egison 4.1.3 → 4.2.0

raw patch · 42 files changed

+534/−64 lines, 42 filesdep ~containersdep ~directorydep ~exceptionsPVP ok

version bump matches the API change (PVP)

Dependency ranges changed: containers, directory, exceptions, filepath, parsec, random, regex-tdfa, sweet-egison, text, transformers, vector

API changes (from Hackage documentation)

Files

• egison.cabal +20/−20
• hs-src/Interpreter/egison.hs +1/−1
• hs-src/Language/Egison/Core.hs +2/−1
• hs-src/Language/Egison/Data.hs +4/−2
• hs-src/Language/Egison/Data/Collection.hs +2/−1
• hs-src/Language/Egison/Eval.hs +1/−0
• hs-src/Language/Egison/EvalState.hs +1/−0
• hs-src/Language/Egison/Math/Expr.hs +8/−8
• hs-src/Language/Egison/Math/Normalize.hs +3/−3
• hs-src/Language/Egison/Math/Rewrite.hs +13/−13
• hs-src/Language/Egison/Parser.hs +4/−2
• hs-src/Language/Egison/Pretty.hs +5/−5
• hs-src/Language/Egison/Primitives.hs +2/−1
• hs-src/Language/Egison/Primitives/IO.hs +2/−2
• hs-src/Language/Egison/Tensor.hs +2/−1
• hs-src/Tool/translator.hs +4/−4
• sample/math/geometry/chern-form-of-CP1.egi +24/−0
• sample/math/geometry/chern-form-of-CP2.egi +28/−0
• sample/math/geometry/euler-form-of-S2.egi +1/−0
• sample/math/geometry/euler-form-of-T2.egi +1/−0
• sample/math/geometry/exterior-derivative.egi +18/−0
• sample/math/geometry/hodge-E3.egi +28/−0
• sample/math/geometry/hodge-Minkowski.egi +30/−0
• sample/math/geometry/hodge-laplacian-spherical.egi +1/−0
• sample/math/geometry/polar-laplacian-2d-2.egi +1/−0
• sample/math/geometry/polar-laplacian-2d-3.egi +1/−0
• sample/math/geometry/polar-laplacian-2d.egi +27/−0
• sample/math/geometry/polar-laplacian-3d-2.egi +1/−0
• sample/math/geometry/polar-laplacian-3d-3.egi +1/−0
• sample/math/geometry/polar-laplacian-3d.egi +36/−0
• sample/math/geometry/riemann-curvature-tensor-of-FLRW-metric.egi +1/−0
• sample/math/geometry/riemann-curvature-tensor-of-S2xS3.egi +1/−0
• sample/math/geometry/riemann-curvature-tensor-of-S3.egi +1/−0
• sample/math/geometry/riemann-curvature-tensor-of-S4.egi +1/−0
• sample/math/geometry/riemann-curvature-tensor-of-S7.egi +1/−0
• sample/math/geometry/riemann-curvature-tensor-of-Schwarzschild-metric.egi +1/−0
• sample/math/geometry/surface.egi +58/−0
• sample/math/geometry/wedge-product.egi +25/−0
• sample/math/geometry/yang-mills-equation-of-U1-gauge-theory.egi +47/−0
• sample/math/number/eisenstein-primes.egi +46/−0
• sample/math/number/euler-totient-function.egi +36/−0
• sample/math/number/gaussian-primes.egi +44/−0

@@ -1,5 +1,5 @@ Name:                egison-Version:             4.1.3+Version:             4.2.0 Synopsis:            Programming language with non-linear pattern-matching against non-free data Description:   An interpreter for Egison, a **pattern-matching-oriented**, purely functional programming language.@@ -82,28 +82,28 @@   location: https://github.com/egison/egison.git  Library-  default-language:    Haskell2010+  default-language:    GHC2021   Build-Depends:       base                 >= 4.8     && < 5-    , random               == 1.*-    , containers           == 0.6.*+    , random               >= 1.0     && < 2.0+    , containers           >= 0.6     && < 0.8     , unordered-containers >= 0.1.0.0 && < 0.3     , haskeline            >= 0.7     && < 0.9-    , transformers         >= 0.4     && < 0.6+    , transformers         >= 0.4     && < 0.7     , mtl                  >= 2.2.2   && < 3.0-    , parsec               >= 3.0+    , parsec               >= 3.0     && < 4.0     , megaparsec           >= 7.0.0   && < 12.0     , parser-combinators   >= 1.0     && < 2.0-    , directory            >= 1.3.0-    , text                 >= 0.2     && < 1.3-    , regex-tdfa           >= 1.2.0+    , directory            >= 1.3.0   && < 2.0+    , text                 >= 0.2     && < 2.2+    , regex-tdfa           >= 1.2.0   && < 2.0     , process              >= 1.0     && < 2.0-    , vector               == 0.12.*+    , vector               >= 0.12    && < 0.14     , hashable             >= 1.0     && < 2.0     , optparse-applicative >= 0.14    && < 0.20     , prettyprinter        >= 1.0     && < 2.0-    , unicode-show         == 0.1.*-    , sweet-egison         == 0.1.1.3+    , unicode-show         >= 0.1     && < 0.2+    , sweet-egison         >= 0.1.2.1 && < 0.2   if !impl(ghc > 8.0)     Build-Depends: fail   Hs-Source-Dirs:  hs-src@@ -150,7 +150,7 @@   ghc-options:  -O3 -Wall -Wno-name-shadowing -Wno-incomplete-patterns  Test-Suite test-  default-language:    Haskell2010+  default-language:    GHC2021   Type:           exitcode-stdio-1.0   Hs-Source-Dirs: test   Main-Is:        Test.hs@@ -169,7 +169,7 @@   ghc-options:  -Wall -Wno-name-shadowing  Test-Suite test-cli-  default-language:    Haskell2010+  default-language:    GHC2021   Type:           exitcode-stdio-1.0   Hs-Source-Dirs: test   Main-Is:        CLITest.hs@@ -185,7 +185,7 @@   ghc-options:  -Wall -Wno-name-shadowing  Benchmark benchmark-  default-language:    Haskell2010+  default-language:    GHC2021   Type: exitcode-stdio-1.0   Hs-Source-Dirs:  benchmark   Main-Is: Benchmark.hs@@ -199,16 +199,16 @@   ghc-options:  -Wall -Wno-name-shadowing  Executable egison-  default-language:    Haskell2010+  default-language:    GHC2021   Main-is:             egison.hs   Build-depends:       egison     , base >= 4.0 && < 5-    , exceptions+    , exceptions           >= 0.10    && < 0.11     , haskeline     , mtl     , directory-    , filepath+    , filepath             >= 1.4     && < 2.0     , text     , regex-tdfa     , optparse-applicative@@ -217,10 +217,10 @@   Hs-Source-Dirs:      hs-src/Interpreter   Other-modules:       Paths_egison   autogen-modules: Paths_egison-  ghc-options:  -O3 -threaded -eventlog -rtsopts -Wall -Wno-name-shadowing+  ghc-options:  -O3 -threaded -rtsopts -Wall -Wno-name-shadowing  Executable egison-translate-  default-language:    Haskell2010+  default-language:    GHC2021   Main-is:          translator.hs   Build-depends:       egison

@@ -3,8 +3,8 @@ module Main where  import           Control.Exception                (AsyncException (..))+import           Control.Monad                    (when) import           Control.Monad.Catch              (catch)-import           Control.Monad.Except import           Control.Monad.Reader  import           Data.List                        (intercalate)

@@ -25,8 +25,9 @@ import           Prelude                         hiding (mapM, mappend, mconcat)  import           Control.Arrow+import           Control.Monad                   (forM_, when, zipWithM, (>=>)) import           Control.Monad.Except            (throwError)-import           Control.Monad.State             hiding (join, mapM)+import           Control.Monad.State import           Control.Monad.Trans.Maybe  import           Data.Char                       (isUpper)

@@ -50,10 +50,12 @@  import           Control.Exception -import           Control.Monad.Except             hiding (join)+import           Control.Monad                    (liftM2)+import           Control.Monad.Except+import           Control.Monad.Trans.Class        (lift) import           Control.Monad.Trans.State.Strict -import           Data.Foldable                    (toList)+import           Data.Foldable                    (msum, toList) import           Data.HashMap.Strict              (HashMap) import qualified Data.HashMap.Strict              as HashMap import           Data.IORef

@@ -18,7 +18,8 @@   , makeICollection   ) where -import           Control.Monad.Except       (lift, liftIO)+import           Control.Monad.IO.Class     (liftIO)+import           Control.Monad.Trans.Class  (lift) import           Control.Monad.Trans.Maybe  (runMaybeT)  import           Data.Foldable              (toList)

@@ -22,6 +22,7 @@   , loadEgisonFile   ) where +import           Control.Monad              (forM_, when) import           Control.Monad.Except       (throwError) import           Control.Monad.Reader       (ask, asks) import           Control.Monad.State

@@ -15,6 +15,7 @@   ) where  import           Control.Monad.Except+import           Control.Monad.Trans.Class        (lift) import           Control.Monad.Trans.State.Strict  import           Language.Egison.IExpr

@@ -94,8 +94,8 @@  term :: Pattern (PP Integer, PP Monomial) TermM TermExpr (Integer, Monomial) term _ _ (Term a mono) = pure (a, mono)-termM :: TermM -> TermExpr -> (Eql, Multiset (Pair SymbolM Eql))-termM TermM _ = (Eql, Multiset (Pair SymbolM Eql))+termM :: TermM -> TermExpr -> (Eql, Multiset (SymbolM, Eql))+termM TermM _ = (Eql, Multiset (SymbolM, Eql))  symbol :: Pattern (PP String) SymbolM SymbolExpr String symbol _ _ (Symbol _ name []) = pure name@@ -126,13 +126,13 @@ negQuoteM :: SymbolM -> p -> ScalarM negQuoteM SymbolM _ = ScalarM -equalMonomial :: Pattern (PP Integer, PP Monomial) (Multiset (Pair SymbolM Eql)) Monomial (Integer, Monomial)+equalMonomial :: Pattern (PP Integer, PP Monomial) (Multiset (SymbolM, Eql)) Monomial (Integer, Monomial) equalMonomial (_, VP xs) _ ys = case isEqualMonomial xs ys of                                   Just sgn -> pure (sgn, xs)                                   Nothing  -> mzero equalMonomial _ _ _ = mzero-equalMonomialM :: Multiset (Pair SymbolM Eql) -> p -> (Eql, Multiset (Pair SymbolM Eql))-equalMonomialM (Multiset (Pair SymbolM Eql)) _ = (Eql, Multiset (Pair SymbolM Eql))+equalMonomialM :: Multiset (SymbolM, Eql) -> p -> (Eql, Multiset (SymbolM, Eql))+equalMonomialM (Multiset (SymbolM, Eql)) _ = (Eql, Multiset (SymbolM, Eql))  zero :: Pattern () ScalarM ScalarData () zero _ _ (Div (Plus []) _) = pure ()@@ -143,8 +143,8 @@ singleTerm :: Pattern (PP Integer, PP Integer, PP Monomial) ScalarM ScalarData (Integer, Integer, Monomial) singleTerm _ _ (Div (Plus [Term c mono]) (Plus [Term c2 []])) = pure (c, c2, mono) singleTerm _ _ _                                              = mzero-singleTermM :: ScalarM -> p -> (Eql, Eql, Multiset (Pair SymbolM Eql))-singleTermM ScalarM _ = (Eql, Eql, Multiset (Pair SymbolM Eql))+singleTermM :: ScalarM -> p -> (Eql, Eql, Multiset (SymbolM, Eql))+singleTermM ScalarM _ = (Eql, Eql, Multiset (SymbolM, Eql))   instance ValuePattern ScalarM ScalarData where@@ -178,7 +178,7 @@  isEqualMonomial :: Monomial -> Monomial -> Maybe Integer isEqualMonomial xs ys =-  match dfs (xs, ys) (Pair (Multiset (Pair SymbolM Eql)) (Multiset (Pair SymbolM Eql)))+  match dfs (xs, ys) (Multiset (SymbolM, Eql), Multiset (SymbolM, Eql))     [ [mc| ((quote $s, $n) : $xss, (negQuote #s, #n) : $yss) ->              case isEqualMonomial xss yss of                Nothing -> Nothing

@@ -63,7 +63,7 @@   divMonomial :: Monomial -> Monomial -> (Integer, Monomial)   divMonomial xs [] = (1, xs)   divMonomial xs ((y, m):ys) =-    match dfs (y, xs) (Pair SymbolM (Multiset (Pair SymbolM Eql)))+    match dfs (y, xs) (SymbolM, Multiset (SymbolM, Eql))       -- Because we've applied |mathFold|, we can only divide the first matching monomial       [ [mc| (quote $s, ($x & negQuote #s, $n) : $xss) ->                let (sgn, xs') = divMonomial xss ys in@@ -106,7 +106,7 @@   g :: Monomial -> (Integer, Monomial)   g [] = (1, [])   g ((x, m):xs) =-    match dfs (x, xs) (Pair SymbolM (Multiset (Pair SymbolM Eql)))+    match dfs (x, xs) (SymbolM, Multiset (SymbolM, Eql))       [ [mc| (quote $s, (negQuote #s, $n) : $xs) ->                let (sgn, ys) = g ((x, m + n) : xs) in                if even n then (sgn, ys) else (- sgn, ys) |]@@ -121,7 +121,7 @@   f :: [TermExpr] -> [TermExpr]   f [] = []   f (t:ts) =-    match dfs (t, ts) (Pair TermM (Multiset TermM))+    match dfs (t, ts) (TermM, Multiset TermM)       [ [mc| (term $a $xs, term $b (equalMonomial $sgn #xs) : $tss) ->                f (Term (sgn * a + b) xs : tss) |]       , [mc| _ -> t : f ts |]

@@ -39,7 +39,7 @@  mapTerms' :: (TermExpr -> ScalarData) -> ScalarData -> ScalarData mapTerms' f (Div (Plus ts1) (Plus ts2)) =-  mathDiv (foldl1 mathPlus (map f ts1)) (foldl1 mathPlus (map f ts2))+  mathDiv (foldl mathPlus (Div (Plus []) (Plus [Term 1 []])) (map f ts1)) (foldl mathPlus (Div (Plus []) (Plus [Term 1 []])) (map f ts2))  mapPolys :: (PolyExpr -> PolyExpr) -> ScalarData -> ScalarData mapPolys f (Div p1 p2) = Div (f p1) (f p2)@@ -48,7 +48,7 @@ rewriteI = mapTerms f  where   f term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (symbol #"i", $k) : $xss ->               if even k                 then Term (a * (-1) ^ (quot k 2)) xss@@ -60,7 +60,7 @@ rewriteW = mapPolys g . mapTerms f  where   f term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (symbol #"w", $k & ?(>= 3)) : $xss ->                Term a ((Symbol "" "w" [], k `mod` 3) : xss) |]       , [mc| _ -> term |]@@ -78,7 +78,7 @@ rewriteLog = mapTerms f  where   f term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"log" [zero], _) : _ -> Term 0 [] |]       , [mc| (apply #"log" [singleTerm _ #1 [(symbol #"e", $n)]], _) : $xss ->               Term (n * a) xss |]@@ -93,7 +93,7 @@ rewriteExp = mapTerms f  where   f term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"exp" [zero], _) : $xss ->                f (Term a xss) |]       , [mc| (apply #"exp" [singleTerm #1 #1 []], _) : $xss ->@@ -111,7 +111,7 @@ rewritePower = mapTerms f  where   f term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"^" [singleTerm #1 #1 [], _], _) : $xss -> f (Term a xss) |]       , [mc| (apply #"^" [$x, $y], $n & ?(>= 2)) : $xss ->                f (Term a ((makeApply "^" [x, mathScalarMult n y], 1) : xss)) |]@@ -124,7 +124,7 @@ rewriteSinCos = mapTerms' h . mapTerms (g . f)  where   f term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"sin" [zero], _) : _ -> Term 0 [] |]       , [mc| (apply #"sin" [singleTerm _ #1 [(symbol #"π", #1)]], _) : _ ->                Term 0 [] |]@@ -133,7 +133,7 @@       , [mc| _ -> term |]       ]   g term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"cos" [zero], _) : $xss -> Term a xss |]       , [mc| (apply #"cos" [singleTerm _ #2 [(symbol #"π", #1)]], _) : _ ->               Term 0 [] |]@@ -142,7 +142,7 @@       , [mc| _ -> term |]       ]   h (Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"cos" [$x], #2) : $mr ->                mathMult                  (mathMinus (SingleTerm 1 []) (SingleTerm 1 [(makeApply "sin" [x], 2)]))@@ -154,7 +154,7 @@ rewriteSqrt = mapTerms' f  where   f (Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"sqrt" [$x], ?(> 1) & $k) : $xss ->                rewriteSqrt                  (mathMult (SingleTerm a ((makeApply "sqrt" [x], k `mod` 2) : xss))@@ -174,7 +174,7 @@ rewriteRt = mapTerms' f  where   f (Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"rt" [singleTerm $n #1 [], $x] & $rtnx, ?(>= n) & $k) : $xss ->                mathMult (SingleTerm a ((rtnx, k `mod` n) : xss))                         (mathPower x (div k n)) |]@@ -185,13 +185,13 @@ rewriteRtu = mapTerms' g . mapTerms f  where   f term@(Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"rtu" [singleTerm $n #1 []] & $rtun, ?(>= n) & $k) : $r ->                Term a ((rtun, k `mod` n) : r) |]       , [mc| _ -> term |]       ]   g (Term a xs) =-    match dfs xs (Multiset (Pair SymbolM Eql))+    match dfs xs (Multiset (SymbolM, Eql))       [ [mc| (apply #"rtu" [singleTerm $n #1 []] & $rtun, ?(== n - 1)) : $mr ->                mathMult                  (foldl mathMinus (SingleTerm (-1) []) (map (\k -> SingleTerm 1 [(rtun, k)]) [1..(n-2)]))

@@ -21,9 +21,11 @@        , readUTF8File        ) where -import           Control.Monad.Except         (lift, liftIO, throwError)+import           Control.Monad                 (unless)+import           Control.Monad.Except         (throwError)+import           Control.Monad.IO.Class       (liftIO) import           Control.Monad.Reader         (asks, local)-import           Control.Monad.State          (unless)+import           Control.Monad.Trans.Class    (lift)  import           System.Directory             (doesFileExist, getHomeDirectory) import           System.IO

@@ -16,11 +16,11 @@     , showTSV     ) where -import           Data.Foldable                           (toList)-import           Data.List                               (intercalate)-import           Data.Text.Prettyprint.Doc-import           Data.Text.Prettyprint.Doc.Render.String (renderString)-import           Text.Show.Unicode                       (ushow)+import           Data.Foldable                  (toList)+import           Data.List                      (intercalate)+import           Prettyprinter+import           Prettyprinter.Render.String    (renderString)+import           Text.Show.Unicode              (ushow)  import           Language.Egison.AST import           Language.Egison.Data

@@ -12,7 +12,8 @@   , primitiveEnvNoIO   ) where -import           Control.Monad.Except+import           Control.Monad                     (forM)+import           Control.Monad.IO.Class            (liftIO)  import           Data.IORef 

@@ -9,11 +9,11 @@   ( ioPrimitives   ) where -import           Control.Monad.Except+import           Control.Monad.IO.Class           (liftIO)  import           Data.IORef -import           System.IO+import           System.IO                        hiding (readFile') import           System.Process                   (readProcess) import           System.Random                    (getStdRandom, randomR) 

@@ -31,7 +31,8 @@  import           Prelude                    hiding (foldr, mappend, mconcat) -import           Control.Monad.Except       (mzero, throwError, zipWithM)+import           Control.Monad              (mzero, zipWithM)+import           Control.Monad.Except       (throwError) import           Data.List                  (delete, intersect, partition, (\\)) import qualified Data.Vector                as V 

@@ -3,10 +3,10 @@  module Main where -import           Control.Arrow                         ((***))-import           Data.Maybe                            (fromJust)-import           Data.Text.Prettyprint.Doc.Render.Text (putDoc)-import           System.Environment                    (getArgs)+import           Control.Arrow              ((***))+import           Data.Maybe                 (fromJust)+import           Prettyprinter.Render.Text  (putDoc)+import           System.Environment         (getArgs)  import           Language.Egison.AST import           Language.Egison.Parser                (readUTF8File, removeShebang)

@@ -0,0 +1,24 @@+--+-- This file has been auto-generated by egison-translator.+--++def params := [|r, θ|]++def u := r * e ^ (2 * π * i * θ)++def ū := r * e ^ ((-2) * π * i * θ)++def d X :=+  WedgeApplyExpr (ApplyExpr (VarExpr "flip") [VarExpr "\8706/\8706"]) [VarExpr "params",VarExpr "X"]++def ω := ū * d u / 1 + u * ū++ω++def Ω := dfNormalize (d ω)++Ω++def c1 := Ω / ((-2) * π * i)++c1

@@ -0,0 +1,28 @@+--+-- This file has been auto-generated by egison-translator.+--++def params := [|z1, z2, z1', z2'|]++def params' := [|z1, z2, #, #|]++def params'' := [|#, #, z1', z2'|]++def d X :=+  WedgeApplyExpr (ApplyExpr (VarExpr "flip") [VarExpr "\8706/\8706"]) [VarExpr "params",VarExpr "X"]++def d' X :=+  WedgeApplyExpr (ApplyExpr (VarExpr "flip") [VarExpr "\8706/\8706"]) [VarExpr "params'",VarExpr "X"]++def d'' X :=+  WedgeApplyExpr (ApplyExpr (VarExpr "flip") [VarExpr "\8706/\8706"]) [VarExpr "params''",VarExpr "X"]++def h := 1 + z1 * z1' + z2 * z2'++def ω := d' (log h)++ω++def Ω := d'' ω++Ω

@@ -0,0 +1,1 @@+"\"egison\" (line 20, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 20, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,18 @@+--+-- This file has been auto-generated by egison-translator.+--++def N := 3++def params := [|x, y, z|]++def g := [|[|1, 0, 0|], [|0, 1, 0|], [|0, 0, 1|]|]++def d X :=+  WedgeApplyExpr (ApplyExpr (VarExpr "flip") [VarExpr "\8706/\8706"]) [VarExpr "params",VarExpr "X"]++def f := function (x, y, z)++d f++dfNormalize (d (d f))

@@ -0,0 +1,28 @@+--+-- This file has been auto-generated by egison-translator.+--++def N := 3++def params := [|x, y, z|]++def g := [|[|1, 0, 0|], [|0, 1, 0|], [|0, 0, 1|]|]++def hodge A :=+  let k := dfOrder A+   in withSymbols [i, j]+        sqrt (abs (M.det g_#_#)) *+        foldl+          (.)+          ((ε' N k)_(i_1)..._(i_N) . A..._(j_1)..._(j_k))+          (map 1#g~(i_%1)~(j_%1) (between 1 k))++def dx := [|1, 0, 0|]++def dy := [|0, 1, 0|]++def dz := [|0, 0, 1|]++hodge dx++hodge (wedge dx dy)

@@ -0,0 +1,30 @@+--+-- This file has been auto-generated by egison-translator.+--++def N := 4++def params := [|t, x, y, z|]++def g := [|[|-1, 0, 0, 0|], [|0, 1, 0, 0|], [|0, 0, 1, 0|], [|0, 0, 0, 1|]|]++def hodge A :=+  let k := dfOrder A+   in withSymbols [i, j]+        sqrt (abs (M.det g_#_#)) *+        foldl+          (.)+          ((ε' N k)_(i_1)..._(i_N) . A..._(j_1)..._(j_k))+          (map 1#g~(i_%1)~(j_%1) (between 1 k))++def dt := [|1, 0, 0, 0|]++def dx := [|0, 1, 0, 0|]++def dy := [|0, 0, 1, 0|]++def dz := [|0, 0, 0, 1|]++hodge (wedge dt dx)++hodge (wedge dy dz)

@@ -0,0 +1,1 @@+"\"egison\" (line 7, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 23, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 23, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,27 @@+--+-- This file has been auto-generated by egison-translator.+--++def x := r * cos θ++def y := r * sin θ++def uR := ∂/∂ (u x y) r++uR++def uRR := ∂/∂ (∂/∂ (u x y) r) r++uRR++def uΘ := ∂/∂ (u x y) θ++uΘ++def uΘΘ := ∂/∂ (∂/∂ (u x y) θ) θ++uΘΘ++uRR + 1 / r ^ 2 * uΘΘ++uRR + 1 / r * uR + 1 / r ^ 2 * uΘΘ

@@ -0,0 +1,1 @@+"\"egison\" (line 26, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 26, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,36 @@+--+-- This file has been auto-generated by egison-translator.+--++def x := r * sin θ * cos φ++def y := r * sin θ * sin φ++def z := r * cos θ++def uR := ∂/∂ (u x y z) r++uR++def uRR := ∂/∂ (∂/∂ (u x y z) r) r++uRR++def uΘ := ∂/∂ (u x y z) θ++uΘ++def uΘΘ := ∂/∂ (∂/∂ (u x y z) θ) θ++uΘΘ++def uΦ := ∂/∂ (u x y z) φ++uΦ++def uΦΦ := ∂/∂ (∂/∂ (u x y z) φ) φ++uΦΦ++uRR + 2 / r * uR + 1 / r ^ 2 * uΘΘ + cos θ / (r ^ 2 * sin θ) * uΘ ++1 / (r * sin θ) ^ 2 * uΦΦ

@@ -0,0 +1,1 @@+"\"egison\" (line 13, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 11, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 27, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 29, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 28, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,1 @@+"\"egison\" (line 11, column 12):\nunexpected \"_\"\nexpecting top-level expression"

@@ -0,0 +1,58 @@+def v1 := [|1, 0, ∂/∂ (f x y) x|]++def v2 := [|0, 1, ∂/∂ (f x y) y|]++v1+-- [| 1, 0, f|1 x y |]++v2+-- [| 0, 1, f|2 x y |]++def v3 := crossProduct v1 v2++v3+-- [| - f|1 x y, - f|2 x y, 1 |]++def e3 := v3 / sqrt '(V.* v3 v3)++e3+-- [| - f|1 x y / sqrt ((f|1 x y)^2 + (f|2 x y)^2 + 1), - f|2 x y / sqrt ((f|1 x y)^2 + (f|2 x y)^2 + 1), 1 / sqrt ((f|1 x y)^2 + (f|2 x y)^2 + 1) |]++def E := V.* v1 v1++def F := V.* v1 v2++def G := V.* v2 v2++E+-- 1 + (f|1 x y)^2++F+-- f|1 x y * f|2 x y++G+-- 1 + (f|2 x y)^2++def L := V.* (∂/∂ v1 x) e3++def M := V.* (∂/∂ v1 y) e3++def N := V.* (∂/∂ v2 y) e3++L+-- f|1|1 x y / sqrt ((f|1 x y)^2 + (f|2 x y)^2 + 1)++M+-- f|1|2 x y / sqrt ((f|1 x y)^2 + (f|2 x y)^2 + 1)++N+-- f|2|2 x y / sqrt ((f|1 x y)^2 + (f|2 x y)^2 + 1)++def K := (L * N - M ^ 2) / '(E * G - F ^ 2)++def H := ('E * N + 'G * L + (-2) * F * M) / 2 * '(E * G - F ^ 2)++K+-- (f|1|1 x y * f|2|2 x y * (f|1 x y)^2 + f|1|1 x y * f|2|2 x y * (f|2 x y)^2 + f|1|1 x y * f|2|2 x y - (f|1|2 x y)^2 * (f|1 x y)^2 - (f|1|2 x y)^2 * (f|2 x y)^2 - (f|1|2 x y)^2) / (3 * (f|1 x y)^4 + 3 * (f|1 x y)^4 * (f|2 x y)^2 + (f|1 x y)^6 + 6 * (f|1 x y)^2 * (f|2 x y)^2 + 3 * (f|1 x y)^2 * (f|2 x y)^4 + 3 * (f|1 x y)^2 + 3 * (f|2 x y)^4 + (f|2 x y)^6 + 3 * (f|2 x y)^2 + 1)+H+-- (f|2|2 x y + f|2|2 x y * (f|2 x y)^2 + 2 * f|2|2 x y * (f|1 x y)^2 + (f|1 x y)^2 * f|2|2 x y * (f|2 x y)^2 + (f|1 x y)^4 * f|2|2 x y + f|1|1 x y + 2 * f|1|1 x y * (f|2 x y)^2 + f|1|1 x y * (f|1 x y)^2 + (f|2 x y)^4 * f|1|1 x y + (f|2 x y)^2 * f|1|1 x y * (f|1 x y)^2 - 2 * f|1 x y * f|2 x y * f|1|2 x y - 2 * f|1 x y * (f|2 x y)^3 * f|1|2 x y - 2 * (f|1 x y)^3 * f|2 x y * f|1|2 x y) / (2 * sqrt ((f|1 x y)^2 + (f|2 x y)^2 + 1))

@@ -0,0 +1,25 @@+--+-- This file has been auto-generated by egison-translator.+--++def N := 3++def params := [|x, y, z|]++def g := [|[|1, 0, 0|], [|0, 1, 0|], [|0, 0, 1|]|]++def wedge X Y := X !. Y++def dx := [|1, 0, 0|]++def dy := [|0, 1, 0|]++def dz := [|0, 0, 1|]++wedge dx dy++dfNormalize (wedge dx dy)++wedge dz dz++dfNormalize (wedge dz dz)

@@ -0,0 +1,47 @@+--+-- This file has been auto-generated by egison-translator.+--++def N := 4++def g := [|[|-1, 0, 0, 0|], [|0, 1, 0, 0|], [|0, 0, 1, 0|], [|0, 0, 0, 1|]|]++def d X :=+  WedgeApplyExpr (ApplyExpr (VarExpr "flip") [VarExpr "\8706/\8706"]) [VectorExpr [VarExpr "t",VarExpr "x",VarExpr "y",VarExpr "z"],VarExpr "X"]++def hodge A :=+  let k := dfOrder A+   in withSymbols [i, j]+        sqrt (abs (M.det g_#_#)) *+        foldl+          (.)+          ((ε' N k)_(i_1)..._(i_N) . A..._(j_1)..._(j_k))+          (map 1#g~(i_%1)~(j_%1) (between 1 k))++def δ A :=+  let r := dfOrder A+   in (-1) ^ (N * r + 1) * hodge (d (hodge A))++def Δ A :=+  match dfrOrder A as integer with+    | #0 -> δ (d A)+    | #4 -> d (δ A)+    | _ -> d (δ A) + δ (d A)++def normalize2 A := withSymbols [t1, t2] A_t1_t2 - A_t2_t1++hodge (wedge [|1, 0, 0, 0|] [|0, 1, 0, 0|])++hodge (wedge [|0, 0, 1, 0|] [|0, 0, 0, 1|])++dfNormalize (d [|φ t x y z, Ax t x y z, Ay t x y z, Az t x y z|])++def F :=+  [|[|0, Ex t x y z, Ey t x y z, Ez t x y z|]+  , [|- Ex t x y z, 0, Bz t x y z, - By t x y z|]+  , [|- Ey t x y z, - Bz t x y z, 0, Bx t x y z|]+  , [|- Ez t x y z, By t x y z, - Bx t x y z, 0|]|]++hodge (d F)++δ F

@@ -0,0 +1,46 @@+map (\(x, y) -> (x + y * w, (x + y * w) * (x + y * w ^ 2)))+    (matchAll take 10 nats as set integer with+      | $x :: $y :: _ -> (x, y))++[(1 + w, 1), (1 + 2 * w, 3), (2 + w, 3), (1 + 3 * w, 7), (2 + 2 * w, 4),+ (3 + w, 7), (1 + 4 * w, 13), (2 + 3 * w, 7), (3 + 2 * w, 7), (4 + w, 13),+ (1 + 5 * w, 21), (2 + 4 * w, 12), (3 + 3 * w, 9), (4 + 2 * w, 12), (5 + w, 21),+ (1 + 6 * w, 31), (2 + 5 * w, 19), (3 + 4 * w, 13), (4 + 3 * w, 13),+ (5 + 2 * w, 19), (6 + w, 31), (1 + 7 * w, 43), (2 + 6 * w, 28),+ (3 + 5 * w, 19), (4 + 4 * w, 16), (5 + 3 * w, 19), (6 + 2 * w, 28),+ (7 + w, 43), (1 + 8 * w, 57), (2 + 7 * w, 39), (3 + 6 * w, 27),+ (4 + 5 * w, 21), (5 + 4 * w, 21), (6 + 3 * w, 27), (7 + 2 * w, 39),+ (8 + w, 57), (1 + 9 * w, 73), (2 + 8 * w, 52), (3 + 7 * w, 37),+ (4 + 6 * w, 28), (5 + 5 * w, 25), (6 + 4 * w, 28), (7 + 3 * w, 37),+ (8 + 2 * w, 52), (9 + w, 73), (1 + 10 * w, 91), (2 + 9 * w, 67),+ (3 + 8 * w, 49), (4 + 7 * w, 37), (5 + 6 * w, 31), (6 + 5 * w, 31),+ (7 + 4 * w, 37), (8 + 3 * w, 49), (9 + 2 * w, 67), (10 + w, 91),+ (2 + 10 * w, 84), (3 + 9 * w, 63), (4 + 8 * w, 48), (5 + 7 * w, 39),+ (6 + 6 * w, 36), (7 + 5 * w, 39), (8 + 4 * w, 48), (9 + 3 * w, 63),+ (10 + 2 * w, 84), (3 + 10 * w, 79), (4 + 9 * w, 61), (5 + 8 * w, 49),+ (6 + 7 * w, 43), (7 + 6 * w, 43), (8 + 5 * w, 49), (9 + 4 * w, 61),+ (10 + 3 * w, 79), (4 + 10 * w, 76), (5 + 9 * w, 61), (6 + 8 * w, 52),+ (7 + 7 * w, 49), (8 + 6 * w, 52), (9 + 5 * w, 61), (10 + 4 * w, 76),+ (5 + 10 * w, 75), (6 + 9 * w, 63), (7 + 8 * w, 57), (8 + 7 * w, 57),+ (9 + 6 * w, 63), (10 + 5 * w, 75), (6 + 10 * w, 76), (7 + 9 * w, 67),+ (8 + 8 * w, 64), (9 + 7 * w, 67), (10 + 6 * w, 76), (7 + 10 * w, 79),+ (8 + 9 * w, 73), (9 + 8 * w, 73), (10 + 7 * w, 79), (8 + 10 * w, 84),+ (9 + 9 * w, 81), (10 + 8 * w, 84), (9 + 10 * w, 91), (10 + 9 * w, 91),+ (10 + 10 * w, 100)]++filter+  (\(_, n) -> isPrime n)+  (map (\(x, y) -> (x + y * w, (x + y * w) * (x + y * w ^ 2)))+       (matchAll take 10 nats as set integer with+         | $x :: $y :: _ -> (x, y)))++[(1 + 2 * w, 3), (2 + w, 3), (1 + 3 * w, 7), (3 + w, 7),+ (1 + 4 * w, 13), (2 + 3 * w, 7), (3 + 2 * w, 7), (4 + w, 13), (1 + 6 * w, 31),+ (2 + 5 * w, 19), (3 + 4 * w, 13), (4 + 3 * w, 13), (5 + 2 * w, 19),+ (6 + w, 31), (1 + 7 * w, 43), (3 + 5 * w, 19), (5 + 3 * w, 19), (7 + w, 43),+ (1 + 9 * w, 73), (3 + 7 * w, 37), (7 + 3 * w, 37), (9 + w, 73),+ (2 + 9 * w, 67), (4 + 7 * w, 37), (5 + 6 * w, 31), (6 + 5 * w, 31),+ (7 + 4 * w, 37), (9 + 2 * w, 67), (3 + 10 * w, 79), (4 + 9 * w, 61),+ (6 + 7 * w, 43), (7 + 6 * w, 43), (9 + 4 * w, 61), (10 + 3 * w, 79),+ (5 + 9 * w, 61), (9 + 5 * w, 61), (7 + 9 * w, 67), (9 + 7 * w, 67),+ (7 + 10 * w, 79), (8 + 9 * w, 73), (9 + 8 * w, 73), (10 + 7 * w, 79)]

@@ -0,0 +1,36 @@+def φ $n := n * product (map (\$p -> 1 - 1 / p) (unique (pF n)))++take 100 (map2 2#(%1, %2, pF %2) nats (map φ nats))++[(1, 1, []), (2, 1, []), (3, 2, [2]), (4, 2, [2]), (5, 4, [2, 2]), (6, 2, [2]),+ (7, 6, [2, 3]), (8, 4, [2, 2]), (9, 6, [2, 3]), (10, 4, [2, 2]),+ (11, 10, [2, 5]), (12, 4, [2, 2]), (13, 12, [2, 2, 3]), (14, 6, [2, 3]),+ (15, 8, [2, 2, 2]), (16, 8, [2, 2, 2]), (17, 16, [2, 2, 2, 2]),+ (18, 6, [2, 3]), (19, 18, [2, 3, 3]), (20, 8, [2, 2, 2]), (21, 12, [2, 2, 3]),+ (22, 10, [2, 5]), (23, 22, [2, 11]), (24, 8, [2, 2, 2]), (25, 20, [2, 2, 5]),+ (26, 12, [2, 2, 3]), (27, 18, [2, 3, 3]), (28, 12, [2, 2, 3]),+ (29, 28, [2, 2, 7]), (30, 8, [2, 2, 2]), (31, 30, [2, 3, 5]),+ (32, 16, [2, 2, 2, 2]), (33, 20, [2, 2, 5]), (34, 16, [2, 2, 2, 2]),+ (35, 24, [2, 2, 2, 3]), (36, 12, [2, 2, 3]), (37, 36, [2, 2, 3, 3]),+ (38, 18, [2, 3, 3]), (39, 24, [2, 2, 2, 3]), (40, 16, [2, 2, 2, 2]),+ (41, 40, [2, 2, 2, 5]), (42, 12, [2, 2, 3]), (43, 42, [2, 3, 7]),+ (44, 20, [2, 2, 5]), (45, 24, [2, 2, 2, 3]), (46, 22, [2, 11]),+ (47, 46, [2, 23]), (48, 16, [2, 2, 2, 2]), (49, 42, [2, 3, 7]),+ (50, 20, [2, 2, 5]), (51, 32, [2, 2, 2, 2, 2]), (52, 24, [2, 2, 2, 3]),+ (53, 52, [2, 2, 13]), (54, 18, [2, 3, 3]), (55, 40, [2, 2, 2, 5]),+ (56, 24, [2, 2, 2, 3]), (57, 36, [2, 2, 3, 3]), (58, 28, [2, 2, 7]),+ (59, 58, [2, 29]), (60, 16, [2, 2, 2, 2]), (61, 60, [2, 2, 3, 5]),+ (62, 30, [2, 3, 5]), (63, 36, [2, 2, 3, 3]), (64, 32, [2, 2, 2, 2, 2]),+ (65, 48, [2, 2, 2, 2, 3]), (66, 20, [2, 2, 5]), (67, 66, [2, 3, 11]),+ (68, 32, [2, 2, 2, 2, 2]), (69, 44, [2, 2, 11]), (70, 24, [2, 2, 2, 3]),+ (71, 70, [2, 5, 7]), (72, 24, [2, 2, 2, 3]), (73, 72, [2, 2, 2, 3, 3]),+ (74, 36, [2, 2, 3, 3]), (75, 40, [2, 2, 2, 5]), (76, 36, [2, 2, 3, 3]),+ (77, 60, [2, 2, 3, 5]), (78, 24, [2, 2, 2, 3]), (79, 78, [2, 3, 13]),+ (80, 32, [2, 2, 2, 2, 2]), (81, 54, [2, 3, 3, 3]), (82, 40, [2, 2, 2, 5]),+ (83, 82, [2, 41]), (84, 24, [2, 2, 2, 3]), (85, 64, [2, 2, 2, 2, 2, 2]),+ (86, 42, [2, 3, 7]), (87, 56, [2, 2, 2, 7]), (88, 40, [2, 2, 2, 5]),+ (89, 88, [2, 2, 2, 11]), (90, 24, [2, 2, 2, 3]), (91, 72, [2, 2, 2, 3, 3]),+ (92, 44, [2, 2, 11]), (93, 60, [2, 2, 3, 5]), (94, 46, [2, 23]),+ (95, 72, [2, 2, 2, 3, 3]), (96, 32, [2, 2, 2, 2, 2]),+ (97, 96, [2, 2, 2, 2, 2, 3]), (98, 42, [2, 3, 7]), (99, 60, [2, 2, 3, 5]),+ (100, 40, [2, 2, 2, 5])]

@@ -0,0 +1,44 @@+map (\(x, y) -> (x + y * i, (x + y * i) * (x - y * i)))+    (matchAll take 10 nats as set integer with+      | $x :: $y :: _ -> (x, y))++[(1 + i, 2), (1 + 2 * i, 5), (2 + i, 5), (1 + 3 * i, 10), (2 + 2 * i, 8),+ (3 + i, 10), (1 + 4 * i, 17), (2 + 3 * i, 13), (3 + 2 * i, 13), (4 + i, 17),+ (1 + 5 * i, 26), (2 + 4 * i, 20), (3 + 3 * i, 18), (4 + 2 * i, 20),+ (5 + i, 26), (1 + 6 * i, 37), (2 + 5 * i, 29), (3 + 4 * i, 25),+ (4 + 3 * i, 25), (5 + 2 * i, 29), (6 + i, 37), (1 + 7 * i, 50),+ (2 + 6 * i, 40), (3 + 5 * i, 34), (4 + 4 * i, 32), (5 + 3 * i, 34),+ (6 + 2 * i, 40), (7 + i, 50), (1 + 8 * i, 65), (2 + 7 * i, 53),+ (3 + 6 * i, 45), (4 + 5 * i, 41), (5 + 4 * i, 41), (6 + 3 * i, 45),+ (7 + 2 * i, 53), (8 + i, 65), (1 + 9 * i, 82), (2 + 8 * i, 68),+ (3 + 7 * i, 58), (4 + 6 * i, 52), (5 + 5 * i, 50), (6 + 4 * i, 52),+ (7 + 3 * i, 58), (8 + 2 * i, 68), (9 + i, 82), (1 + 10 * i, 101),+ (2 + 9 * i, 85), (3 + 8 * i, 73), (4 + 7 * i, 65), (5 + 6 * i, 61),+ (6 + 5 * i, 61), (7 + 4 * i, 65), (8 + 3 * i, 73), (9 + 2 * i, 85),+ (10 + i, 101), (2 + 10 * i, 104), (3 + 9 * i, 90), (4 + 8 * i, 80),+ (5 + 7 * i, 74), (6 + 6 * i, 72), (7 + 5 * i, 74), (8 + 4 * i, 80),+ (9 + 3 * i, 90), (10 + 2 * i, 104), (3 + 10 * i, 109), (4 + 9 * i, 97),+ (5 + 8 * i, 89), (6 + 7 * i, 85), (7 + 6 * i, 85), (8 + 5 * i, 89),+ (9 + 4 * i, 97), (10 + 3 * i, 109), (4 + 10 * i, 116), (5 + 9 * i, 106),+ (6 + 8 * i, 100), (7 + 7 * i, 98), (8 + 6 * i, 100), (9 + 5 * i, 106),+ (10 + 4 * i, 116), (5 + 10 * i, 125), (6 + 9 * i, 117), (7 + 8 * i, 113),+ (8 + 7 * i, 113), (9 + 6 * i, 117), (10 + 5 * i, 125), (6 + 10 * i, 136),+ (7 + 9 * i, 130), (8 + 8 * i, 128), (9 + 7 * i, 130), (10 + 6 * i, 136),+ (7 + 10 * i, 149), (8 + 9 * i, 145), (9 + 8 * i, 145), (10 + 7 * i, 149),+ (8 + 10 * i, 164), (9 + 9 * i, 162), (10 + 8 * i, 164), (9 + 10 * i, 181),+ (10 + 9 * i, 181), (10 + 10 * i, 200)]++filter+  (\(_, n) -> isPrime n)+  (map (\(x, y) -> (x + y * i, (x + y * i) * (x - y * i)))+       (matchAll take 10 nats as set integer with+         | $x :: $y :: _ -> (x, y)))++[(1 + i, 2), (1 + 2 * i, 5), (2 + i, 5), (1 + 4 * i, 17), (2 + 3 * i, 13),+ (3 + 2 * i, 13), (4 + i, 17), (1 + 6 * i, 37), (2 + 5 * i, 29),+ (5 + 2 * i, 29), (6 + i, 37), (2 + 7 * i, 53), (4 + 5 * i, 41),+ (5 + 4 * i, 41), (7 + 2 * i, 53), (1 + 10 * i, 101), (3 + 8 * i, 73),+ (5 + 6 * i, 61), (6 + 5 * i, 61), (8 + 3 * i, 73), (10 + i, 101),+ (3 + 10 * i, 109), (4 + 9 * i, 97), (5 + 8 * i, 89), (8 + 5 * i, 89),+ (9 + 4 * i, 97), (10 + 3 * i, 109), (7 + 8 * i, 113), (8 + 7 * i, 113),+ (7 + 10 * i, 149), (10 + 7 * i, 149), (9 + 10 * i, 181), (10 + 9 * i, 181)]