├── .gitignore ├── Interpreter.hs ├── Krivine.hs ├── LICENSE ├── Lambda.hs ├── Main.hs ├── Parser.hs ├── README.md └── Show.hs /.gitignore: -------------------------------------------------------------------------------- 1 | dist 2 | dist-* 3 | cabal-dev 4 | *.o 5 | *.hi 6 | *.hie 7 | *.chi 8 | *.chs.h 9 | *.dyn_o 10 | *.dyn_hi 11 | .hpc 12 | .hsenv 13 | .cabal-sandbox/ 14 | cabal.sandbox.config 15 | *.prof 16 | *.aux 17 | *.hp 18 | *.eventlog 19 | .stack-work/ 20 | cabal.project.local 21 | cabal.project.local~ 22 | .HTF/ 23 | .ghc.environment.* 24 | Main 25 | -------------------------------------------------------------------------------- /Interpreter.hs: -------------------------------------------------------------------------------- 1 | module Interpreter where 2 | 3 | import Krivine 4 | import Show 5 | import Text.Megaparsec (runParser) 6 | import Parser (parseTerm) 7 | 8 | runKrivine :: String -> Context -> Either String [KMachine] 9 | runKrivine s initContext = krivine (runParser parseTerm "" s) initContext 10 | 11 | cmd :: [String] -> IO () 12 | cmd args = putStr $ showKrivine $ runKrivine (head args) [] 13 | 14 | repl :: Context -> IO () 15 | repl context = do 16 | x <- getLine 17 | let k = runKrivine x context 18 | putStr $ showKrivine k 19 | case k of 20 | Left b -> repl $ context 21 | Right a -> repl $ snd $ last a 22 | -------------------------------------------------------------------------------- /Krivine.hs: -------------------------------------------------------------------------------- 1 | module Krivine where 2 | import Lambda 3 | import Data.List (find) 4 | 5 | type Context = [(String, Term)] 6 | type KMachine = (State, Context) 7 | 8 | krivine1 :: KMachine -> KMachine 9 | krivine1 ((Var "call/cc", (f:stack), n),c) = ((f, (Cont stack):stack, n+1),c) 10 | krivine1 ((Cont stack1, s:_, n),c) = ((s, stack1, n+1),c) 11 | krivine1 ((Var "clock", (s:stack), n),c) = ((s, (Instr (n+1):stack), n+1),c) 12 | krivine1 ((t@(Lambda _ _), (s:stack), n),c) = ((beta t s, stack, n+1),c) 13 | krivine1 ((App a b, stack, n),c) = ((a, b:stack, n+1),c) 14 | 15 | krivine1 ((Var "define", (Var a:b:x:s), n), c) = ((x, s, n+1), (a, b):c) 16 | krivine1 ((v@(Var "define"), (Var a:b:[]), n), c) = ((v, [], n+1), (a, b):c) 17 | 18 | krivine1 ((t@(Var a), stack, n), context) = 19 | ((maybe t snd $ find ((==a) . fst) context, stack, n), context) 20 | 21 | krivine1 a = a 22 | 23 | krivine2 :: KMachine -> [KMachine] 24 | krivine2 a 25 | | eval == a = [] 26 | | otherwise = eval : krivine2 eval 27 | where eval = krivine1 a 28 | 29 | krivine3 :: Term -> Context -> [KMachine] 30 | krivine3 a c = ((alphaeq, [], 0), c) : (krivine2 ((alphaeq, [], 0), c)) 31 | where alphaeq = alpha a 32 | 33 | krivine :: Either a Term -> Context -> Either String [KMachine] 34 | krivine (Left _) _ = Left "Parsing Error" 35 | krivine (Right k) initContext = Right $ krivine3 k initContext 36 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /Lambda.hs: -------------------------------------------------------------------------------- 1 | {-# LANGUAGE GADTs #-} 2 | module Lambda where 3 | import Data.List (find) 4 | 5 | type Stack = [Term] 6 | type State = (Term, Stack, Integer) 7 | 8 | data Term where 9 | Var :: String -> Term 10 | Lambda :: Term -> Term -> Term 11 | App :: Term -> Term -> Term 12 | Cont :: Stack -> Term 13 | Instr :: Integer -> Term deriving Eq 14 | 15 | alpha1 :: Int -> [(String, Int)] -> Term -> Term 16 | 17 | alpha1 n bound term@(Var name) = 18 | maybe term (\x -> Var $ name ++ ";" ++ (show $ snd $ x)) p 19 | where p = find (\(s,i) -> s == name) bound 20 | 21 | alpha1 n bound (Lambda (Var x) t) = Lambda (Var $ x++";"++(show n)) (alpha1 (n+1) ((x,n):bound) t) 22 | alpha1 n bound (App a b) = App (alpha1 n bound a) (alpha1 n bound b) 23 | alpha1 _ _ a = a 24 | 25 | alpha :: Term -> Term 26 | alpha = alpha1 0 [] 27 | 28 | beta1 :: Term -> Term -> Term -> Term 29 | beta1 a b (Var t) 30 | | (Var t) == a = b 31 | | otherwise = Var t 32 | beta1 a b (Lambda x t) = Lambda x $ beta1 a b t 33 | beta1 a b (App t u) = App (beta1 a b t) (beta1 a b u) 34 | beta1 a b t = t 35 | 36 | beta :: Term -> Term -> Term 37 | beta (Lambda x t) s = beta1 x s t 38 | beta a _ = a 39 | 40 | mulLambda :: [Term] -> Term -> Term 41 | mulLambda args t = foldr Lambda t args 42 | 43 | mulApp :: [Term] -> Term 44 | mulApp = foldl1 App 45 | -------------------------------------------------------------------------------- /Main.hs: -------------------------------------------------------------------------------- 1 | import Interpreter 2 | import Data.Maybe (listToMaybe) 3 | import System.Environment (getArgs) 4 | 5 | main :: IO () 6 | main = do 7 | args <- getArgs 8 | case listToMaybe args of 9 | Nothing -> repl [] 10 | Just a -> cmd args 11 | -------------------------------------------------------------------------------- /Parser.hs: -------------------------------------------------------------------------------- 1 | {-# LANGUAGE OverloadedStrings #-} 2 | module Parser where 3 | 4 | import Data.Void 5 | import Control.Monad (void) 6 | import Text.Megaparsec 7 | import Text.Megaparsec.Char 8 | import qualified Text.Megaparsec.Char.Lexer as L 9 | 10 | import Lambda 11 | 12 | type Parser = Parsec Void String 13 | 14 | sc :: Parser () 15 | sc = L.space (void $ some (char ' ' <|> char '\t')) empty empty 16 | 17 | lexeme :: Parser a -> Parser a 18 | lexeme = L.lexeme sc 19 | 20 | symbol :: String -> Parser String 21 | symbol = L.symbol sc 22 | 23 | parseVar :: Parser Term 24 | parseVar = lexeme $ Var <$> some (alphaNumChar <|> char '/') 25 | 26 | parseLambda :: Parser Term 27 | parseLambda = lexeme $ symbol "\\" *> (mulLambda <$> some parseVar <* symbol ".") <*> parseTerm 28 | 29 | parseParens :: Parser Term 30 | parseParens = symbol "(" *> parseTerm <* symbol ")" 31 | 32 | parseAtom :: Parser Term 33 | parseAtom = parseCont <|> parseVar <|> parseLambda <|> parseParens 34 | 35 | parseCont :: Parser Term 36 | parseCont = lexeme $ (optional $ symbol "continuation") *> parseCont1 37 | 38 | parseCont1 :: Parser Term 39 | parseCont1 = Cont <$> (symbol "[" *> sepBy parseTerm (symbol ",") <* symbol "]") 40 | 41 | parseApply :: Parser Term 42 | parseApply = foldl1 App <$> some parseAtom 43 | 44 | parseTerm :: Parser Term 45 | parseTerm = (many $ char ' ') *> parseApply 46 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # call-cc-krivine 2 | 3 | **Work in progress.** 4 | 5 | [A web version, compiled with the GHC 9.6 Javascript build, is available here](https://aramya.neocities.org/) 6 | 7 | A Krivine machine for the call-by-name reduction of lambda calculus (with call/cc & clock) expressions in Haskell. 8 | 9 | ``t ⋆ π`` describes a state, where ``t`` is a term and ``π`` is a stack of terms. Pushing ``u`` on ``π`` is written ``u : π``. ``n`` is the number of instructions executed so far. 10 | 11 | To implement ``call/cc``, we allow ourselves to have a term that carries a stack in the form ``continuation π``. 12 | 13 | *Before* |*After*| 14 | |- |- 15 | |``t s ⋆ π`` | ``t ⋆ s : π`` 16 | |``λx.t ⋆ s : π`` | ``t[x := s] ⋆ π`` 17 | |``call/cc ⋆ f : π`` |``f ⋆ continuation π : π`` 18 | | ``continuation π₁ ⋆ s : π₂`` | ``s ⋆ π₁`` 19 | | ``clock ⋆ s : π`` | ``s ⋆ n : π`` 20 | -------------------------------------------------------------------------------- /Show.hs: -------------------------------------------------------------------------------- 1 | module Show where 2 | import Lambda 3 | import Data.List (intercalate) 4 | import Krivine 5 | 6 | removeTags1 :: String -> Bool -> String 7 | removeTags1 [] _ = [] 8 | removeTags1 (';':s) _ = removeTags1 s True 9 | removeTags1 (' ':s) _ = ' ' : (removeTags1 s False) 10 | removeTags1 ('.':s) _ = '.' : (removeTags1 s False) 11 | removeTags1 (a:s) b 12 | | elem a ['0'..'9'] && b = removeTags1 s b 13 | | otherwise = a : (removeTags1 s b) 14 | 15 | removeTags :: String -> String 16 | removeTags s = removeTags1 s False 17 | 18 | removeCommaR :: String -> String 19 | removeCommaR (' ':',':xs) = xs 20 | removeCommaR (x:xs) = x : removeComma xs 21 | removeCommaR [] = [] 22 | 23 | removeComma :: String -> String 24 | removeComma = (reverse . removeCommaR . reverse) 25 | 26 | t2str :: Term -> String 27 | t2str (Var a) = a 28 | t2str (Lambda x e) = "λ"++(t2str x)++"."++(t2str e) 29 | t2str (App a b) = "("++(t2str a)++" "++(t2str b)++")" 30 | t2str (Cont c) = removeComma $ "continuation " ++ "[" ++ (concat $ (map (\x -> (t2str x ++ ", ")) c)) ++ "]" 31 | t2str (Instr n) = "instr n°" ++ show n 32 | 33 | s2str :: [Term] -> String -> String 34 | s2str s i = intercalate i (map t2str s) 35 | 36 | showKrivine1 :: Either String [KMachine] -> String 37 | showKrivine1 (Left s) = s++"\n" 38 | showKrivine1 (Right []) = "" 39 | 40 | showKrivine1 (Right [((t@(Var x), s@(a:as), n),c)]) = 41 | (t2str t)++" *** "++ "[" ++ (s2str s ", ")++"]\nnot evaluated.\n" 42 | 43 | showKrivine1 (Right (((t,s,n),c):kr)) = 44 | (t2str t)++" *** " ++ "["++ (s2str s ", ")++"]\n" ++ (showKrivine1 (Right kr)) 45 | 46 | showKrivine :: Either String [KMachine] -> String 47 | showKrivine s@(Left _) = showKrivine1 s 48 | showKrivine a = removeTags $ showKrivine1 a 49 | --------------------------------------------------------------------------------