates of size 9 --- looking through 2252 candidates of size 10 --- looking through 4090 candidates of size 11 --- looking through 13481 candidates of size 12 --- tested 22094 candidates -cannot conjure - diff --git a/eg/sort.txt b/eg/sort.txt new file mode 100644 --- /dev/null +++ b/eg/sort.txt @@ -0,0 +1,61 @@ +sort :: [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 6/7 rules +-- looking through 2 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 4 candidates of size 3 +-- looking through 11 candidates of size 4 +-- looking through 23 candidates of size 5 +-- tested 22 candidates +sort [] = [] +sort (x:xs) = insert x (sort xs) + +sort :: [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 1/2 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 4 candidates of size 4 +-- tested 5 candidates +sort xs = foldr insert [] xs + +qsort :: [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 8/8 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 1 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 6 candidates of size 5 +-- looking through 9 candidates of size 6 +-- looking through 22 candidates of size 7 +-- looking through 37 candidates of size 8 +-- looking through 84 candidates of size 9 +-- looking through 169 candidates of size 10 +-- looking through 352 candidates of size 11 +-- looking through 767 candidates of size 12 +-- looking through 1600 candidates of size 13 +-- looking through 3499 candidates of size 14 +-- tested 3667 candidates +qsort [] = [] +qsort (x:xs) = filter (x >) (qsort xs) ++ (x:filter (x <=) (qsort xs)) + +merge :: [Int] -> [Int] -> [Int] +-- testing 360 combinations of argument values +-- pruning with 4/4 rules +-- looking through 3 candidates of size 1 +-- looking through 8 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 23 candidates of size 4 +-- looking through 86 candidates of size 5 +-- looking through 72 candidates of size 6 +-- looking through 297 candidates of size 7 +-- looking through 322 candidates of size 8 +-- looking through 939 candidates of size 9 +-- looking through 1966 candidates of size 10 +-- looking through 2972 candidates of size 11 +-- looking through 11011 candidates of size 12 +-- tested 17710 candidates +cannot conjure + diff --git a/eg/spec.out b/eg/spec.out deleted file mode 100644 --- a/eg/spec.out +++ /dev/null @@ -1,39 +0,0 @@ -square :: Int -> Int --- pruning with 14/25 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 6 candidates of size 3 --- tested 9 candidates -square x = x * x - -square :: Int -> Int --- pruning with 14/25 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 6 candidates of size 3 --- tested 9 candidates -square x = x * x - -sum :: [Int] -> Int --- pruning with 4/8 rules --- looking through 1 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 3 candidates of size 3 --- looking through 4 candidates of size 4 --- looking through 5 candidates of size 5 --- tested 11 candidates -sum [] = 0 -sum (x:xs) = x + sum xs - -(++) :: [Int] -> [Int] -> [Int] --- pruning with 3/3 rules --- looking through 2 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 11 candidates of size 3 --- looking through 32 candidates of size 4 --- looking through 100 candidates of size 5 --- looking through 244 candidates of size 6 --- tested 234 candidates -[] ++ xs = xs -(x:xs) ++ ys = x:(xs ++ ys) - diff --git a/eg/spec.txt b/eg/spec.txt new file mode 100644 --- /dev/null +++ b/eg/spec.txt @@ -0,0 +1,39 @@ +square :: Int -> Int +-- pruning with 14/25 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 6 candidates of size 3 +-- tested 9 candidates +square x = x * x + +square :: Int -> Int +-- pruning with 14/25 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 6 candidates of size 3 +-- tested 9 candidates +square x = x * x + +sum :: [Int] -> Int +-- pruning with 4/8 rules +-- looking through 1 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 3 candidates of size 4 +-- looking through 5 candidates of size 5 +-- tested 9 candidates +sum [] = 0 +sum (x:xs) = x + sum xs + +(++) :: [Int] -> [Int] -> [Int] +-- pruning with 3/3 rules +-- looking through 2 candidates of size 1 +-- looking through 4 candidates of size 2 +-- looking through 11 candidates of size 3 +-- looking through 31 candidates of size 4 +-- looking through 94 candidates of size 5 +-- looking through 225 candidates of size 6 +-- tested 212 candidates +[] ++ xs = xs +(x:xs) ++ ys = x:(xs ++ ys) + diff --git a/eg/subset.hs b/eg/subset.hs --- a/eg/subset.hs +++ b/eg/subset.hs @@ -1,6 +1,6 @@ -- subset.hs: conjuring the subset function -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# LANGUAGE CPP #-} import Conjure diff --git a/eg/subset.out b/eg/subset.out deleted file mode 100644 --- a/eg/subset.out +++ /dev/null @@ -1,26 +0,0 @@ -subset :: [Int] -> [Int] -> Bool --- testing 44 combinations of argument values --- pruning with 29/39 rules --- looking through 2 candidates of size 1 --- looking through 4 candidates of size 2 --- looking through 8 candidates of size 3 --- looking through 34 candidates of size 4 --- looking through 88 candidates of size 5 --- looking through 40 candidates of size 6 --- looking through 138 candidates of size 7 --- looking through 644 candidates of size 8 --- tested 790 candidates -subset [] xs = True -subset (x:xs) ys = subset xs ys && elem x ys - -subset :: [Int] -> [Int] -> Bool --- testing 44 combinations of argument values --- pruning with 3/3 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 2 candidates of size 5 --- tested 9 candidates -subset xs ys = sort xs `isSubsequenceOf` sort ys - diff --git a/eg/subset.txt b/eg/subset.txt new file mode 100644 --- /dev/null +++ b/eg/subset.txt @@ -0,0 +1,26 @@ +subset :: [Int] -> [Int] -> Bool +-- testing 44 combinations of argument values +-- pruning with 29/39 rules +-- looking through 2 candidates of size 1 +-- looking through 4 candidates of size 2 +-- looking through 8 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 64 candidates of size 5 +-- looking through 40 candidates of size 6 +-- looking through 64 candidates of size 7 +-- looking through 522 candidates of size 8 +-- tested 553 candidates +subset [] xs = True +subset (x:xs) ys = subset xs ys && elem x ys + +subset :: [Int] -> [Int] -> Bool +-- testing 44 combinations of argument values +-- pruning with 3/3 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 2 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 2 candidates of size 5 +-- tested 9 candidates +subset xs ys = sort xs `isSubsequenceOf` sort ys + diff --git a/eg/tapps.hs b/eg/tapps.hs --- a/eg/tapps.hs +++ b/eg/tapps.hs @@ -1,6 +1,6 @@ -- tapps.hs: conjure with (portable) type applications -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# LANGUAGE CPP #-} #if __GLASGOW_HASKELL__ < 800 diff --git a/eg/tapps.out b/eg/tapps.out deleted file mode 100644 --- a/eg/tapps.out +++ /dev/null @@ -1,32 +0,0 @@ -third :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 14/25 rules --- looking through 2 candidates of size 1 --- looking through 5 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 12 candidates of size 4 --- tested 16 candidates -third xs = head (tail (tail xs)) - -product :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 14/25 rules --- looking through 2 candidates of size 1 --- looking through 5 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 12 candidates of size 4 --- looking through 18 candidates of size 5 --- tested 30 candidates -product [] = 1 -product (x:xs) = x * product xs - -product :: [Int] -> Int --- testing 360 combinations of argument values --- pruning with 15/26 rules --- looking through 2 candidates of size 1 --- looking through 5 candidates of size 2 --- looking through 5 candidates of size 3 --- looking through 15 candidates of size 4 --- tested 18 candidates -product xs = foldr (*) 1 xs - diff --git a/eg/tapps.txt b/eg/tapps.txt new file mode 100644 --- /dev/null +++ b/eg/tapps.txt @@ -0,0 +1,32 @@ +third :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 14/25 rules +-- looking through 2 candidates of size 1 +-- looking through 5 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 10 candidates of size 4 +-- tested 12 candidates +third xs = head (tail (tail xs)) + +product :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 14/25 rules +-- looking through 2 candidates of size 1 +-- looking through 5 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 10 candidates of size 4 +-- looking through 18 candidates of size 5 +-- tested 26 candidates +product [] = 1 +product (x:xs) = x * product xs + +product :: [Int] -> Int +-- testing 360 combinations of argument values +-- pruning with 15/26 rules +-- looking through 2 candidates of size 1 +-- looking through 5 candidates of size 2 +-- looking through 3 candidates of size 3 +-- looking through 13 candidates of size 4 +-- tested 14 candidates +product xs = foldr (*) 1 xs + diff --git a/eg/tree.hs b/eg/tree.hs --- a/eg/tree.hs +++ b/eg/tree.hs @@ -1,6 +1,6 @@ -- tree.hs: conjuring functions over trees -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# LANGUAGE CPP, TemplateHaskell #-} diff --git a/eg/tree.out b/eg/tree.out deleted file mode 100644 --- a/eg/tree.out +++ /dev/null @@ -1,155 +0,0 @@ -leftmost :: Tree -> Int --- testing 360 combinations of argument values --- pruning with 3/3 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 4 candidates of size 6 --- looking through 16 candidates of size 7 --- tested 9 candidates -leftmost Leaf = undefined -leftmost (Node t1 x t2) = if nil t1 - then x - else leftmost t1 - -rightmost :: Tree -> Int --- testing 360 combinations of argument values --- pruning with 3/3 rules --- looking through 1 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 4 candidates of size 6 --- looking through 16 candidates of size 7 --- tested 18 candidates -rightmost Leaf = undefined -rightmost (Node t1 x t2) = if nil t2 - then x - else rightmost t2 - -size :: Tree -> Int --- testing 360 combinations of argument values --- pruning with 4/8 rules --- looking through 2 candidates of size 1 --- looking through 2 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 2 candidates of size 4 --- looking through 4 candidates of size 5 --- looking through 8 candidates of size 6 --- looking through 12 candidates of size 7 --- looking through 24 candidates of size 8 --- tested 42 candidates -size Leaf = 0 -size (Node t1 x t2) = size t1 + (size t2 + 1) - -height :: Tree -> Int --- testing 360 combinations of argument values --- pruning with 49/65 rules --- looking through 3 candidates of size 1 --- looking through 3 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 6 candidates of size 4 --- looking through 14 candidates of size 5 --- looking through 34 candidates of size 6 --- looking through 98 candidates of size 7 --- looking through 283 candidates of size 8 --- tested 202 candidates -height Leaf = -1 -height (Node t1 x t2) = 1 + max (height t1) (height t2) - -mem :: Int -> Tree -> Bool --- testing 360 combinations of argument values --- pruning with 11/17 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 0 candidates of size 3 --- looking through 5 candidates of size 4 --- looking through 0 candidates of size 5 --- looking through 0 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 20 candidates of size 8 --- looking through 0 candidates of size 9 --- looking through 0 candidates of size 10 --- looking through 0 candidates of size 11 --- looking through 96 candidates of size 12 --- tested 92 candidates -mem x Leaf = False -mem x (Node t1 y t2) = mem x t1 || (mem x t2 || x == y) - -ordered :: Tree -> Bool --- testing 360 combinations of argument values --- pruning with 29/39 rules --- looking through 2 candidates of size 1 --- looking through 1 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 0 candidates of size 4 --- looking through 10 candidates of size 5 --- looking through 20 candidates of size 6 --- looking through 0 candidates of size 7 --- looking through 32 candidates of size 8 --- looking through 80 candidates of size 9 --- looking through 56 candidates of size 10 --- looking through 450 candidates of size 11 --- looking through 708 candidates of size 12 --- tested 1361 candidates -cannot conjure - -ordered :: Tree -> Bool --- testing 360 combinations of argument values --- pruning with 0/0 rules --- looking through 0 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 3 candidates of size 3 --- tested 3 candidates -ordered t1 = strictlyOrdered (inorder t1) - -preorder :: Tree -> [Int] --- testing 360 combinations of argument values --- pruning with 4/4 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 5 candidates of size 6 --- looking through 4 candidates of size 7 --- looking through 9 candidates of size 8 --- tested 17 candidates -preorder Leaf = [] -preorder (Node t1 x t2) = x:(preorder t1 ++ preorder t2) - -inorder :: Tree -> [Int] --- testing 360 combinations of argument values --- pruning with 4/4 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 5 candidates of size 6 --- looking through 4 candidates of size 7 --- looking through 9 candidates of size 8 --- tested 21 candidates -inorder Leaf = [] -inorder (Node t1 x t2) = inorder t1 ++ (x:inorder t2) - -posorder :: Tree -> [Int] --- testing 360 combinations of argument values --- pruning with 4/4 rules --- looking through 1 candidates of size 1 --- looking through 0 candidates of size 2 --- looking through 2 candidates of size 3 --- looking through 1 candidates of size 4 --- looking through 2 candidates of size 5 --- looking through 5 candidates of size 6 --- looking through 4 candidates of size 7 --- looking through 9 candidates of size 8 --- looking through 14 candidates of size 9 --- looking through 17 candidates of size 10 --- tested 52 candidates -posorder Leaf = [] -posorder (Node t1 x t2) = posorder t1 ++ (posorder t2 ++ [x]) - diff --git a/eg/tree.txt b/eg/tree.txt new file mode 100644 --- /dev/null +++ b/eg/tree.txt @@ -0,0 +1,155 @@ +leftmost :: Tree -> Int +-- testing 360 combinations of argument values +-- pruning with 3/3 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 4 candidates of size 6 +-- looking through 16 candidates of size 7 +-- tested 7 candidates +leftmost Leaf = undefined +leftmost (Node t1 x t2) = if nil t1 + then x + else leftmost t1 + +rightmost :: Tree -> Int +-- testing 360 combinations of argument values +-- pruning with 3/3 rules +-- looking through 1 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 4 candidates of size 6 +-- looking through 16 candidates of size 7 +-- tested 16 candidates +rightmost Leaf = undefined +rightmost (Node t1 x t2) = if nil t2 + then x + else rightmost t2 + +size :: Tree -> Int +-- testing 360 combinations of argument values +-- pruning with 4/8 rules +-- looking through 2 candidates of size 1 +-- looking through 2 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 2 candidates of size 4 +-- looking through 4 candidates of size 5 +-- looking through 8 candidates of size 6 +-- looking through 12 candidates of size 7 +-- looking through 24 candidates of size 8 +-- tested 40 candidates +size Leaf = 0 +size (Node t1 x t2) = size t1 + (size t2 + 1) + +height :: Tree -> Int +-- testing 360 combinations of argument values +-- pruning with 49/65 rules +-- looking through 3 candidates of size 1 +-- looking through 3 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 6 candidates of size 4 +-- looking through 14 candidates of size 5 +-- looking through 34 candidates of size 6 +-- looking through 98 candidates of size 7 +-- looking through 283 candidates of size 8 +-- tested 200 candidates +height Leaf = -1 +height (Node t1 x t2) = 1 + max (height t1) (height t2) + +mem :: Int -> Tree -> Bool +-- testing 360 combinations of argument values +-- pruning with 11/17 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 0 candidates of size 5 +-- looking through 0 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 20 candidates of size 8 +-- looking through 0 candidates of size 9 +-- looking through 0 candidates of size 10 +-- looking through 0 candidates of size 11 +-- looking through 96 candidates of size 12 +-- tested 88 candidates +mem x Leaf = False +mem x (Node t1 y t2) = mem x t1 || (mem x t2 || x == y) + +ordered :: Tree -> Bool +-- testing 360 combinations of argument values +-- pruning with 29/39 rules +-- looking through 2 candidates of size 1 +-- looking through 1 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 0 candidates of size 4 +-- looking through 10 candidates of size 5 +-- looking through 20 candidates of size 6 +-- looking through 0 candidates of size 7 +-- looking through 32 candidates of size 8 +-- looking through 80 candidates of size 9 +-- looking through 56 candidates of size 10 +-- looking through 450 candidates of size 11 +-- looking through 708 candidates of size 12 +-- tested 1359 candidates +cannot conjure + +ordered :: Tree -> Bool +-- testing 360 combinations of argument values +-- pruning with 0/0 rules +-- looking through 0 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 1 candidates of size 3 +-- tested 1 candidates +ordered t1 = strictlyOrdered (inorder t1) + +preorder :: Tree -> [Int] +-- testing 360 combinations of argument values +-- pruning with 4/4 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 4 candidates of size 7 +-- looking through 9 candidates of size 8 +-- tested 15 candidates +preorder Leaf = [] +preorder (Node t1 x t2) = x:(preorder t1 ++ preorder t2) + +inorder :: Tree -> [Int] +-- testing 360 combinations of argument values +-- pruning with 4/4 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 4 candidates of size 7 +-- looking through 9 candidates of size 8 +-- tested 19 candidates +inorder Leaf = [] +inorder (Node t1 x t2) = inorder t1 ++ (x:inorder t2) + +posorder :: Tree -> [Int] +-- testing 360 combinations of argument values +-- pruning with 4/4 rules +-- looking through 1 candidates of size 1 +-- looking through 0 candidates of size 2 +-- looking through 0 candidates of size 3 +-- looking through 1 candidates of size 4 +-- looking through 2 candidates of size 5 +-- looking through 5 candidates of size 6 +-- looking through 4 candidates of size 7 +-- looking through 9 candidates of size 8 +-- looking through 14 candidates of size 9 +-- looking through 17 candidates of size 10 +-- tested 50 candidates +posorder Leaf = [] +posorder (Node t1 x t2) = posorder t1 ++ (posorder t2 ++ [x]) + diff --git a/mk/depend.mk b/mk/depend.mk --- a/mk/depend.mk +++ b/mk/depend.mk @@ -8,23 +8,48 @@ mk/toplibs bench/candidates.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ bench/candidates.hs +bench/erroneous: \ + bench/erroneous.hs \ + mk/toplibs +bench/erroneous.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ + src/Conjure/Prim.hs \ + src/Conjure.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ + src/Conjure/Defn.hs \ + src/Conjure/Conjurable.hs \ + src/Conjure/Conjurable/Derive.hs \ + bench/erroneous.hs bench/gps2: \ bench/gps2.hs \ mk/toplibs bench/gps2.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -34,10 +59,14 @@ mk/toplibs bench/gps.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -47,10 +76,14 @@ mk/toplibs bench/ill-hit.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -60,10 +93,14 @@ mk/toplibs bench/longshot.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -73,10 +110,14 @@ mk/toplibs bench/lowtests.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -86,10 +127,14 @@ mk/toplibs bench/p12.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -99,10 +144,14 @@ mk/toplibs bench/p30.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -112,10 +161,14 @@ mk/toplibs bench/redundants.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -125,10 +178,14 @@ mk/toplibs bench/self.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -138,10 +195,14 @@ mk/toplibs bench/take-drop.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -151,10 +212,14 @@ mk/toplibs bench/terpret.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -164,10 +229,14 @@ mk/toplibs bench/weird.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -177,10 +246,14 @@ mk/toplibs eg/arith.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -190,10 +263,14 @@ mk/toplibs eg/bools.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -203,10 +280,14 @@ mk/toplibs eg/bst.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -216,10 +297,14 @@ mk/toplibs eg/count.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -229,23 +314,48 @@ mk/toplibs eg/dupos.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ eg/dupos.hs +eg/either: \ + eg/either.hs \ + mk/toplibs +eg/either.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ + src/Conjure/Prim.hs \ + src/Conjure.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ + src/Conjure/Defn.hs \ + src/Conjure/Conjurable.hs \ + src/Conjure/Conjurable/Derive.hs \ + eg/either.hs eg/factorial: \ eg/factorial.hs \ mk/toplibs eg/factorial.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -255,10 +365,14 @@ mk/toplibs eg/fib01.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -268,10 +382,14 @@ mk/toplibs eg/fibonacci.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -281,10 +399,14 @@ mk/toplibs eg/gcd.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -294,10 +416,14 @@ mk/toplibs eg/higher.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -307,10 +433,14 @@ mk/toplibs eg/id.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -320,10 +450,14 @@ mk/toplibs eg/ints.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -333,23 +467,65 @@ mk/toplibs eg/list.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ eg/list.hs +eg/maybe: \ + eg/maybe.hs \ + mk/toplibs +eg/maybe.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ + src/Conjure/Prim.hs \ + src/Conjure.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ + src/Conjure/Defn.hs \ + src/Conjure/Conjurable.hs \ + src/Conjure/Conjurable/Derive.hs \ + eg/maybe.hs +eg/oddeven: \ + eg/oddeven.hs \ + mk/toplibs +eg/oddeven.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ + src/Conjure/Prim.hs \ + src/Conjure.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ + src/Conjure/Defn.hs \ + src/Conjure/Conjurable.hs \ + src/Conjure/Conjurable/Derive.hs \ + eg/oddeven.hs eg/pow: \ eg/pow.hs \ mk/toplibs eg/pow.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -359,10 +535,14 @@ mk/toplibs eg/replicate.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -372,10 +552,14 @@ mk/toplibs eg/setelem.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -385,10 +569,14 @@ mk/toplibs eg/sort.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -398,10 +586,14 @@ mk/toplibs eg/spec.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -411,10 +603,14 @@ mk/toplibs eg/subset.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -424,10 +620,14 @@ mk/toplibs eg/tapps.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -437,20 +637,28 @@ mk/toplibs eg/tree.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ eg/tree.hs mk/All.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -459,10 +667,14 @@ test/Test.hs \ test/Test/ListableExpr.hs \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs \ @@ -487,11 +699,26 @@ src/Conjure/Utils.hs \ src/Conjure/Expr.hs \ src/Conjure/Defn.hs +src/Conjure/Defn/Redundancy.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Defn/Redundancy.hs \ + src/Conjure/Defn.hs +src/Conjure/Defn/Test.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn.hs \ + src/Conjure/Conjurable.hs src/Conjure/Engine.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs src/Conjure/Expr.o: \ @@ -499,10 +726,14 @@ src/Conjure/Expr.hs src/Conjure.o: \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs @@ -512,6 +743,16 @@ src/Conjure/Expr.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs +src/Conjure/Reason.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Reason.hs \ + src/Conjure/Expr.hs +src/Conjure/Red.o: \ + src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Defn.hs \ + src/Conjure/Conjurable.hs src/Conjure/Utils.o: \ src/Conjure/Utils.hs test/conjurable.o: \ @@ -519,10 +760,14 @@ test/Test/ListableExpr.hs \ test/conjurable.hs \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs @@ -536,10 +781,14 @@ test/Test/ListableExpr.hs \ test/defn.hs \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs @@ -553,10 +802,14 @@ test/Test/ListableExpr.hs \ test/derive.hs \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs @@ -570,10 +823,14 @@ test/Test/ListableExpr.hs \ test/expr.hs \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs @@ -582,16 +839,41 @@ test/Test/ListableExpr.hs \ test/expr.hs \ mk/toplibs +test/red.o: \ + test/Test.hs \ + test/Test/ListableExpr.hs \ + test/red.hs \ + src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ + src/Conjure/Prim.hs \ + src/Conjure.hs \ + src/Conjure/Expr.hs \ + src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ + src/Conjure/Defn.hs \ + src/Conjure/Conjurable.hs \ + src/Conjure/Conjurable/Derive.hs +test/red: \ + test/Test.hs \ + test/Test/ListableExpr.hs \ + test/red.hs \ + mk/toplibs test/Test/ListableExpr.o: \ test/Test/ListableExpr.hs test/Test.o: \ test/Test.hs \ test/Test/ListableExpr.hs \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs @@ -604,10 +886,14 @@ test/Test.hs \ test/Test/ListableExpr.hs \ src/Conjure/Utils.hs \ + src/Conjure/Red.hs \ + src/Conjure/Reason.hs \ src/Conjure/Prim.hs \ src/Conjure.hs \ src/Conjure/Expr.hs \ src/Conjure/Engine.hs \ + src/Conjure/Defn/Test.hs \ + src/Conjure/Defn/Redundancy.hs \ src/Conjure/Defn.hs \ src/Conjure/Conjurable.hs \ src/Conjure/Conjurable/Derive.hs diff --git a/mk/ghcdeps b/mk/ghcdeps --- a/mk/ghcdeps +++ b/mk/ghcdeps @@ -2,7 +2,7 @@ # # ghcdeps: generate Haskell make dependencies for compiling with GHC. # -# Copyright (c) 2015-2021 Rudy Matela. +# Copyright (c) 2015-2024 Rudy Matela. # Distributed under the 3-Clause BSD licence. # # From a list of files provided on standard input, diff --git a/mk/haddock-i b/mk/haddock-i --- a/mk/haddock-i +++ b/mk/haddock-i @@ -2,7 +2,7 @@ # # haddock-i: list haddock's -i parameters. # -# Copyright (c) 2015-2021 Rudy Matela. +# Copyright (c) 2015-2024 Rudy Matela. # Distributed under the 3-Clause BSD licence. # # $ haddock-i ... diff --git a/mk/install-on b/mk/install-on --- a/mk/install-on +++ b/mk/install-on @@ -2,7 +2,7 @@ # # mk/install-on: install or updates the mk folder on a Haskell project # -# Copyright (c) 2019-2021 Rudy Matela. +# Copyright (c) 2019-2024 Rudy Matela. # Distributed under the 3-Clause BSD licence. # # usage: ./mk/install-on path/to/project diff --git a/proto/u-conjure.hs b/proto/u-conjure.hs --- a/proto/u-conjure.hs +++ b/proto/u-conjure.hs @@ -4,7 +4,7 @@ -- out of partially implemented functions. -- -- --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). -- -- diff --git a/proto/u-conjure.out b/proto/u-conjure.out deleted file mode 100644 --- a/proto/u-conjure.out +++ /dev/null @@ -1,24 +0,0 @@ -square :: Int -> Int -square x = x * x - -add :: Int -> Int -> Int -add x y = x + y - -factorial :: Int -> Int -cannot conjure - -factorial :: Int -> Int -factorial x = foldr (*) 1 (enumFromTo 1 x) - -second :: [Int] -> Int -second xs = head (tail xs) - -(++) :: [Int] -> [Int] -> [Int] -xs ++ ys = foldr (:) ys xs - -reverse :: [Int] -> [Int] -cannot conjure - -reverse :: [Int] -> [Int] -reverse xs = foldr (foldr (:) . unit) [] xs - diff --git a/proto/u-conjure.txt b/proto/u-conjure.txt new file mode 100644 --- /dev/null +++ b/proto/u-conjure.txt @@ -0,0 +1,24 @@ +square :: Int -> Int +square x = x * x + +add :: Int -> Int -> Int +add x y = x + y + +factorial :: Int -> Int +cannot conjure + +factorial :: Int -> Int +factorial x = foldr (*) 1 (enumFromTo 1 x) + +second :: [Int] -> Int +second xs = head (tail xs) + +(++) :: [Int] -> [Int] -> [Int] +xs ++ ys = foldr (:) ys xs + +reverse :: [Int] -> [Int] +cannot conjure + +reverse :: [Int] -> [Int] +reverse xs = foldr (foldr (:) . unit) [] xs + diff --git a/src/Conjure.hs b/src/Conjure.hs --- a/src/Conjure.hs +++ b/src/Conjure.hs @@ -1,6 +1,6 @@ -- | -- Module : Conjure --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- diff --git a/src/Conjure/Conjurable.hs b/src/Conjure/Conjurable.hs --- a/src/Conjure/Conjurable.hs +++ b/src/Conjure/Conjurable.hs @@ -1,6 +1,6 @@ -- | -- Module : Conjure.Conjurable --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- @@ -23,12 +23,12 @@ , conjurePats , conjureHoles , conjureTiersFor + , conjureListFor + , conjureSizeFor + , conjureGrounds , conjureAreEqual , conjureMkEquation , A, B, C, D, E, F - , conjureIsDeconstruction - , candidateDeconstructionsFrom - , candidateDeconstructionsFromHoled , conjureIsUnbreakable , conjureReification , conjureReification1 @@ -49,7 +49,6 @@ import Test.LeanCheck.Error (errorToFalse) import Conjure.Expr hiding (application) import Conjure.Defn -import Test.Speculate.Expr import Data.Functor ((<$>)) import Control.Applicative ((<*>)) import Data.Dynamic @@ -214,7 +213,6 @@ -- 'conjureMkEquation', -- 'conjureAreEqual', -- 'conjureTiersFor', --- 'conjureIsDeconstructor', -- 'conjureNamesFor', -- 'conjureIsUnbreakable', -- etc. @@ -297,7 +295,7 @@ (-==-) = conjureMkEquation f e1 === e2 = isTrue $ e1 -==- e2 isTrue = all (errorToFalse . eval False) . gs - gs = take maxTests . grounds (conjureTiersFor f) + gs = take maxTests . conjureGrounds f -- | Compute 'tiers' of values encoded as 'Expr's -- of the type of the given 'Expr'. @@ -311,8 +309,16 @@ ((e':_):_) | typ e' == typ e -> etiers _ -> tf etc +conjureGrounds :: Conjurable f => f -> Expr -> [Expr] +conjureGrounds = grounds . conjureTiersFor + +-- | Compure a 'list' of values encoded as 'Expr's +-- of the type of the given 'Expr'. +conjureListFor :: Conjurable f => f -> Expr -> [Expr] +conjureListFor f = concat . conjureTiersFor f + conjureIsNumeric :: Conjurable f => f -> Expr -> Bool -conjureIsNumeric f e = case concat $ conjureTiersFor f e of +conjureIsNumeric f e = case conjureListFor f e of -- We assume tiers of numeric values start with 0 -- not so unfair... (Value "0" _):_ -> True @@ -328,78 +334,22 @@ conjureMostGeneralCanonicalVariation f = canonicalizeWith (conjureNamesFor f) . fastMostGeneralVariation --- | Checks if an expression is a deconstruction. --- --- There should be a single 'hole' in the expression. --- --- It should decrease the size of all arguments that have --- a size greater than 0. --- --- (cf. 'conjureIsDeconstructor') -conjureIsDeconstruction :: Conjurable f => f -> Int -> Expr -> Bool -conjureIsDeconstruction f maxTests ed = length (holes ed) == 1 - && typ h == typ ed - && all is gs - where - gs = take maxTests $ grounds (conjureTiersFor f) ed - [h] = holes ed - sz = head [sz | (_, _, _, _, _, sz) <- conjureReification f - , isWellTyped (sz :$ h)] - esz e = eval (0::Int) (sz :$ e) - x << 0 = True - x << y = x < y - is e = errorToFalse $ esz e << esz (holeValue e) - holeValue e = fromMaybe err - . lookup h - . fromMaybe err - $ e `match` ed - err = error "conjureIsDeconstructor: the impossible happened" - --- | Compute candidate deconstructions from an 'Expr'. --- --- This is used in the implementation of 'Conjure.Engine.candidateDefnsC' --- followed by 'conjureIsDeconstruction'. --- --- > > candidateDeconstructionsFrom (xx `mod'` yy) --- > [ _ `mod` y --- > , x `mod` _ --- > ] --- --- To be constrasted with 'candidateDeconstructionsFromHoled'. -candidateDeconstructionsFrom :: Expr -> [Expr] -candidateDeconstructionsFrom e = - [ e' - | v <- vars e - , typ v == typ e - , let e' = e //- [(v, holeAsTypeOf v)] - , length (holes e') == 1 - ] - --- | Compute candidate deconstructions from an 'Expr'. --- --- This is used in the implementation of 'Conjure.Engine.candidateExprs' --- followed by 'conjureIsDeconstruction'. +-- | Conjures an 'Expr'-encoded size function for the given expression type. -- --- This is similar to 'canonicalVariations' --- but always leaves a hole --- of the same return type as the given expression. +-- > > conjureSizeFor (undefined :: [Int] -> [Bool]) i_ +-- > conjureSize :: Int -> Int -- --- > > candidateDeconstructionsFrom (i_ `mod'` i_) --- > [ _ `mod` x --- > , x `mod` _ --- > ] +-- > > conjureSizeFor (undefined :: [Int] -> [Bool]) is_ +-- > conjureSize :: [Int] -> Int -- --- To be contrasted with 'candidateDeconstructionsFrom' -candidateDeconstructionsFromHoled :: Expr -> [Expr] -candidateDeconstructionsFromHoled e = map (//- [(v, h)]) - $ concatMap canonicalVariations - $ deholings v e - where - h = holeAsTypeOf e - v = "_#_" `varAsTypeOf` e -- a marker variable with an invalid name - -- at some point I should get rid of candidateDeconstructionsFrom in favour - -- of this one +-- > > conjureSizeFor (undefined :: [Int] -> [Bool]) bs_ +-- > conjureSize :: [Bool] -> Int +conjureSizeFor :: Conjurable f => f -> Expr -> Expr +conjureSizeFor f eh = + case [esz | (_,_,_,_,_,esz) <- conjureReification f, isWellTyped (esz :$ eh)] of + (esz:_) -> esz + _ -> error $ "Conjure.conjureSizeFor: could not find size for " ++ show eh -- | Checks if an 'Expr' is of an unbreakable type. conjureIsUnbreakable :: Conjurable f => f -> Expr -> Bool @@ -551,8 +501,8 @@ , value "Right" (Right ->: exy) :$ hole y ] where - x = Left undefined -: exy - y = Right undefined -: exy + Left x = Left undefined -: exy + Right y = Right undefined -: exy conjureEquality elr = from <$> conjureEquality l <*> conjureEquality r where Left l = elr diff --git a/src/Conjure/Conjurable/Derive.hs b/src/Conjure/Conjurable/Derive.hs --- a/src/Conjure/Conjurable/Derive.hs +++ b/src/Conjure/Conjurable/Derive.hs @@ -1,7 +1,7 @@ {-# LANGUAGE TemplateHaskell, CPP #-} -- | -- Module : Conjure.Conjurable.Derive --- Copyright : (c) 2019-2021 Rudy Matela +-- Copyright : (c) 2019-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- diff --git a/src/Conjure/Defn.hs b/src/Conjure/Defn.hs --- a/src/Conjure/Defn.hs +++ b/src/Conjure/Defn.hs @@ -1,6 +1,6 @@ -- | -- Module : Conjure.Defn --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- @@ -21,21 +21,14 @@ , showDefn , printDefn , defnApparentlyTerminates - , isRedundantDefn - , isRedundantBySubsumption - , isRedundantByRepetition - , isRedundantByIntroduction - , hasRedundantRecursion , isCompleteDefn , isCompleteBndn - , simplifyDefn , canonicalizeBndn , canonicalizeBndnLast , hasUnbound , noUnbound , isUndefined , isDefined - , introduceVariableAt , isBaseCase , isRecursiveCase , isRecursiveDefn @@ -229,155 +222,6 @@ defnApparentlyTerminates [(efxs, e)] = apparentlyTerminates efxs e defnApparentlyTerminates _ = True --- | Returns whether the given 'Defn' is redundant --- with regards to repetitions on RHSs. --- --- Here is an example of a redundant 'Defn': --- --- > 0 ? 0 = 1 --- > 0 ? x = 1 --- > x ? 0 = x --- > x ? y = x --- --- It is redundant because it is equivalent to: --- --- > 0 ? _ = 1 --- > x ? _ = x --- --- This function safely handles holes on the RHSs --- by being conservative in cases these are found: --- nothing can be said before their fillings. -isRedundantDefn :: Defn -> Bool -isRedundantDefn d = isRedundantBySubsumption d - || isRedundantByRepetition d --- || isRedundantByIntroduction d --- we do not use isRedundantByIntroduction above --- as it does not pay off in terms of runtime vs number of pruned candidates --- --- The number of candidates is reduced usually by less than 1% --- and the runtime increases by 50% or sometimes 100%. - --- | Returns whether the given 'Defn' is redundant --- with regards to repetitions on RHSs. --- --- Here is an example of a redundant 'Defn': --- --- > 0 ? 0 = 1 --- > 0 ? x = 1 --- > x ? 0 = x --- > x ? y = x --- --- It is redundant because it is equivalent to: --- --- > 0 ? _ = 1 --- > x ? _ = x --- --- @1@ and @x@ are repeated in the results for when --- the first arguments are @0@ and @x@. -isRedundantByRepetition :: Defn -> Bool -isRedundantByRepetition d = any anyAllEqual shovels - where - nArgs = length . tail . unfoldApp . fst $ head d - shovels :: [Expr -> Expr] - shovels = [digApp n | n <- [1..nArgs]] - anyAllEqual :: (Expr -> Expr) -> Bool - anyAllEqual shovel = any (\bs -> allEqual2 bs && isDefined bs) - . classifyOn fst - . map (canonicalizeBndn . first shovel) - $ d - --- | Returns whether the given 'Defn' is redundant --- with regards to case elimination --- --- The following is redundant according to this criterium: --- --- > foo [] = [] --- > foo (x:xs) = x:xs --- --- It is equivalent to: --- --- > foo xs = xs --- --- The following is also redundant: --- --- > [] ?? xs = [] --- > (x:xs) ?? ys = x:xs --- --- as it is equivalent to: --- --- > xs ?? ys == xs --- --- This function is not used as one of the criteria in 'isRedundantDefn' --- because it does not pay-off --- in terms of runtime vs number of pruned candidates. -isRedundantByIntroduction :: Defn -> Bool -isRedundantByIntroduction d = any anyAllEqual [1..nArgs] - where - nArgs = length . tail . unfoldApp . fst $ head d - anyAllEqual :: Int -> Bool - anyAllEqual i = any (\bs -> length bs >= 2 && isDefined bs && noConflicts i bs) - . classifyOn (digApp i . fst) - . map (canonicalizeBndnLast i) - $ d - noConflicts :: Int -> [Bndn] -> Bool - noConflicts i bs = case listConflicts (map snd bs) of - [] -> True - [es] -> es == [efxs $!! i | (efxs,_) <- bs] - _ -> False - --- | Returns whether the given 'Defn' is redundant --- with regards to recursions --- --- The following is redundant: --- --- > xs ?? [] = [] --- > xs ?? (x:ys) = xs ?? [] --- --- The LHS of a base-case pattern, matches the RHS of a recursive pattern. --- The second RHS may be replaced by simply @[]@ which makes it redundant. -hasRedundantRecursion :: Defn -> Bool -hasRedundantRecursion d = not (null rs) && any matchesRHS bs - where - (bs,rs) = partition isBaseCase d - matchesRHS (lhs,_) = any ((`hasAppInstanceOf` lhs) . snd) rs - --- | Introduces a hole at a given position in the binding: --- --- > > introduceVariableAt 1 (xxs -?- (yy -:- yys), (yy -:- yys) -++- (yy -:- yys)) --- > (xs ? (y:ys) :: [Int],(y:ys) ++ (y:ys) :: [Int]) --- --- > > introduceVariableAt 2 (xxs -?- (yy -:- yys), (yy -:- yys) -++- (yy -:- yys)) --- > (xs ? x :: [Int],x ++ x :: [Int]) --- --- Relevant occurrences are replaced. -introduceVariableAt :: Int -> Bndn -> Bndn -introduceVariableAt i b@(l,r) - | isVar p = b -- already a variable --- | isGround p = (newVar, r) -- enabling catches a different set of candidates - | otherwise = unfoldPair - $ foldPair b // [(p,newVar)] - where - p = l $!! i - newVar = newName `varAsTypeOf` p - newName = head $ variableNamesFromTemplate "x" \\ varnames l - varnames :: Expr -> [String] - varnames e = [n | Value ('_':n) _ <- vars e] - --- | Returns whether the given 'Defn' is redundant --- with regards to subsumption by latter patterns --- --- Here is an example of a redundant 'Defn' by this criterium: --- --- > foo 0 = 0 --- > foo x = x -isRedundantBySubsumption :: Defn -> Bool -isRedundantBySubsumption = is . map foldPair . filter isCompleteBndn - -- above, we could have used noUnbound instead of isCompleteBndn - -- we use isCompleteBndn as it is faster - where - is [] = False - is (b:bs) = any (b `isInstanceOf`) bs || is bs - -- | Returns whether the definition is complete, -- i.e., whether it does not have any holes in the RHS. isCompleteDefn :: Defn -> Bool @@ -387,21 +231,6 @@ -- i.e., whether it does not have any holes in the RHS. isCompleteBndn :: Bndn -> Bool isCompleteBndn (_,rhs) = isComplete rhs - --- | Simplifies a definition by removing redundant patterns --- --- This may be useful in the following case: --- --- > 0 ^^^ 0 = 0 --- > 0 ^^^ x = x --- > x ^^^ 0 = x --- > _ ^^^ _ = 0 --- --- The first pattern is subsumed by the last pattern. -simplifyDefn :: Defn -> Defn -simplifyDefn [] = [] -simplifyDefn (b:bs) = [b | none (foldPair b `isInstanceOf`) $ map foldPair bs] - ++ simplifyDefn bs canonicalizeBndn :: Bndn -> Bndn canonicalizeBndn = unfoldPair . canonicalize . foldPair diff --git a/src/Conjure/Defn/Redundancy.hs b/src/Conjure/Defn/Redundancy.hs new file mode 100644 --- /dev/null +++ b/src/Conjure/Defn/Redundancy.hs @@ -0,0 +1,246 @@ +-- | +-- Module : Conjure.Defn.Redundancy +-- Copyright : (c) 2021-2024 Rudy Matela +-- License : 3-Clause BSD (see the file LICENSE) +-- Maintainer : Rudy Matela +-- +-- This module is part of "Conjure". +-- +-- This module exports functions that check redundancy in 'Defn's. +-- +-- You are probably better off importing "Conjure". +module Conjure.Defn.Redundancy + ( isRedundantDefn + , isRedundantBySubsumption + , isRedundantByRepetition + , isRedundantByIntroduction + , isRedundantModuloRewriting + , hasRedundantRecursion + , subsumedWith + , simplifyDefn + , introduceVariableAt + ) +where + +import Conjure.Defn + +-- | Returns whether the given 'Defn' is redundant +-- with regards to repetitions on RHSs. +-- +-- Here is an example of a redundant 'Defn': +-- +-- > 0 ? 0 = 1 +-- > 0 ? x = 1 +-- > x ? 0 = x +-- > x ? y = x +-- +-- It is redundant because it is equivalent to: +-- +-- > 0 ? _ = 1 +-- > x ? _ = x +-- +-- This function safely handles holes on the RHSs +-- by being conservative in cases these are found: +-- nothing can be said before their fillings. +isRedundantDefn :: Defn -> Bool +isRedundantDefn d = isRedundantBySubsumption d + || isRedundantByRepetition d + || isRedundantByRootRecursions d +-- || isRedundantByIntroduction d +-- we do not use isRedundantByIntroduction above +-- as it does not pay off in terms of runtime vs number of pruned candidates +-- +-- The number of candidates is reduced usually by less than 1% +-- and the runtime increases by 50% or sometimes 100%. + + +-- | Returns whether the given 'Defn' is redundant +-- with regards to repetitions on RHSs. +-- +-- Here is an example of a redundant 'Defn': +-- +-- > 0 ? 0 = 1 +-- > 0 ? x = 1 +-- > x ? 0 = x +-- > x ? y = x +-- +-- It is redundant because it is equivalent to: +-- +-- > 0 ? _ = 1 +-- > x ? _ = x +-- +-- @1@ and @x@ are repeated in the results for when +-- the first arguments are @0@ and @x@. +isRedundantByRepetition :: Defn -> Bool +isRedundantByRepetition d = any anyAllEqual shovels + where + nArgs = length . tail . unfoldApp . fst $ head d + shovels :: [Expr -> Expr] + shovels = [digApp n | n <- [1..nArgs]] + anyAllEqual :: (Expr -> Expr) -> Bool + anyAllEqual shovel = any (\bs -> allEqual2 bs && isDefined bs) + . classifyOn fst + . map (canonicalizeBndn . first shovel) + $ d + +-- | Returns whether the given 'Defn' is redundant +-- with regards to case elimination +-- +-- The following is redundant according to this criterium: +-- +-- > foo [] = [] +-- > foo (x:xs) = x:xs +-- +-- It is equivalent to: +-- +-- > foo xs = xs +-- +-- The following is also redundant: +-- +-- > [] ?? xs = [] +-- > (x:xs) ?? ys = x:xs +-- +-- as it is equivalent to: +-- +-- > xs ?? ys == xs +-- +-- This function is not used as one of the criteria in 'isRedundantDefn' +-- because it does not pay-off +-- in terms of runtime vs number of pruned candidates. +isRedundantByIntroduction :: Defn -> Bool +isRedundantByIntroduction d = any anyAllEqual [1..nArgs] + where + nArgs = length . tail . unfoldApp . fst $ head d + anyAllEqual :: Int -> Bool + anyAllEqual i = any (\bs -> length bs >= 2 && isDefined bs && noConflicts i bs) + . classifyOn (digApp i . fst) + . map (canonicalizeBndnLast i) + $ d + noConflicts :: Int -> [Bndn] -> Bool + noConflicts i bs = case listConflicts (map snd bs) of + [] -> True + [es] -> es == [efxs $!! i | (efxs,_) <- bs] + _ -> False + +-- | Returns whether the given 'Defn' is redundant +-- with regards to recursions +-- +-- The following is redundant: +-- +-- > xs ?? [] = [] +-- > xs ?? (x:ys) = xs ?? [] +-- +-- The LHS of a base-case pattern, matches the RHS of a recursive pattern. +-- The second RHS may be replaced by simply @[]@ which makes it redundant. +hasRedundantRecursion :: Defn -> Bool +hasRedundantRecursion d = not (null rs) && any matchesRHS bs + where + (bs,rs) = partition isBaseCase d + matchesRHS (lhs,_) = any ((`hasAppInstanceOf` lhs) . snd) rs + +-- | Returns whether a given 'Defn' is redundant +-- with regards to root recursions. +-- +-- When there is a single base case and all recursive calls +-- are at the root: we have a redundant function. +-- (Modulo error functions, which are undesired anyway.) +-- +-- > xs ? [] = [] +-- > xs ? (x:ys) = xs ? ys +-- +-- Above it does not really pays off to follow the recursive calls, +-- at the end we always reach an empty list. +-- +-- The same goes for the following: +-- +-- > xs ? [] = xs +-- > xs ? (x:ys) = xs ? ys +isRedundantByRootRecursions :: Defn -> Bool +isRedundantByRootRecursions d = case partition isGround $ map snd d of + ([b], rs@(_:_)) -> all isHole rs + (bs@(_:_), rs@(_:_)) -> all isHole rs && all isGround bs && allEqual bs + _ -> False + +-- | Introduces a hole at a given position in the binding: +-- +-- > > introduceVariableAt 1 (xxs -?- (yy -:- yys), (yy -:- yys) -++- (yy -:- yys)) +-- > (xs ? (y:ys) :: [Int],(y:ys) ++ (y:ys) :: [Int]) +-- +-- > > introduceVariableAt 2 (xxs -?- (yy -:- yys), (yy -:- yys) -++- (yy -:- yys)) +-- > (xs ? x :: [Int],x ++ x :: [Int]) +-- +-- Relevant occurrences are replaced. +introduceVariableAt :: Int -> Bndn -> Bndn +introduceVariableAt i b@(l,r) + | isVar p = b -- already a variable +-- | isGround p = (newVar, r) -- enabling catches a different set of candidates + | otherwise = unfoldPair + $ foldPair b // [(p,newVar)] + where + p = l $!! i + newVar = newName `varAsTypeOf` p + newName = head $ variableNamesFromTemplate "x" \\ varnames l + varnames :: Expr -> [String] + varnames e = [n | Value ('_':n) _ <- vars e] + +-- | Returns whether the given 'Defn' is redundant +-- with regards to subsumption by latter patterns +-- +-- Here is an example of a redundant 'Defn' by this criterium: +-- +-- > foo 0 = 0 +-- > foo x = x +isRedundantBySubsumption :: Defn -> Bool +isRedundantBySubsumption = is . map foldPair . filter isCompleteBndn + -- above, we could have used noUnbound instead of isCompleteBndn + -- we use isCompleteBndn as it is faster + where + is [] = False + is (b:bs) = any (b `isInstanceOf`) bs || is bs + +-- | Returns whether the given 'Defn' is redundant modulo +-- subsumption and rewriting. +-- +-- (cf. 'subsumedWith') +isRedundantModuloRewriting :: (Expr -> Expr) -> Defn -> Bool +isRedundantModuloRewriting normalize = is + where + is [] = False + is (b:bs) = any (subsumedWith normalize b) bs + || is bs + +-- | Simplifies a definition by removing redundant patterns +-- +-- This may be useful in the following case: +-- +-- > 0 ^^^ 0 = 0 +-- > 0 ^^^ x = x +-- > x ^^^ 0 = x +-- > _ ^^^ _ = 0 +-- +-- The first pattern is subsumed by the last pattern. +simplifyDefn :: Defn -> Defn +simplifyDefn [] = [] +simplifyDefn (b:bs) = [b | none (foldPair b `isInstanceOf`) $ map foldPair bs] + ++ simplifyDefn bs + +-- | Returns whether a binding is subsumed by another modulo rewriting +-- +-- > > let normalize = (// [(zero -+- zero, zero)]) +-- > > subsumedWith normalize (ff zero, zero) (ff xx, xx -+- xx) +-- > True +-- +-- > > subsumedWith normalize (ff zero, zero) (ff xx, xx -+- one) +-- > False +-- +-- > > subsumedWith normalize (zero -?- xx, zero) (xx -?- yy, xx -+- xx) +-- > True +-- +-- (cf. 'isRedundantModuloRewriting') +subsumedWith :: (Expr -> Expr) -> Bndn -> Bndn -> Bool +subsumedWith normalize (lhs1,rhs1) (lhs2,rhs2) + | hasHole rhs2 = False + | otherwise = case lhs1 `match` lhs2 of + Nothing -> False + Just bs -> snd (canonicalizeBndn (lhs2, normalize $ rhs2 //- bs)) + == snd (canonicalizeBndn (lhs1, rhs1)) diff --git a/src/Conjure/Defn/Test.hs b/src/Conjure/Defn/Test.hs new file mode 100644 --- /dev/null +++ b/src/Conjure/Defn/Test.hs @@ -0,0 +1,86 @@ +-- | +-- Module : Conjure.Defn.Test +-- Copyright : (c) 2021-2024 Rudy Matela +-- License : 3-Clause BSD (see the file LICENSE) +-- Maintainer : Rudy Matela +-- +-- This module is part of "Conjure". +-- +-- This module exports functions that test 'Defn's using ground values. +-- +-- You are probably better off importing "Conjure". +module Conjure.Defn.Test + ( equalModuloTesting + , erroneousCandidate + , findDefnError + ) +where + +import Conjure.Defn +import Conjure.Conjurable + +import Test.LeanCheck.Error (errorToFalse, errorToNothing) + +import Data.Dynamic (fromDyn, dynApp) + + +equalModuloTesting :: Conjurable f => Int -> Int -> String -> f -> Defn -> Defn -> Bool +equalModuloTesting maxTests maxEvalRecursions nm f = (===) + where + testGrounds = nonNegativeAppGrounds maxTests maxEvalRecursions nm f + d1 === d2 = all are $ testGrounds + where + -- silences errors, ok since this is for optional measuring of optimal pruning + are :: Expr -> Bool + are e = isError (ee d1 d1 e) + && isError (ee d2 d2 e) + || errorToFalse (ee d1 d2 e) + where ee = devlEqual maxEvalRecursions f + + +-- | For debugging purposes. +-- +-- This may be taken out of the API at any moment. +erroneousCandidate :: Conjurable f => Int -> Int -> String -> f -> Defn -> Bool +erroneousCandidate maxTests maxEvalRecursions nm f = + isJust . findDefnError maxTests maxEvalRecursions nm f + + +-- | For debugging purposes, +-- finds a set of arguments that triggers an error in the candidate 'Defn'. +-- +-- Warning: this is an experimental function +-- which may be taken out of the API at any moment. +findDefnError :: Conjurable f => Int -> Int -> String -> f -> Defn -> Maybe Expr +findDefnError maxTests maxEvalRecursions nm f d = + find is testGrounds + where + testGrounds = nonNegativeAppGrounds maxTests maxEvalRecursions nm f + is :: Expr -> Bool + is e = isError (devlEqual maxEvalRecursions f d d e) + + +nonNegativeAppGrounds :: Conjurable f => Int -> Int -> String -> f -> [Expr] +nonNegativeAppGrounds maxTests maxEvalRecursions nm f + = filter (none isNegative . unfoldApp) + $ take maxTests + $ conjureGrounds f (conjureVarApplication nm f) + + +devlEqual :: Conjurable f => Int -> f -> Defn -> Defn -> Expr -> Bool +devlEqual maxEvalRecursions f d1 d2 e = + eq `dynApp` evalDyn d1 e + `dynApp` evalDyn d2 e `fromDyn` err + where + evalDyn d e = fromMaybe err (toDynamicWithDefn (conjureExpress f) maxEvalRecursions d e) + eq = conjureDynamicEq f + err = error "Conjure.devlEqual: evaluation error" + -- We cannot use conjureMkEquation here because + -- we need different Defns at each side of the equation + -- so they have to be evaluated independently. + +-- | Is the argument value an error value? +isError :: a -> Bool +isError = isNothing . errorToNothing +-- There should not be a problem if this ever appears in LeanCheck: +-- imports are qualfied in this module. diff --git a/src/Conjure/Engine.hs b/src/Conjure/Engine.hs --- a/src/Conjure/Engine.hs +++ b/src/Conjure/Engine.hs @@ -1,6 +1,6 @@ -- | -- Module : Conjure.Engine --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- @@ -31,11 +31,9 @@ , candidateDefnsC , conjureTheory , conjureTheoryWith - , equalModuloTesting , module Data.Express , module Data.Express.Fixtures - , module Test.Speculate.Engine - , module Test.Speculate.Reason + , module Conjure.Reason ) where @@ -43,22 +41,20 @@ import Data.Express import Data.Express.Fixtures hiding ((-==-)) -import qualified Data.Express.Triexpr as T -import Data.Dynamic (fromDyn, dynApp) - import Test.LeanCheck import Test.LeanCheck.Tiers -import Test.LeanCheck.Error (errorToTrue, errorToFalse, errorToNothing) +import Test.LeanCheck.Error (errorToFalse) import Test.LeanCheck.Utils (classifyOn) -import Test.Speculate.Reason (Thy, rules, equations, invalid, canReduceTo, printThy, closureLimit, doubleCheck) -import Test.Speculate.Engine (theoryFromAtoms, grounds, groundBinds, boolTy) - import Conjure.Expr import Conjure.Conjurable import Conjure.Prim import Conjure.Defn +import Conjure.Defn.Redundancy +import Conjure.Defn.Test +import Conjure.Red +import Conjure.Reason -- | Conjures an implementation of a partially defined function. @@ -338,25 +334,6 @@ else candidateDefns1 -nubCandidates :: Conjurable f => Args -> String -> f -> [[Defn]] -> [[Defn]] -nubCandidates Args{..} nm f = - discardLaterT $ equalModuloTesting maxTests maxEvalRecursions nm f - - -equalModuloTesting :: Conjurable f => Int -> Int -> String -> f -> Defn -> Defn -> Bool -equalModuloTesting maxTests maxEvalRecursions nm f = (===) - where - err = error "nubCandidates: unexpected evaluation error." - eq = conjureDynamicEq f - d1 === d2 = all are $ take maxTests $ grounds (conjureTiersFor f) (conjureVarApplication nm f) - where - are :: Expr -> Bool - are e = errorToFalse -- silences errors, ok since this is for optional measuring of optimal pruning - $ (`fromDyn` err) - $ eq `dynApp` fromMaybe err (toDynamicWithDefn (conjureExpress f) maxEvalRecursions d1 e) - `dynApp` fromMaybe err (toDynamicWithDefn (conjureExpress f) maxEvalRecursions d2 e) - - -- | Return apparently unique candidate definitions -- where there is a single body. candidateDefns1 :: Conjurable f => Args -> String -> f -> [Prim] -> ([[Defn]], Thy) @@ -435,8 +412,8 @@ keepNumeric e = isFun e || isConst e || not (isGround e) ps2fss :: [Expr] -> [[Defn]] - ps2fss pats = discardT isRedundantDefn - . discardT (allEqual2 . map snd) + ps2fss pats = discardT (isRedundantModuloRewriting $ normalize thy) + . discardT isRedundantDefn . products $ map p2eess pats where @@ -508,78 +485,6 @@ errRV = error "candidateDefnsC: unexpected variables. You have found a bug, please report it." --- | Returns whether the given recursive call --- deconstructs one of its arguments. --- --- > > deconstructs1 ... (factorial' (dec' xx)) --- > True --- --- > > deconstructs1 ... (factorial' (xx -+- one)) --- > False --- --- > > deconstructs1 ... (xxs -++- yys) --- > False --- --- > > deconstructs1 ... (xxs -++- tail' yys) --- > True --- --- > > deconstructs1 ... (zero-:-xxs -++- tail' yys) --- > True --- --- 'deconstructs1' implies 'descends'. -deconstructs1 :: (Expr -> Bool) -> Expr -> Expr -> Bool -deconstructs1 isDec _ e = any isDeconstruction exs - where - (ef:exs) = unfoldApp e - isDeconstruction e = not (null cs) && all isDec cs - where - cs = consts e - --- | Returns whether a non-empty subset of arguments --- descends arguments by deconstruction. --- --- > > descends isDec (xxs -++- yys) (xxs -++- tail' yys) --- > True --- --- > > descends isDec (xxs -++- yys) (xxs -++- yys) --- > False --- --- > > descends isDec (xxs -++- yys) (head' xxs -:- tail xxs -++- head' yys -:- tail yys) --- > False - --- > > descends isDec (xxs -\/- yys) (yys -\/- tail' xxs) --- > True --- --- The following are not so obvious: --- --- > > descends isDec (xxs -++- yys) (tail' yys -++- yys) --- > False --- --- > > descends isDec (xxs -++- yys) (xx-:-xxs -++- tail' yys) --- > True --- --- For all possible sets of arguments (2^n - 1 elements: 1 3 7 15 31), --- see if any projects the same variables while only using deconstructions --- and where there is at least a single deconstruction. -descends :: (Expr -> Expr -> Bool) -> Expr -> Expr -> Bool -descends isDecOf e' e = any d1 ss - where - desc = any d1 . uncurry useMatches . unzip - d1 exys = all isNotConstruction exys - && any isDeconstruction exys - ss = init $ sets exys - exys = zip exs eys - (_:exs) = unfoldApp e' - (_:eys) = unfoldApp e - isDeconstruction (p,e) | isVar p = e `isDecOf` p - | otherwise = size e < size p - where - cs = consts e - isNotConstruction (p,e) | isVar p = e == p || e `isDecOf` p - | otherwise = size e <= size p -- TODO: allow filter and id somehow --- TODO: improve this function with better isNotConstruction - - -- | Checks if the given pattern is a ground pattern. -- -- A pattern is a ground pattern when its arguments are fully defined @@ -635,44 +540,22 @@ keepIf _ = error "Conjure.Engine.keepIf: not an if" +-- equality between candidates ---- normality checks --- +nubCandidates :: Conjurable f => Args -> String -> f -> [[Defn]] -> [[Defn]] +nubCandidates Args{..} nm f = + discardLaterT $ equalModuloTesting maxTests maxEvalRecursions nm f -isRootNormal :: Thy -> Expr -> Bool -isRootNormal thy e = null $ T.lookup e trie - where - trie = T.fromList (rules thy) --- the logic of this function is a bit twisted for performance --- but nevertheless correct -isRootNormalC :: Thy -> Expr -> Bool -isRootNormalC thy e | not (isRootNormal thy e) = False -isRootNormalC thy (ef :$ ex :$ ey) - | ex <= ey = True - | not (isCommutative thy ef) = True - | isRootNormal thy (ef :$ ey :$ ex) = False -isRootNormalC _ _ = True - -isRootNormalE :: Thy -> Expr -> Bool -isRootNormalE thy e = isRootNormal thy e - && null (filter (e ->-) [e2 //- bs | (_,bs,e2) <- T.lookup e trie]) - where - trie = T.fromList $ equations thy ++ map swap (equations thy) - (->-) = canReduceTo thy - -isCommutative :: Thy -> Expr -> Bool -isCommutative thy eo = eo `elem` commutativeOperators thy - -commutativeOperators :: Thy -> [Expr] -commutativeOperators thy = [ ef - | (ef :$ ex :$ ey, ef' :$ ey' :$ ex') <- equations thy - , ef == ef' - , ex == ex' - , ey == ey' - ] +--- tiers utils --- +productsThat :: (a -> [a] -> Bool) -> [ [[a]] ] -> [[ [a] ]] +productsThat p = foldr (productWithThat (:) p) [[[]]] ---- tiers utils --- +productWithThat :: (a->b->c) -> (a->b->Bool) -> [[a]] -> [[b]] -> [[c]] +productWithThat f p xss yss = mapT (uncurry f) + . filterT (uncurry p) + $ xss >< yss productsWith :: ([a] -> a) -> [ [[a]] ] -> [[a]] productsWith f = mapT f . products @@ -684,3 +567,6 @@ foldAppProducts :: Expr -> [ [[Expr]] ] -> [[Expr]] foldAppProducts ef = delayedProductsWith (foldApp . (ef:)) + +boolTy :: TypeRep +boolTy = typ b_ diff --git a/src/Conjure/Expr.hs b/src/Conjure/Expr.hs --- a/src/Conjure/Expr.hs +++ b/src/Conjure/Expr.hs @@ -1,6 +1,6 @@ -- | -- Module : Conjure.Expr --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- @@ -31,6 +31,8 @@ , deholings , varToConst , hasAppInstanceOf + , isNegative + , isStrictSubexprOf , enumerateAppsFor , enumerateFillings @@ -43,6 +45,11 @@ , conflicts , listConflicts + , grounds + , groundBinds + + , rvars + , module Conjure.Utils ) where @@ -60,6 +67,8 @@ import Test.LeanCheck.Tiers (products) import Test.LeanCheck.Utils.Types (A, B, C, D, E, F) +import Test.Speculate.Expr (grounds, groundBinds) + -- | /O(n)/. -- Compares the simplicity of two 'Expr's. -- An expression /e1/ is /strictly simpler/ than another expression /e2/ @@ -530,6 +539,36 @@ where fun (ef :$ _) = ef arg (_ :$ ex) = ex + +-- | Is the expression encoding a negative number. +-- +-- This function is sort of a hack. +isNegative :: Expr -> Bool +isNegative (Value ('-':_) _) = True +isNegative _ = False + +-- | Lists all variables in an expression +-- that are of the same type of the expression itself. +-- +-- > > rvars (ff xx) +-- > [x :: Int] +-- +-- > > rvars (xx -:- xxs -++- yys) +-- > [xs :: [Int], ys :: [Int]] +-- +-- They are listed and without repetitions in 'Expr' order: +-- +-- > > rvars (xx -:- yys -++- xxs -++- xxs) +-- > [xs :: [Int],ys :: [Int]] +-- +-- (cf. nubVars) +rvars :: Expr -> [Expr] +rvars e = [ex | ex <- nubVars e, typ ex == typ e] + +-- | Is this a /strict/ subexpression? +isStrictSubexprOf :: Expr -> Expr -> Bool +isStrictSubexprOf e1 e2 = e1 /= e2 + && e1 `isSubexprOf` e2 instance Express A where expr = val instance Express B where expr = val diff --git a/src/Conjure/Prim.hs b/src/Conjure/Prim.hs --- a/src/Conjure/Prim.hs +++ b/src/Conjure/Prim.hs @@ -1,6 +1,6 @@ -- | -- Module : Conjure.Prim --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- @@ -27,7 +27,6 @@ import Conjure.Utils import Test.LeanCheck.Error (errorToFalse) import Test.LeanCheck.Utils -import Test.Speculate.Expr -- | A primtive expression (paired with instance reification). @@ -91,7 +90,13 @@ (-==-) = cjMkEquation ps e1 === e2 = isTrue $ e1 -==- e2 isTrue = all (errorToFalse . eval False) . gs - gs = take maxTests . grounds (cjTiersFor ps) + gs = take maxTests . cjGrounds ps + +-- | Given a list of 'Prim's, +-- computes a grounds function that lists +-- ground expressions of an 'Expr'. +cjGrounds :: [Prim] -> Expr -> [Expr] +cjGrounds = grounds . cjTiersFor -- | Given a list of 'Prim's, -- returns a function that given an 'Expr' diff --git a/src/Conjure/Reason.hs b/src/Conjure/Reason.hs new file mode 100644 --- /dev/null +++ b/src/Conjure/Reason.hs @@ -0,0 +1,80 @@ +-- | +-- Module : Conjure.Reason +-- Copyright : (c) 2021-2024 Rudy Matela +-- License : 3-Clause BSD (see the file LICENSE) +-- Maintainer : Rudy Matela +-- +-- An internal module of "Conjure", +-- a library for Conjuring function implementations +-- from tests or partial definitions. +-- (a.k.a.: functional inductive programming) +-- +-- This module re-exports some functions from "Test.Speculate" +-- along with a few additional utilities. +module Conjure.Reason + ( Thy + , rules + , equations + , invalid + , canReduceTo + , printThy + , closureLimit + , doubleCheck + , normalize + , theoryFromAtoms + , isRootNormalC + , isRootNormalE + , isCommutative + , commutativeOperators + ) +where + +import Test.Speculate.Reason + ( Thy + , rules + , equations + , invalid + , canReduceTo + , printThy + , closureLimit + , doubleCheck + , normalize + ) +import Test.Speculate.Engine (theoryFromAtoms) +import Conjure.Expr +import qualified Data.Express.Triexpr as T + +--- normality checks --- + +isRootNormal :: Thy -> Expr -> Bool +isRootNormal thy e = null $ T.lookup e trie + where + trie = T.fromList (rules thy) + +-- the logic of this function is a bit twisted for performance +-- but nevertheless correct +isRootNormalC :: Thy -> Expr -> Bool +isRootNormalC thy e | not (isRootNormal thy e) = False +isRootNormalC thy (ef :$ ex :$ ey) + | ex <= ey = True + | not (isCommutative thy ef) = True + | isRootNormal thy (ef :$ ey :$ ex) = False +isRootNormalC _ _ = True + +isRootNormalE :: Thy -> Expr -> Bool +isRootNormalE thy e = isRootNormal thy e + && null (filter (e ->-) [e2 //- bs | (_,bs,e2) <- T.lookup e trie]) + where + trie = T.fromList $ equations thy ++ map swap (equations thy) + (->-) = canReduceTo thy + +isCommutative :: Thy -> Expr -> Bool +isCommutative thy eo = eo `elem` commutativeOperators thy + +commutativeOperators :: Thy -> [Expr] +commutativeOperators thy = [ ef + | (ef :$ ex :$ ey, ef' :$ ey' :$ ex') <- equations thy + , ef == ef' + , ex == ex' + , ey == ey' + ] diff --git a/src/Conjure/Red.hs b/src/Conjure/Red.hs new file mode 100644 --- /dev/null +++ b/src/Conjure/Red.hs @@ -0,0 +1,150 @@ +-- | +-- Module : Conjure.Red +-- Copyright : (c) 2021-2024 Rudy Matela +-- License : 3-Clause BSD (see the file LICENSE) +-- Maintainer : Rudy Matela +-- +-- This module is part of "Conjure". +-- +-- This defines functions that deal with recursive descent and deconstructions +module Conjure.Red + ( conjureIsDeconstruction + , descends + , candidateDeconstructionsFrom + , candidateDeconstructionsFromHoled + ) +where + +import Conjure.Defn +import Conjure.Conjurable +import Test.LeanCheck.Error (errorToFalse) + +-- | Checks if an expression is a deconstruction. +-- +-- There should be a single 'hole' in the expression. +-- +-- It should decrease the size of all arguments that have +-- a size greater than 0. +conjureIsDeconstruction :: Conjurable f => f -> Int -> Expr -> Bool +conjureIsDeconstruction f maxTests ed + = length (holes ed) == 1 -- Well formed deconstruction, single hole. + && typ h == typ ed -- We can only deconstruct to the same type. + && all is sizes -- Do we always reduce size? + && not (all iz sizes) -- Disallow always mapping to values of size 0. + -- In this case, we are better off not recursing + -- and returning a constant value! + where + x << 0 = True + x << y = x < y + is (sd,sx) = errorToFalse $ sd << sx + iz (sd,sx) = errorToFalse $ sd == 0 || sx == 0 + -- We cannot simply conjureTiers for h here, because the deconstruction + -- expression may contain variables, e.g.: @x `mod` _@. + -- So conjureGrounds and the holeValue trick are required. + sizes = map evalSize2 . take maxTests $ conjureGrounds f ed + [h] = holes ed + evalSize2 e = (evalSize e, evalSize $ holeValue e) + evalSize e = eval (0::Int) (esize :$ e) + esize = conjureSizeFor f h + holeValue e = fromMaybe err . lookup h . fromMaybe err $ e `match` ed + err = error "Conjure.conjureIsDeconstruction: the impossible happened" + +-- | Returns whether a non-empty subset of arguments +-- descends arguments by deconstruction. +-- +-- > > descends isDec (xxs -++- yys) (xxs -++- tail' yys) +-- > True +-- +-- > > descends isDec (xxs -++- yys) (xxs -++- yys) +-- > False +-- +-- > > descends isDec (xxs -++- yys) (head' xxs -:- tail xxs -++- head' yys -:- tail yys) +-- > False + +-- > > descends isDec (xxs -\/- yys) (yys -\/- tail' xxs) +-- > True +-- +-- The following are not so obvious: +-- +-- > > descends isDec (xxs -++- yys) (tail' yys -++- yys) +-- > False +-- +-- > > descends isDec (xxs -++- yys) (xx-:-xxs -++- tail' yys) +-- > True +-- +-- For all possible sets of arguments (2^n - 1 elements: 1 3 7 15 31), +-- see if any projects the same variables while only using deconstructions +-- and where there is at least a single deconstruction. +descends :: (Expr -> Expr -> Bool) -> Expr -> Expr -> Bool +descends isDecOf efls efrs = any hasDeconstruction + $ classifyOn (typ . fst) (zip ls rs) + where + (_:ls) = unfoldApp efls + (_:rs) = unfoldApp efrs + + hasDeconstruction :: [(Expr,Expr)] -> Bool + hasDeconstruction lrs = or [b *<< bs | (b,bs) <- choices lrs] + + r << l = any (r `isDecOf`) (rvars l) + || r `isStrictSubexprOf` l + || isGround r && not (isGround l) && size r < size l + + r <<= l = r == l + || r << l + + (l,r) *<< bs = r << l + || or [ (l',r) *<<= bs' + | ((l',r'),bs') <- choices bs + , r' << l + ] + + (l,r) *<<= bs = r <<= l + || or [ (l',r) *<<= bs' + | ((l',r'),bs') <- choices bs + , r' <<= l + ] + +-- | Compute candidate deconstructions from an 'Expr'. +-- +-- This is used in the implementation of 'Conjure.Engine.candidateDefnsC' +-- followed by 'conjureIsDeconstruction'. +-- +-- > > candidateDeconstructionsFrom (xx `mod'` yy) +-- > [ _ `mod` y +-- > , x `mod` _ +-- > ] +-- +-- To be constrasted with 'candidateDeconstructionsFromHoled'. +candidateDeconstructionsFrom :: Expr -> [Expr] +candidateDeconstructionsFrom e = + [ e' + | v <- vars e + , typ v == typ e + , let e' = e //- [(v, holeAsTypeOf v)] + , length (holes e') == 1 + ] + +-- | Compute candidate deconstructions from an 'Expr'. +-- +-- This is used in the implementation of 'Conjure.Engine.candidateExprs' +-- followed by 'conjureIsDeconstruction'. +-- +-- This is similar to 'canonicalVariations' +-- but always leaves a hole +-- of the same return type as the given expression. +-- +-- > > candidateDeconstructionsFrom (i_ `mod'` i_) +-- > [ _ `mod` x +-- > , x `mod` _ +-- > ] +-- +-- To be contrasted with 'candidateDeconstructionsFrom' +candidateDeconstructionsFromHoled :: Expr -> [Expr] +candidateDeconstructionsFromHoled e = map (//- [(v, h)]) + $ concatMap canonicalVariations + $ deholings v e + where + h = holeAsTypeOf e + v = "_#_" `varAsTypeOf` e -- a marker variable with an invalid name + -- at some point I should get rid of candidateDeconstructionsFrom in favour + -- of this one diff --git a/src/Conjure/Utils.hs b/src/Conjure/Utils.hs --- a/src/Conjure/Utils.hs +++ b/src/Conjure/Utils.hs @@ -1,6 +1,6 @@ -- | -- Module : Conjure.Utils --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- @@ -45,6 +45,7 @@ , second , both , (+++) + , isSubsetOf ) where @@ -57,6 +58,7 @@ import System.IO.Unsafe +import Data.Express.Utils.List (isSubsetOf) import Test.LeanCheck.Stats (classify, classifyBy, classifyOn) diff --git a/stack.yaml b/stack.yaml --- a/stack.yaml +++ b/stack.yaml @@ -1,6 +1,6 @@ # Stack file for the Conjure program generation library. # -# Copyright (C) 2021 Rudy Matela +# Copyright (C) 2021-2024 Rudy Matela # Distributed under the 3-Clause BSD licence (see the file LICENSE). resolver: lts-19.19 # or ghc-9.0.2 @@ -11,4 +11,4 @@ extra-deps: - leancheck-1.0.2 - speculate-0.4.14 -- express-1.0.14 +- express-1.0.16 diff --git a/test/Test.hs b/test/Test.hs --- a/test/Test.hs +++ b/test/Test.hs @@ -1,6 +1,6 @@ -- | -- Module : Test --- Copyright : (c) 2021 Rudy Matela +-- Copyright : (c) 2021-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- @@ -15,6 +15,7 @@ , module Test.ListableExpr , mainTest + , conjurableOK ) where @@ -51,3 +52,20 @@ printLines :: Show a => [a] -> IO () printLines = putStrLn . unlines . map show + + +-- checks if the functions conjureEquality, conjureExpress and conjureTiers +-- were correctly generated. +conjurableOK :: (Eq a, Show a, Express a, Listable a, Conjurable a) => a -> Bool +conjurableOK x = and + [ holds 60 $ (-==-) ==== (==) + , holds 60 $ expr' === expr + , tiers =| 6 |= (tiers -: [[x]]) + , all isWellTyped cases' + , all (\c -> typ c == typeOf x) cases' + ] + where + (-==-) = evl (fromJust $ conjureEquality x) -:> x + tiers' = mapT evl (fromJust $ conjureTiers x) -: [[x]] + expr' = (conjureExpress x . val) -:> x + cases' = conjureCases x diff --git a/test/Test/ListableExpr.hs b/test/Test/ListableExpr.hs --- a/test/Test/ListableExpr.hs +++ b/test/Test/ListableExpr.hs @@ -1,6 +1,6 @@ -- | -- Module : Test.ListableExpr --- Copyright : (c) 2019-2021 Rudy Matela +-- Copyright : (c) 2019-2024 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela -- diff --git a/test/conjurable.hs b/test/conjurable.hs --- a/test/conjurable.hs +++ b/test/conjurable.hs @@ -1,4 +1,4 @@ --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# Language DeriveDataTypeable, StandaloneDeriving #-} -- for GHC < 7.10 @@ -224,42 +224,6 @@ ] ] - , isDecon (minus :$ i_ :$ one) == True - , isDecon (minusOne -+- i_) == True - , isDecon (div' i_ two) == True - , isDecon (tail' is_) == True - , isDecon (init' is_) == True - - -- counter-intuitive but true: x `mod` y is a deconstruction of y: - -- x `mod` y < y for y > 0 - , isDecon (mod' xx i_) == True - - , isDecon (mod' i_ two) == False -- does not deconstruct 1 - , isDecon (mod' i_ xx) == False -- may not deconstruct 1 - , isDecon (div' xx yy) == False -- must have a hole to indicate the value being deconstructed - , isDecon (div' i_ i_) == False -- two holes are not allowed - , isDecon (head' is_) == False -- must deconstruct to the same type - , isDecon (i_ -*- two) == False -- increases the size - - , candidateDeconstructionsFrom (div' xx yy) == [ div' i_ yy - , div' xx i_ - ] - , candidateDeconstructionsFrom (div' xx xx) == [] - , candidateDeconstructionsFrom ((xx -+- xx) -+- yy) == [(xx -+- xx) -+- i_] - - , candidateDeconstructionsFromHoled (div' i_ i_) == [ div' i_ xx - , div' xx i_ - ] - , candidateDeconstructionsFromHoled (div' xx yy) == [] - , candidateDeconstructionsFromHoled ((i_ -+- i_) -+- i_) == - [ (i_ -+- xx) -+- yy - , (i_ -+- xx) -+- xx - , (xx -+- i_) -+- yy - , (xx -+- i_) -+- xx - , (xx -+- yy) -+- i_ - , (xx -+- xx) -+- i_ - ] - , fromDynamic (conjureDynamicEq ((+) :: Int -> Int -> Int) `dynApp` toDyn (1::Int) `dynApp` toDyn (2::Int)) == Just False , fromDynamic (conjureDynamicEq ((+) :: Int -> Int -> Int) `dynApp` toDyn (1::Int) `dynApp` toDyn (1::Int)) @@ -270,10 +234,66 @@ , isNumeric bee == False , isNumeric (expr [0::Int]) == False , isNumeric true == False - ] -isDecon :: Expr -> Bool -isDecon = conjureIsDeconstruction (undefined :: [Int] -> [Char] -> [Bool]) 60 + -- the following conjurableOK calls take 5 seconds to compile! + , conjurableOK (undefined :: ()) + , conjurableOK (undefined :: Bool) + , conjurableOK (undefined :: Int) + , conjurableOK (undefined :: Char) + , conjurableOK (undefined :: Integer) + , conjurableOK (undefined :: Ordering) + , conjurableOK (undefined :: Float) + , conjurableOK (undefined :: Double) + , conjurableOK (undefined :: Rational) + + , conjurableOK (undefined :: A) + , conjurableOK (undefined :: B) + , conjurableOK (undefined :: C) + , conjurableOK (undefined :: D) + , conjurableOK (undefined :: E) + , conjurableOK (undefined :: F) + + , conjurableOK (undefined :: [()]) + , conjurableOK (undefined :: [Bool]) + , conjurableOK (undefined :: [Int]) + , conjurableOK (undefined :: String) + + , conjurableOK (undefined :: ((),())) + , conjurableOK (undefined :: (Bool,Bool)) + , conjurableOK (undefined :: (Int,Int)) + , conjurableOK (undefined :: (Char,String)) + , conjurableOK (undefined :: (Bool,[Int])) + + , conjurableOK (undefined :: (Int,Int,Int)) + , conjurableOK (undefined :: (Bool,Int,Char)) + , conjurableOK (undefined :: ([Int],[Bool],String)) + + , conjurableOK (undefined :: Maybe ()) + , conjurableOK (undefined :: Maybe Bool) + , conjurableOK (undefined :: Maybe Int) + , conjurableOK (undefined :: Maybe Char) + , conjurableOK (undefined :: Maybe String) + + , conjurableOK (undefined :: Either () ()) + , conjurableOK (undefined :: Either Bool Bool) + , conjurableOK (undefined :: Either Int Int) + , conjurableOK (undefined :: Either String Int) + , conjurableOK (undefined :: Either String Char) + + , conjurableOK (undefined :: (Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int,Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int,Int,Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int,Int,Int,Int,Int,Int,Int)) + , conjurableOK (undefined :: (Int,Int,Int,Int,Int,Int,Int,Int,Int,Int,Int,Int)) + + -- little sanity check (conjurableOK should catch it anyway) + , take 6 (conjureListFor (undefined :: Int) i_) + == [zero, one, minusOne, two, minusTwo, three] + ] isNumeric :: Expr -> Bool isNumeric = conjureIsNumeric (undefined :: [Int] -> [Char] -> [Bool] -> [Integer]) diff --git a/test/defn.hs b/test/defn.hs --- a/test/defn.hs +++ b/test/defn.hs @@ -1,8 +1,9 @@ --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Test import Conjure.Defn +import Conjure.Defn.Redundancy import Test.LeanCheck.Error (errorToLeft) import Test.LeanCheck.Function () import Data.Express.Fixtures @@ -153,6 +154,36 @@ , not $ isBaseCase (ff (xx -:- xxs), ff xxs) , isRecursiveCase (ff (xx -:- xxs), ff xxs) , not $ isRecursiveCase (ff (xx -:- nil), xx) + + , subsumedWith (// [(zero -+- zero, zero)]) (ff zero, zero) (ff xx, xx -+- xx) == True + , subsumedWith (// [(zero -+- zero, zero)]) (ff zero, zero) (ff xx, xx -+- zero) == True + , subsumedWith (// [(zero -+- zero, zero)]) (ff zero, zero) (ff xx, xx -+- one) == False + , subsumedWith (// [(zero -+- zero, zero)]) (zero -?- xx, zero) (xx -?- yy, xx -+- xx) == True + , subsumedWith (// [(zero -+- zero, zero)]) (zero -?- xx, zero) (xx -?- yy, xx -+- zero) == True + , subsumedWith (// [(zero -+- zero, zero)]) (zero -?- xx, zero) (xx -?- yy, xx -+- one) == False + , subsumedWith (// [(zero -+- zero, zero)]) (zero -?- xx, zero) (xx -?- yy, xx -+- yy) == False + + , isRedundantModuloRewriting (// [(zero -+- zero, zero)]) [(ff zero, zero),(ff xx, xx -+- xx)] == True + , isRedundantModuloRewriting (// [(zero -+- zero, zero)]) [(ff zero, zero),(ff xx, xx -+- zero)] == True + , isRedundantModuloRewriting (// [(zero -+- zero, zero)]) [(ff zero, zero),(ff xx, xx -+- one)] == False + , isRedundantModuloRewriting (// [(zero -+- zero, zero)]) [(zero -?- xx, zero),(xx -?- yy, xx -+- xx)] == True + , isRedundantModuloRewriting (// [(zero -+- zero, zero)]) [(zero -?- xx, zero),(xx -?- yy, xx -+- zero)] == True + , isRedundantModuloRewriting (// [(zero -+- zero, zero)]) [(zero -?- xx, zero),(xx -?- yy, xx -+- one)] == False + , isRedundantModuloRewriting (// [(zero -+- zero, zero)]) [(zero -?- xx, zero),(xx -?- yy, xx -+- yy)] == False + + , isRedundantModuloRewriting (// [(xx -+- zero, xx)]) + [ (zero -?- xx, xx) + , (xx -?- zero, xx) + , (xx -?- yy, xx -+- xx) + ] == False + + , subsumedWith (// [(xx -+- zero, xx)]) (xx -?- zero, xx) (xx -?- yy, xx -+- yy) == True + + , isRedundantModuloRewriting (// [(xx -+- zero, xx)]) + [ (zero -?- xx, xx) + , (xx -?- zero, xx) + , (xx -?- yy, xx -+- yy) + ] == True ] dvl :: Typeable a => Defn -> Expr -> a diff --git a/test/derive.hs b/test/derive.hs --- a/test/derive.hs +++ b/test/derive.hs @@ -1,4 +1,4 @@ --- Copyright (c) 2019-2021 Rudy Matela. +-- Copyright (c) 2019-2024 Rudy Matela. -- Distributed under the 3-Clause BSD licence (see the file LICENSE). {-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE DeriveDataTypeable #-} @@ -150,20 +150,6 @@ , hole (undefined :: Bool) ] ] - - --- checks if the functions conjureEquality, conjureExpress and conjureTiers --- were correctly generated. -conjurableOK :: (Eq a, Show a, Express a, Listable a, Conjurable a) => a -> Bool -conjurableOK x = and - [ holds 60 $ (-==-) ==== (==) - , holds 60 $ expr' === expr - , tiers =| 6 |= (tiers -: [[x]]) - ] - where - (-==-) = evl (fromJust $ conjureEquality x) -:> x - tiers' = mapT evl (fromJust $ conjureTiers x) -: [[x]] - expr' = (conjureExpress x . val) -:> x -- proxies -- diff --git a/test/expr.hs b/test/expr.hs --- a/test/expr.hs +++ b/test/expr.hs @@ -1,4 +1,4 @@ --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Test @@ -151,6 +151,27 @@ , listConflicts [(one -+- zz), (two -+- yy), (three -+- xx)] == [[zz,yy,xx],[one,two,three]] , holds n $ \e1 e2 -> map listPair (conflicts e1 e2) == listConflicts [e1,e2] + + , rvars xx == [xx] + , rvars (xx -?- yy) == [xx, yy] + , rvars (xx -?- yy -?- zz) == [xx, yy, zz] + , rvars (yy -?- yy -?- xx) == [xx, yy] + + , rvars xxs == [xxs] + , rvars (xx -:- xxs) == [xxs] + , rvars (xx -:- yy -:- xxs) == [xxs] + , rvars (xxs -++- yys) == [xxs, yys] + , rvars (xx -:- xxs -++- yys) == [xxs, yys] + , rvars (xx -:- yys -++- xxs -++- xxs) == [xxs, yys] + + , rvars (pp -&&- qq) == [pp, qq] + , rvars (qq -&&- pp) == [pp, qq] + , rvars (pp -||- qq -&&- pp) == [pp, qq] + + , xx `isStrictSubexprOf` xx == False + , xx `isStrictSubexprOf` (xx -+- yy) == True + , xx `isStrictSubexprOf` (yy -+- yy) == False + , (xx -+- yy) `isStrictSubexprOf` (xx -+- yy) == False ] listPair :: (a,a) -> [a] diff --git a/test/mk b/test/mk new file mode 100644 --- /dev/null +++ b/test/mk @@ -0,0 +1,35 @@ +#!/bin/bash +# +# test/mk: tests the makefile of Conjure itself +# +# This tests that the makefile is thorough and actually +# runs all tests scripts and benchmarks when asked to do so. +# +# Copyright (c) 2024 Rudy Matela. +# Distributed under the 3-Clause BSD licence. + +set -xe + +export LC_ALL=C # consistent sort +diff="diff --color -rud" + +tmp=`mktemp -d /tmp/test-mk-XXXXXXXXXX` +[ -d "$tmp" ] || exit 1 + +rmhs() { sed -e 's/.hs$//'; } +rmtarget() { sed -e 's/:.*//'; } +flt() { + rmhs | # excludes extensions from the result of find + rmtarget | # exclude Makefile target indicators + grep -v '^bench/avgs$' | # not an actual benchmark + grep -v '^.*/[A-Z].*$' # test/benchmark/example scripts begin with lowercase +} + +make -s ls-eg ls-test | sort >$tmp/ls-mk +find eg bench proto test -name '*.hs' -maxdepth 1 | flt | sort >$tmp/ls-find +grep -E "^[^/]*/[^.]*:" mk/depend.mk | flt | sort >$tmp/ls-depend +grep -E "(eg|bench|proto|test)/" .gitignore | flt | sort >$tmp/ls-gitignore +$diff $tmp/ls-{mk,find} # compares make variables with actual directory +$diff $tmp/ls-{mk,depend} # compares make variables with mk/depend.mk +$diff $tmp/ls-{mk,gitignore} # compare make variables with .gitignore +rm -r $tmp diff --git a/test/red.hs b/test/red.hs new file mode 100644 --- /dev/null +++ b/test/red.hs @@ -0,0 +1,165 @@ +-- Copyright (C) 2021-2024 Rudy Matela +-- Distributed under the 3-Clause BSD licence (see the file LICENSE). + +import Test +import Conjure.Red +import Data.Dynamic + +main :: IO () +main = mainTest tests 5040 + +tests :: Int -> [Bool] +tests n = + [ True + + -- tests of conjureIsDeconstruction -- + + -- obvious deconstructions + , isDecon (minus :$ i_ :$ one) == True + , isDecon (minus :$ i_ :$ two) == True + , isDecon (div' i_ two) == True + , isDecon (tail' is_) == True + , isDecon (init' is_) == True + , isDecon (drop' one is_) == True + + -- obvious constructions + , isDecon (i_ -+- one) == False + , isDecon (i_ -+- two) == False + , isDecon (i_ -*- two) == False + , isDecon (xx -:- is_) == False + , isDecon (is_ -++- unit xx) == False + + -- doing nothing is not deconstructing + , isDecon (i_) == False + , isDecon (is_) == False + + -- double deconstructions & constructions + , isDecon (minusOne -+- i_) == True + , isDecon (minus :$ (minus :$ i_ :$ one) :$ one) == True + , isDecon (minus :$ i_ :$ three) == True + , isDecon (minus :$ i_ :$ four) == True + , isDecon (minus :$ i_ :$ five) == True + , isDecon (minus :$ i_ :$ six) == True + , isDecon (drop' two is_) == True + , isDecon (drop' three is_) == True + , isDecon (drop' xx is_) == False -- may not deconstruct! + + , isDecon (tail' (tail' is_)) == False -- does not deconstruct [1] + , isDecon (init' (init' is_)) == False -- does not deconstruct [1] + , isDecon (init' (tail' is_)) == False -- does not deconstruct [1] + + , isDecon (drop' one (drop' one is_)) == True + , isDecon (drop' one (tail' is_)) == True + + , isDecon (take' one is_) == False -- does not deconstruct [1] + , isDecon (take' two is_) == False -- does not deconstruct [1,1] + + -- counter-intuitive but true: x `mod` y is a deconstruction of y: + -- x `mod` y < y for y > 0 + , isDecon (mod' xx i_) == True + + , isDecon (mod' i_ two) == False -- does not deconstruct 1 + , isDecon (mod' i_ xx) == False -- may not deconstruct 1 + , isDecon (div' xx yy) == False -- must have a hole to indicate the value being deconstructed + , isDecon (div' i_ i_) == False -- two holes are not allowed + , isDecon (head' is_) == False -- must deconstruct to the same type + + -- constant "deconstructions" + , isDecon (const' zero i_) == False -- always mapping to size 0 is not allowed! + , isDecon (const' nil is_) == False -- always mapping to size 0 is not allowed! + , isDecon (const' one i_) == False -- does not deconstruct 1 + + -- negative "deconstructions" + , isDecon (minus :$ zero :$ i_) == False + , isDecon (minus :$ one :$ i_) == False + + -- boolean "deconstructions" + , isDecon (not' b_) == False -- always mapping to size 0 is not allowed! + , isDecon (false -||- b_) == False -- always mapping to size 0 is not allowed! + + , candidateDeconstructionsFrom (div' xx yy) == [ div' i_ yy + , div' xx i_ + ] + , candidateDeconstructionsFrom (div' xx xx) == [] + , candidateDeconstructionsFrom ((xx -+- xx) -+- yy) == [(xx -+- xx) -+- i_] + + , candidateDeconstructionsFromHoled (div' i_ i_) == [ div' i_ xx + , div' xx i_ + ] + , candidateDeconstructionsFromHoled (div' xx yy) == [] + , candidateDeconstructionsFromHoled ((i_ -+- i_) -+- i_) == + [ (i_ -+- xx) -+- yy + , (i_ -+- xx) -+- xx + , (xx -+- i_) -+- yy + , (xx -+- i_) -+- xx + , (xx -+- yy) -+- i_ + , (xx -+- xx) -+- i_ + ] + + -- simple integer descent + , descends isDecOf (ff xx) (ff xx) == False + , descends isDecOf (ff xx) (ff (xx -+- one)) == False + , descends isDecOf (ff xx) (ff (dec xx)) == True + , descends isDecOf (ff xx) (ff (yy `mod'` xx)) == True + + -- simple list descent + , descends isDecOf (ff xxs) (ff xxs) == False + , descends isDecOf (ff xxs) (ff (tail' xxs)) == True + , descends isDecOf (ff (xx -:- xxs)) (ff xxs) == True + , descends isDecOf (ff xxs) (ff (xxs -++- xxs)) == False + + -- double integer descent + , descends isDecOf (ff2 xx yy) (ff2 xx yy) == False + , descends isDecOf (ff2 xx yy) (ff2 (xx -+- one) yy) == False + , descends isDecOf (ff2 xx yy) (ff2 (dec xx) yy) == True + , descends isDecOf (ff2 xx yy) (ff2 (dec yy) xx) == True + , descends isDecOf (ff2 xx yy) (ff2 xx (dec yy)) == True + , descends isDecOf (ff2 xx yy) (ff2 yy (dec xx)) == True + , descends isDecOf (ff2 xx yy) (ff2 (dec xx) (dec yy)) == True + , descends isDecOf (ff2 xx yy) (ff2 (dec yy) (dec xx)) == True + + -- double list descent + , descends isDecOf (xxs -++- yys) (xxs -++- yys) == False + , descends isDecOf (xxs -++- yys) (xxs -++- tail' yys) == True + + , descends isDecOf (xxs -++- yys) (tail' yys -++- yys) == False + , descends isDecOf (xxs -++- yys) ((xx -:- xxs) -++- tail' yys) == True + + , descends isDecOf (xxs -++- yys) (head' xxs -:- tail' xxs -++- head' yys -:- tail' yys) == False + + -- gcd descent + , descends isDecOf (ff2 xx yy) (ff2 yy (xx `mod'` yy)) == True -- actual gcd descent + , descends isDecOf (ff2 xx yy) (ff2 yy (yy `mod'` yy)) == True -- other + + -- interleave descent + , descends isDecOf (xxs -\/- yys) (yys -\/- tail' xxs) == True + , descends isDecOf (xxs -\/- yys) (tail' yys -\/- xxs) == True + , descends isDecOf (xxs -\/- yys) (tail' yys -\/- tail' xxs) == True + , descends isDecOf ((xx -:- xxs) -\/- yys) (yys -\/- xxs) == True + , descends isDecOf (xxs -\/- (yy -:- yys)) (yys -\/- xxs) == True + , descends isDecOf ((xx -:- xxs) -\/- (yy -:- yys)) (yys -\/- xxs) == True + + -- disallowed descents + , descends isDecOf ((xx -:- xxs) -?- (yy -:- yys)) (yys -?- (xx -:- yys)) == False + , descends isDecOf ((xx -:- xxs) -?- (yy -:- yys)) (yys -?- (yy -:- yys)) == False + ] + +isDecOf :: Expr -> Expr -> Bool +e1 `isDecOf` e2 = any ((e1 -|- e2) `isInstanceOf`) + [ tail' xxs -|- xxs + , dec xx -|- xx + , yy `mod'` xx -|- xx + ] + +(-\/-) :: Expr -> Expr -> Expr +exs -\/- eys = interleaveE :$ exs :$ eys + where + interleaveE = value "\\/" ((\/) :: [Int] -> [Int] -> [Int]) + [] \/ ys = ys + (x:xs) \/ ys = x : (ys \/ xs) + +isDecon :: Expr -> Bool +isDecon = conjureIsDeconstruction (undefined :: [Int] -> [Char] -> [Bool]) 60 + +dec :: Expr -> Expr +dec ex = minus :$ ex :$ one diff --git a/test/utils.hs b/test/utils.hs --- a/test/utils.hs +++ b/test/utils.hs @@ -1,4 +1,4 @@ --- Copyright (C) 2021 Rudy Matela +-- Copyright (C) 2021-2024 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Test