diff --git a/egison.cabal b/egison.cabal --- a/egison.cabal +++ b/egison.cabal @@ -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 diff --git a/hs-src/Interpreter/egison.hs b/hs-src/Interpreter/egison.hs --- a/hs-src/Interpreter/egison.hs +++ b/hs-src/Interpreter/egison.hs @@ -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) diff --git a/hs-src/Language/Egison/Core.hs b/hs-src/Language/Egison/Core.hs --- a/hs-src/Language/Egison/Core.hs +++ b/hs-src/Language/Egison/Core.hs @@ -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) diff --git a/hs-src/Language/Egison/Data.hs b/hs-src/Language/Egison/Data.hs --- a/hs-src/Language/Egison/Data.hs +++ b/hs-src/Language/Egison/Data.hs @@ -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 diff --git a/hs-src/Language/Egison/Data/Collection.hs b/hs-src/Language/Egison/Data/Collection.hs --- a/hs-src/Language/Egison/Data/Collection.hs +++ b/hs-src/Language/Egison/Data/Collection.hs @@ -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) diff --git a/hs-src/Language/Egison/Eval.hs b/hs-src/Language/Egison/Eval.hs --- a/hs-src/Language/Egison/Eval.hs +++ b/hs-src/Language/Egison/Eval.hs @@ -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 diff --git a/hs-src/Language/Egison/EvalState.hs b/hs-src/Language/Egison/EvalState.hs --- a/hs-src/Language/Egison/EvalState.hs +++ b/hs-src/Language/Egison/EvalState.hs @@ -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 diff --git a/hs-src/Language/Egison/Math/Expr.hs b/hs-src/Language/Egison/Math/Expr.hs --- a/hs-src/Language/Egison/Math/Expr.hs +++ b/hs-src/Language/Egison/Math/Expr.hs @@ -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 diff --git a/hs-src/Language/Egison/Math/Normalize.hs b/hs-src/Language/Egison/Math/Normalize.hs --- a/hs-src/Language/Egison/Math/Normalize.hs +++ b/hs-src/Language/Egison/Math/Normalize.hs @@ -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 |] diff --git a/hs-src/Language/Egison/Math/Rewrite.hs b/hs-src/Language/Egison/Math/Rewrite.hs --- a/hs-src/Language/Egison/Math/Rewrite.hs +++ b/hs-src/Language/Egison/Math/Rewrite.hs @@ -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)])) diff --git a/hs-src/Language/Egison/Parser.hs b/hs-src/Language/Egison/Parser.hs --- a/hs-src/Language/Egison/Parser.hs +++ b/hs-src/Language/Egison/Parser.hs @@ -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 diff --git a/hs-src/Language/Egison/Pretty.hs b/hs-src/Language/Egison/Pretty.hs --- a/hs-src/Language/Egison/Pretty.hs +++ b/hs-src/Language/Egison/Pretty.hs @@ -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 diff --git a/hs-src/Language/Egison/Primitives.hs b/hs-src/Language/Egison/Primitives.hs --- a/hs-src/Language/Egison/Primitives.hs +++ b/hs-src/Language/Egison/Primitives.hs @@ -12,7 +12,8 @@ , primitiveEnvNoIO ) where -import Control.Monad.Except +import Control.Monad (forM) +import Control.Monad.IO.Class (liftIO) import Data.IORef diff --git a/hs-src/Language/Egison/Primitives/IO.hs b/hs-src/Language/Egison/Primitives/IO.hs --- a/hs-src/Language/Egison/Primitives/IO.hs +++ b/hs-src/Language/Egison/Primitives/IO.hs @@ -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) diff --git a/hs-src/Language/Egison/Tensor.hs b/hs-src/Language/Egison/Tensor.hs --- a/hs-src/Language/Egison/Tensor.hs +++ b/hs-src/Language/Egison/Tensor.hs @@ -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 diff --git a/hs-src/Tool/translator.hs b/hs-src/Tool/translator.hs --- a/hs-src/Tool/translator.hs +++ b/hs-src/Tool/translator.hs @@ -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) diff --git a/sample/math/geometry/chern-form-of-CP1.egi b/sample/math/geometry/chern-form-of-CP1.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/chern-form-of-CP1.egi @@ -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 diff --git a/sample/math/geometry/chern-form-of-CP2.egi b/sample/math/geometry/chern-form-of-CP2.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/chern-form-of-CP2.egi @@ -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 diff --git a/sample/math/geometry/euler-form-of-S2.egi b/sample/math/geometry/euler-form-of-S2.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/euler-form-of-S2.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 20, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/euler-form-of-T2.egi b/sample/math/geometry/euler-form-of-T2.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/euler-form-of-T2.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 20, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/exterior-derivative.egi b/sample/math/geometry/exterior-derivative.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/exterior-derivative.egi @@ -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)) diff --git a/sample/math/geometry/hodge-E3.egi b/sample/math/geometry/hodge-E3.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/hodge-E3.egi @@ -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) diff --git a/sample/math/geometry/hodge-Minkowski.egi b/sample/math/geometry/hodge-Minkowski.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/hodge-Minkowski.egi @@ -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) diff --git a/sample/math/geometry/hodge-laplacian-spherical.egi b/sample/math/geometry/hodge-laplacian-spherical.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/hodge-laplacian-spherical.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 7, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/polar-laplacian-2d-2.egi b/sample/math/geometry/polar-laplacian-2d-2.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/polar-laplacian-2d-2.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 23, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/polar-laplacian-2d-3.egi b/sample/math/geometry/polar-laplacian-2d-3.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/polar-laplacian-2d-3.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 23, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/polar-laplacian-2d.egi b/sample/math/geometry/polar-laplacian-2d.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/polar-laplacian-2d.egi @@ -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 diff --git a/sample/math/geometry/polar-laplacian-3d-2.egi b/sample/math/geometry/polar-laplacian-3d-2.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/polar-laplacian-3d-2.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 26, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/polar-laplacian-3d-3.egi b/sample/math/geometry/polar-laplacian-3d-3.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/polar-laplacian-3d-3.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 26, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/polar-laplacian-3d.egi b/sample/math/geometry/polar-laplacian-3d.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/polar-laplacian-3d.egi @@ -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 diff --git a/sample/math/geometry/riemann-curvature-tensor-of-FLRW-metric.egi b/sample/math/geometry/riemann-curvature-tensor-of-FLRW-metric.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/riemann-curvature-tensor-of-FLRW-metric.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 13, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/riemann-curvature-tensor-of-S2xS3.egi b/sample/math/geometry/riemann-curvature-tensor-of-S2xS3.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/riemann-curvature-tensor-of-S2xS3.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 11, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/riemann-curvature-tensor-of-S3.egi b/sample/math/geometry/riemann-curvature-tensor-of-S3.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/riemann-curvature-tensor-of-S3.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 27, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/riemann-curvature-tensor-of-S4.egi b/sample/math/geometry/riemann-curvature-tensor-of-S4.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/riemann-curvature-tensor-of-S4.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 29, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/riemann-curvature-tensor-of-S7.egi b/sample/math/geometry/riemann-curvature-tensor-of-S7.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/riemann-curvature-tensor-of-S7.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 28, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/riemann-curvature-tensor-of-Schwarzschild-metric.egi b/sample/math/geometry/riemann-curvature-tensor-of-Schwarzschild-metric.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/riemann-curvature-tensor-of-Schwarzschild-metric.egi @@ -0,0 +1,1 @@ +"\"egison\" (line 11, column 12):\nunexpected \"_\"\nexpecting top-level expression" diff --git a/sample/math/geometry/surface.egi b/sample/math/geometry/surface.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/surface.egi @@ -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)) diff --git a/sample/math/geometry/wedge-product.egi b/sample/math/geometry/wedge-product.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/wedge-product.egi @@ -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) diff --git a/sample/math/geometry/yang-mills-equation-of-U1-gauge-theory.egi b/sample/math/geometry/yang-mills-equation-of-U1-gauge-theory.egi new file mode 100644 --- /dev/null +++ b/sample/math/geometry/yang-mills-equation-of-U1-gauge-theory.egi @@ -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 diff --git a/sample/math/number/eisenstein-primes.egi b/sample/math/number/eisenstein-primes.egi new file mode 100644 --- /dev/null +++ b/sample/math/number/eisenstein-primes.egi @@ -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)] diff --git a/sample/math/number/euler-totient-function.egi b/sample/math/number/euler-totient-function.egi new file mode 100644 --- /dev/null +++ b/sample/math/number/euler-totient-function.egi @@ -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])] diff --git a/sample/math/number/gaussian-primes.egi b/sample/math/number/gaussian-primes.egi new file mode 100644 --- /dev/null +++ b/sample/math/number/gaussian-primes.egi @@ -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)]