diff --git a/Format.hs b/Format.hs new file mode 100644 --- /dev/null +++ b/Format.hs @@ -0,0 +1,103 @@ +{-| +Module: Format +Description: Formatting the output of the interpreter +License: GPL-3 + +This module controls the format of the text and expressions printed by the +interpreter. Uses ANSI escape sequences to color the terminal and mark text +as bold or italics. It also stores the texts showed by the interpreter. +-} + +module Format + ( formatFormula + , formatIntro + , formatPrompt + , formatName + , formatSubs1 + , formatSubs2 + , end + , promptText + , helpText + , initialText + ) +where + +import System.Console.ANSI + + + +-- Colors +-- | Prompt messages color +promptColor :: Color +promptColor = Blue + +-- | Named variables color +nameColor :: Color +nameColor = Green + +-- | Substitutions are marked with this color +substColor :: Color +substColor = Red + +-- | To-be-substituted expressions are marked with this color +subst2Color :: Color +subst2Color = Yellow + + +-- Format sequences +-- | Sequence of characters that signals the format of a formula to the terminal. +formatFormula :: String +formatFormula = setSGRCode [SetConsoleIntensity NormalIntensity, SetColor Foreground Dull promptColor] + +-- | Sequence of characters that signals the format of the introduction to the terminal. +formatIntro :: String +formatIntro = setSGRCode [SetConsoleIntensity BoldIntensity, SetColor Foreground Dull promptColor] + +-- | Sequence of characters that signals the format of the prompt to the terminal. +formatPrompt :: String +formatPrompt = setSGRCode [SetConsoleIntensity BoldIntensity, SetColor Foreground Vivid promptColor] + +-- | Sequence of characters that signals the format of a name to the terminal. +formatName :: String +formatName = setSGRCode [SetColor Foreground Dull nameColor] + +-- | Sequence of characters that signals the format of a substitution to the terminal. +formatSubs1 :: String +formatSubs1 = setSGRCode [SetConsoleIntensity BoldIntensity, SetColor Foreground Dull substColor] + +-- | Sequence of characters that signals the format of a expression which will +-- be substituted in the next reduction step to the terminal. +formatSubs2 :: String +formatSubs2 = setSGRCode [SetColor Foreground Dull subst2Color] + +-- | Sequence of characters that cleans all the format. +end :: String +end = setSGRCode [] + + + + +-- | Prompt line. It is shown when the interpreter asks the user +-- to introduce a new command. +promptText :: String +promptText = formatPrompt ++ "mikroλ> " ++ end + +-- | Help line. It is shown when the user uses the :help command. +helpText :: String +helpText = unlines [ + formatFormula ++ + "Commands available from the prompt:", + "\t\t evaluates the expression", + "\t:quit \t quits the interpreter", + "\t:load \t loads the given .mkr library or script", + "\t:verbose \t sets verbose mode on/off", + "\t:help \t shows this help" + ++ end + ] + +-- | Initial text on the interpreter. It is shown at startup. +initialText :: String +initialText = unlines [ + formatIntro ++ "Welcome to the Mikrokosmos Lambda Interpreter!" ++ end, + formatFormula ++ "Version 0.1.0. GNU General Public License Version 3." ++ end + ] diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Lambda.hs b/Lambda.hs new file mode 100644 --- /dev/null +++ b/Lambda.hs @@ -0,0 +1,130 @@ +{-| +Module: Lambda +Description: DeBruijn lambda expressions. +License: GPL-3 + +This package deals with the parsing, reduction and printing of lambda +expressions using DeBruijn notation. +-} +module Lambda + ( Exp (Var, Lambda, App) + , simplifyAll + , simplifySteps + , showReduction + ) +where + +import Format + +-- DeBruijn Expressions +-- The interpreter uses DeBruijn notation as an internal representation and +-- as output format. It is easier to do beta reduction with DeBruijn indexes. + +-- | A lambda expression using DeBruijn indexes. +data Exp = Var Integer -- ^ integer indexing the variable. + | Lambda Exp -- ^ lambda abstraction + | App Exp Exp -- ^ function application + deriving (Eq, Ord) + +instance Show Exp where + show = showexp + + +-- | Shows an expression with DeBruijn indexes. +showexp :: Exp -> String +showexp (Var n) = show n +showexp (Lambda e) = "λ" ++ showexp e ++ "" +showexp (App f g) = "(" ++ showexp f ++ " " ++ showexp g ++ ")" + +-- | Shows an expression coloring the next reduction. +showReduction :: Exp -> String +showReduction (Lambda e) = "λ" ++ showReduction e +showReduction (App (Lambda f) x) = betaColor (App (Lambda f) x) +showReduction (Var e) = show e +showReduction (App rs x) = "(" ++ showReduction rs ++ " " + ++ showReduction x ++ ")" + +-- | Colors a beta reduction +betaColor :: Exp -> String +betaColor (App (Lambda e) x) = + "(" ++ + formatSubs1 ++ "λ" ++ formatFormula ++ + indexColor 1 e ++ + " " ++ + formatSubs2 ++ showexp x ++ formatFormula + ++ ")" +betaColor e = show e + +-- | Colors all the appearances of a given color +indexColor :: Integer -> Exp -> String +indexColor n (Lambda e) = "λ" ++ indexColor (succ n) e +indexColor n (App f g) = "(" ++ indexColor n f ++ " " ++ indexColor n g ++ ")" +indexColor n (Var m) + | n == m = formatSubs1 ++ show m ++ formatFormula + | otherwise = show m + + + + +-- Reductions of lambda expressions. + +-- | Applies repeated simplification to the expression until it stabilizes and +-- returns the final simplified expression. +-- +-- >>> simplifyAll $ App (Lambda (Var 1)) (Lambda (Var 1)) +-- λ1 +-- +simplifyAll :: Exp -> Exp +simplifyAll = last . simplifySteps + +-- | Applies repeated simplification to the expression until it stabilizes and +-- returns all the intermediate results. +-- +-- >>> simplifySteps $ App (Lambda (Var 1)) (Lambda (Var 1)) +-- [(λ1 λ1),λ1] +-- +simplifySteps :: Exp -> [Exp] +simplifySteps e + | e == s = [e] + | otherwise = e : simplifySteps s + where s = simplify e + +-- | Simplifies the expression recursively. +-- Applies only a beta reduction at each step. +simplify :: Exp -> Exp +simplify (Lambda e) = Lambda (simplify e) +simplify (App (Lambda f) x) = betared (App (Lambda f) x) +simplify (App (Var e) x) = App (Var e) (simplify x) +simplify (App (App f g) x) = App (simplify (App f g)) x +simplify (Var e) = Var e + +-- | Applies beta-reduction to a function application. +-- Leaves the rest of the operations untouched. +betared :: Exp -> Exp +betared (App (Lambda e) x) = substitute 1 x e +betared e = e + +-- | Substitutes an index for a lambda expression +substitute :: Integer -- ^ deBruijn index of the desired target + -> Exp -- ^ replacement for the index + -> Exp -- ^ initial expression + -> Exp +substitute n x (Lambda e) = Lambda (substitute (succ n) (incrementFreeVars 0 x) e) +substitute n x (App f g) = App (substitute n x f) (substitute n x g) +substitute n x (Var m) + -- The lambda is replaced directly + | n == m = x + -- A more exterior lambda decreases a number + | n < m = Var (m-1) + -- An unrelated variable remains untouched + | otherwise = Var m + +-- | Increments free variables assuming they are bind to an +-- external lambda. This is done to substitute them correctly in +-- internal expressions. +incrementFreeVars :: Integer -> Exp -> Exp +incrementFreeVars n (App f g) = App (incrementFreeVars n f) (incrementFreeVars n g) +incrementFreeVars n (Lambda e) = Lambda (incrementFreeVars (succ n) e) +incrementFreeVars n (Var m) + | m > n = Var (succ m) + | otherwise = Var m diff --git a/Main.hs b/Main.hs new file mode 100644 --- /dev/null +++ b/Main.hs @@ -0,0 +1,266 @@ +module Main where + +import Control.Applicative ((<$>), (<*>)) +import Control.Monad.Trans +import Data.Char +import Data.List +import qualified Data.Map.Strict as Map +import Data.Maybe +import System.Environment +import System.Console.Haskeline +import Text.ParserCombinators.Parsec +import Format +import MultiBimap +import NamedLambda +import Lambda + +type Filename = String +type Context = MultiBimap Exp String + + + + +-- | Translates a named variable expression into a DeBruijn one. +-- Uses a dictionary of already binded numbers and variables. +tobruijn :: Map.Map String Integer -- ^ dictionary of the names of the variables used + -> Context -- ^ dictionary of the names already binded on the scope + -> NamedLambda -- ^ initial expression + -> Exp +-- Every lambda abstraction is inserted in the variable dictionary, +-- and every number in the dictionary increases to reflect we are entering +-- into a deeper context. +tobruijn d context (LambdaAbstraction c e) = Lambda $ tobruijn newdict context e + where newdict = Map.insert c 1 (Map.map succ d) +-- Translation of applications is trivial. +tobruijn d context (LambdaApplication f g) = App (tobruijn d context f) (tobruijn d context g) +-- Every variable is checked on the variable dictionary and in the current scope. +tobruijn d context (LambdaVariable c) = + case Map.lookup c d of + Just n -> Var n + Nothing -> fromMaybe (Var 0) (MultiBimap.lookupR c context) + +-- | Transforms a lambda expression with named variables to a deBruijn index expression. +-- Uses only the dictionary of the variables in the current context. +toBruijn :: Context -- ^ Variable context + -> NamedLambda -- ^ Initial lambda expression with named variables + -> Exp +toBruijn = tobruijn Map.empty + + + + +-- Lambda interpreter +-- The logic of the interpreter is written here. It allows to execute normal +-- actions (bindings and evaluation), and interpreter specific actions, as +-- "quit" or "load". + +-- | Runs the interpreter with default settings and an empty context. +main :: IO () +main = do + args <- getArgs + case args of + [] -> runInputT defaultSettings (outputStrLn initialText + >> interpreterLoop defaultOptions emptyContext) + [filename] -> executeFile filename + _ -> putStrLn "Wrong number of arguments" + + +-- | Executes the commands inside a file. A .mkr file can contain a sequence of +-- expressions and variable bindings, and it is interpreted sequentially. +executeFile :: Filename -- Input file + -> IO () +executeFile filename = do + maybeloadfile <- loadFile filename + case maybeloadfile of + Nothing -> putStrLn "Error loading file" + Just actions -> case multipleAct emptyContext actions of + (_, outputs) -> mapM_ (putStr . format) outputs + where + format :: String -> String + format "" = "" + format s = (++"\n") . last . lines $ s + + +-- | Empty context without any bindings +emptyContext :: Context +emptyContext = MultiBimap.empty + + +-- | Configuration options for the interpreter. They can be changed dinamically. +data InterpreterOptions = InterpreterOptions { verbose :: Bool -- ^ true if produces verbose output + , color :: Bool -- ^ true if colors the output + } + +-- | Default config options +defaultOptions :: InterpreterOptions +defaultOptions = InterpreterOptions { verbose = False + , color = True + } + +-- | Interpreter action. It can be a language action (binding and evaluation) +-- or an interpreter specific one, such as "quit". +data InterpreterAction = Interpret Action -- ^ Language action + | EmptyLine -- ^ Empty line, it will be ignored + | Error -- ^ Error on the interpreter + | Quit -- ^ Close the interpreter + | Load String -- ^ Load the given file + | SetVerbose -- ^ Changes verbosity + | SetColors -- ^ Changes colors + | Help -- ^ Shows help + +-- | Language action. The language has a number of possible valid statements; +-- all on the following possible forms. +data Action = Bind (String, NamedLambda) -- ^ bind a name to an expression + | EvalBind (String, NamedLambda) -- ^ bind a name to an expression and simplify it + | Execute NamedLambda -- ^ execute an expression + | Comment -- ^ comment + + +-- | Executes a language action. Given a context and an action, returns +-- the new context after the action and a text output. +act :: Context -> Action -> (Context, String) +act context Comment = (context,"") +act context (Bind (s,le)) = (MultiBimap.insert (toBruijn context le) s context, "") +act context (EvalBind (s,le)) = (MultiBimap.insert (simplifyAll $ toBruijn context le) s context, "") +act context (Execute le) = (context, + unlines $ + [ show le ] ++ + [ unlines $ map showReduction $ simplifySteps $ toBruijn context le ] ++ + [ showCompleteExp context $ simplifyAll $ toBruijn context le ] + ) + +showCompleteExp :: Context -> Exp -> String +showCompleteExp context expr = case getExpressionName context expr of + Nothing -> show expr + Just expName -> show expr ++ formatName ++ " ⇒ " ++ expName ++ end + +getExpressionName :: Context -> Exp -> Maybe String +getExpressionName context expr = case MultiBimap.lookup expr context of + [] -> Nothing + xs -> Just $ intercalate ", " xs + +-- TODO: Writer monad +-- TODO: Use Text instead of String for efficiency +-- TODO: Lists of string are inefficient +-- | Executes multiple actions. Given a context and a set of actions, returns +-- the new context after the sequence of actions and a text output. +multipleAct :: Context -> [Action] -> (Context, [String]) +multipleAct context = foldl (\(ccontext,text) action -> + (fst $ act ccontext action, text ++ [snd (act ccontext action)])) + (context,[]) + + + +-- TODO: State Monad +-- | Interpreter awaiting for an instruction. +interpreterLoop :: InterpreterOptions -> Context -> InputT IO () +interpreterLoop options context = do + minput <- getInputLine promptText + let interpreteraction = + case minput of + Nothing -> Quit + Just "" -> EmptyLine + Just input -> case parse interpreteractionParser "" input of + Left _ -> Error + Right a -> a + case interpreteraction of + EmptyLine -> interpreterLoop options context + Quit -> return () + Error -> outputStrLn "Error" + SetVerbose -> do + outputStrLn $ "verbose mode: " ++ if verbose options then "off" else "on" + interpreterLoop (options {verbose = not $ verbose options}) context + SetColors -> interpreterLoop (options {color = not $ color options}) context + Help -> outputStr helpText >> interpreterLoop options context + Load filename -> do + maybeloadfile <- lift $ loadFile filename + case maybeloadfile of + Nothing -> outputStrLn "Error loading file" + Just actions -> case multipleAct context actions of + (ccontext, outputs) -> do + outputStr formatFormula + outputActions options outputs + outputStr end + interpreterLoop options ccontext + Interpret action -> case act context action of + (ccontext, output) -> do + outputStr formatFormula + outputActions options [output] + outputStr end + interpreterLoop options ccontext + +-- | Outputs results from actions. Given a list of options and outputs, +-- formats and prints them in console. +outputActions :: InterpreterOptions -> [String] -> InputT IO () +outputActions options = mapM_ (outputStr . format) + where + format :: String -> String + format "" = "" + format s + | not (verbose options) = (++"\n") . last . lines $ s + | otherwise = s + +-- | Loads the given filename and returns the complete list of actions. +-- Returns Nothing if there is an error reading or parsing the file. +loadFile :: String -> IO (Maybe [Action]) +loadFile filename = do + putStrLn filename + input <- readFile filename + let parsing = map (parse actionParser "") $ filter (/="") $ lines input + let actions = map (\x -> case x of + Left _ -> Nothing + Right a -> Just a) parsing + return $ sequence actions + +-- | Parses an interpreter action. +interpreteractionParser :: Parser InterpreterAction +interpreteractionParser = choice [ try interpretParser + , try quitParser + , try loadParser + , try verboseParser + , try helpParser + ] + +-- | Parses a language action as an interpreter action. +interpretParser :: Parser InterpreterAction +interpretParser = Interpret <$> actionParser + +-- | Parses a language action. +actionParser :: Parser Action +actionParser = choice [ try bindParser + , try evalbindParser + , try executeParser + , try commentParser + ] + +-- | Parses a binding between a variable an its representation. +bindParser :: Parser Action +bindParser = fmap Bind $ (,) <$> many1 alphaNum <*> (spaces >> string "!=" >> spaces >> lambdaexp) + +-- | Parses a binding and evaluation expression between a variable an its representation +evalbindParser :: Parser Action +evalbindParser = fmap EvalBind $ (,) <$> many1 alphaNum <*> (spaces >> string "=" >> spaces >> lambdaexp) + +-- | Parses an expression in order to execute it. +executeParser :: Parser Action +executeParser = Execute <$> lambdaexp + +-- | Parses comments. +commentParser :: Parser Action +commentParser = string "#" >> many anyChar >> return Comment + +-- | Parses a "quit" command. +quitParser :: Parser InterpreterAction +quitParser = string ":quit" >> return Quit + +-- | Parses a "help" command. +helpParser :: Parser InterpreterAction +helpParser = string ":help" >> return Help + +-- | Parses a change in verbosity. +verboseParser :: Parser InterpreterAction +verboseParser = string ":verbose" >> return SetVerbose + +-- | Parses a "load-file" command. +loadParser :: Parser InterpreterAction +loadParser = Load <$> (string ":load" >> between spaces spaces (many1 (satisfy (not . isSpace)))) diff --git a/MultiBimap.hs b/MultiBimap.hs new file mode 100644 --- /dev/null +++ b/MultiBimap.hs @@ -0,0 +1,52 @@ +{-| +Module: MultiBimap +Description: A multibimap implementation +License: GPL-3 + +This module allows us to abstract a bidirectional multimap without +having to worry about implementation details. It is useful in the translation +between lambda expressions and names. + +Based on the bimap package: + +-} +module MultiBimap + ( MultiBimap + , empty + , null + , insert + , lookup + , lookupR + ) +where + + + +import qualified Data.Map as M +import qualified Data.MultiMap as MM +import Prelude hiding (null,lookup) + +data MultiBimap k v = MkMultiBimap (MM.MultiMap k v) (M.Map v k) + +-- | The empty multi-bimap +empty :: MultiBimap k v +empty = MkMultiBimap MM.empty M.empty + +-- | True if the multi-bimap is empty +null :: MultiBimap k v -> Bool +null (MkMultiBimap _ right) = M.null right + +-- | Inserts a key-value in the multi-bimap. +-- The value can have been used earlier. +insert :: (Ord k, Ord v) => k -> v -> MultiBimap k v -> MultiBimap k v +insert k v (MkMultiBimap left right) = + MkMultiBimap (MM.insert k v left) (M.insert v k right) + +-- | Lookup a key in the multi-bimap, returning the list of +-- associated values. +lookup :: (Ord k, Ord v) => k -> MultiBimap k v -> [v] +lookup k (MkMultiBimap left _) = MM.lookup k left + +-- | Lookup a right value in the multi-bimap, returning the associated key. +lookupR :: (Ord k, Ord v) => v -> MultiBimap k v -> Maybe k +lookupR v (MkMultiBimap _ right) = M.lookup v right diff --git a/NamedLambda.hs b/NamedLambda.hs new file mode 100644 --- /dev/null +++ b/NamedLambda.hs @@ -0,0 +1,78 @@ +{-| +Module: NamedLambda +Description: Lambda expressions with named variables +License: GPL-3 + +This package deals with lambda expressions containing named variables +instead of DeBruijn indexes. It contains parsing and printing fuctions. +-} + +module NamedLambda + ( NamedLambda (LambdaVariable, LambdaAbstraction, LambdaApplication) + , lambdaexp + ) +where + +import Text.ParserCombinators.Parsec +import Control.Applicative ((<$>), (<*>)) + +-- Parsing of Lambda Expressions. +-- The user can input a lambda expression with named variables, of +-- the form of "\x.x" or "(\a.(\b.a b))". The interpreter will parse +-- it into an internal representation. + +-- | A lambda expression with named variables. +data NamedLambda = LambdaVariable String -- ^ variable + | LambdaAbstraction String NamedLambda -- ^ lambda abstraction + | LambdaApplication NamedLambda NamedLambda -- ^ function application + +-- | Parses a lambda expression with named variables. +-- A lambda expression is a sequence of one or more autonomous +-- lambda expressions. They are parsed assuming left-associativity. +-- +-- >>> parse lambdaexp "" "\\f.\\x.f x" +-- Right λf.λx.(f x) +-- +-- Note that double backslashes are neccessary only when we quote strings; +-- it will work only with a simple backslash in the interpreter. +lambdaexp :: Parser NamedLambda +lambdaexp = foldl1 LambdaApplication <$> (spaces >> sepBy1 simpleexp spaces) + +-- | Parses a simple lambda expression, without function applications +-- at the top level. It can be a lambda abstraction, a variable or another +-- potentially complex lambda expression enclosed in parentheses. +simpleexp :: Parser NamedLambda +simpleexp = choice [lambdaAbstractionParser, variableParser, parens lambdaexp] + +-- | The returned parser parenthesizes the given parser +parens :: Parser a -> Parser a +parens = between (char '(') (char ')') + +-- | Parses a variable. Any name can form a lambda variable. +variableParser :: Parser NamedLambda +variableParser = LambdaVariable <$> nameParser + +-- | Allowed variable names +nameParser :: Parser String +nameParser = many1 alphaNum + +-- | Parses a lambda abstraction. The '\' is used as lambda. +lambdaAbstractionParser :: Parser NamedLambda +lambdaAbstractionParser = LambdaAbstraction <$> + (char lambdaChar >> nameParser) <*> (char '.' >> lambdaexp) + +-- | Char used to represent lambda in user's input. +lambdaChar :: Char +lambdaChar = '\\' + +-- | Shows a lambda expression with named variables. +-- Parentheses are ignored; they are written only around applications. +showNamedLambda :: NamedLambda -> String +showNamedLambda (LambdaVariable c) = c +showNamedLambda (LambdaAbstraction c e) = "λ" ++ c ++ "." ++ showNamedLambda e ++ "" +showNamedLambda (LambdaApplication f g) = "(" ++ showNamedLambda f ++ " " ++ showNamedLambda g ++ ")" + +instance Show NamedLambda where + show = showNamedLambda + + diff --git a/README.md b/README.md new file mode 100644 --- /dev/null +++ b/README.md @@ -0,0 +1,70 @@ +# mikrokosmos + +**Mikrokosmos** is an untyped lambda calculus interpreter, borrowing its name from the series of +progressive piano études *[Mikrokosmos](https://www.youtube.com/watch?v=VEsMk3DAzWM)* written by *Bela Bartok*. +It aims to provide students with a tool to learn and understand lambda calculus. +If you want to start learning about lambda calculus, I suggest you to read: + + * [The wikipedia page on Lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus#Informal_description) + * [A tutorial introduction to the Lambda calculus by Raúl Rojas](www.inf.fu-berlin.de/lehre/WS03/alpi/lambda.pdf) + +And to install and to tinker with this interpreter. + +## Installation + +Mikrokosmos will be soon installable from [Hackage](http://hackage.haskell.org/). Meanwhile, you can install it +cloning the repository and using [cabal](https://www.haskell.org/cabal/): + +``` bash +git clone https://github.com/M42/mikrokosmos.git +cd mikrokosmos +cabal install +``` + +## First steps + +Once installed, you can open the interpreter typing `mikrokosmos` in your terminal. It will show you a prompt where +you can write lambda expressions to evaluate them: + +![First steps](https://cloud.githubusercontent.com/assets/5337877/18393670/92728f10-76b6-11e6-88cc-88e7f2cb9114.png) + +You can write expressions using `\var.` to denote a lambda abstraction on the `var` variable and +you can bind names to expressions using `=`. *But why am I getting this weird output?* Well, the interpreter +outputs the lambda expressions in [De Bruijn notation](https://en.wikipedia.org/wiki/De_Bruijn_notation); it is more +compact and the interpreter works internally with it. However, as you can see in the image, whenever the interpreter finds a known constant, it labels the expression with its name. + +If you need help at any moment, you can type `:help` into the prompt to get a summary of the available options: + +![Help screen](https://cloud.githubusercontent.com/assets/5337877/18393812/33e86b6c-76b7-11e6-818b-76b68f599a44.png) + +## The standard library + +Mikrokosmos comes bundled with a standard library. It allows you to experiment with Church encoding of booleans, +integers and much more. You can load it with `:load std.mkr`; after that, you can use a lot of new constants: + +![Standard library](https://cloud.githubusercontent.com/assets/5337877/18394001/1a238ec2-76b8-11e6-90ad-b2385ba60268.png) + +All this is written in lambda calculus! You can check the definitions on the `std.mkr` file. + +## Debugging and verbose mode + +If you want to check how the lambda reductions are being performed you can use the **verbose mode**. +It can be activated and deactivated writing `:verbose`, and it will show you every step on the reduction of +the expression, coloring the substitution at every step. + +![Verbose mode](https://cloud.githubusercontent.com/assets/5337877/18394177/e4925bd4-76b8-11e6-886e-6bd33fe02e88.png) + +## Advanced data structures + +There are representations of structures such as linked lists or trees in the standard library. +You can use them to do a bit of your usual functional programming: + +![Trees](https://cloud.githubusercontent.com/assets/5337877/18394894/5cd41d1e-76bc-11e6-9564-8817992392af.png) + +Oh! And you can insert comments with `#`, both in the interpreter and in the files the interpreter can load. + +### References & interesting links +* [Build you a Haskell - Stephen Diehl](http://dev.stephendiehl.com/fun/003_lambda_calculus.html) +* [Haskell from Scratch - Jekor](https://www.youtube.com/playlist?list=PLxj9UAX4Em-Ij4TKwKvo-SLp-Zbv-hB4B) +* [The Glambda interpreter](https://github.com/goldfirere/glambda) +* [Lecture notes on the lambda calculus - Peter Selinger](http://www.mscs.dal.ca/~selinger/papers/lambdanotes.pdf) diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/mikrokosmos.cabal b/mikrokosmos.cabal new file mode 100644 --- /dev/null +++ b/mikrokosmos.cabal @@ -0,0 +1,42 @@ +name: mikrokosmos +version: 0.1.0 +synopsis: Lambda calculus interpreter +description: A didactic untyped lambda calculus interpreter. +homepage: https://github.com/M42/mikrokosmos +bug-reports: https://github.com/M42/mikrokosmos/issues +license: GPL-3 +license-file: LICENSE +author: Mario Román (M42) +maintainer: mromang08+github@gmail.com +category: Language +build-type: Simple +extra-source-files: README.md +cabal-version: >=1.10 +tested-with: GHC == 7.8.3 +extra-source-files: std.mkr + +source-repository head + type: git + location: git://github.com/M42/mikrokosmos.git + +executable mikrokosmos + main-is: Main.hs + build-depends: base >=4.7 && <5, + mtl >=2.2, + containers >= 0.5, + haskeline >=0.7, + parsec >=3, + ansi-terminal, + multimap, + HUnit >=1.0 + + other-modules: Format + Lambda + NamedLambda + MultiBimap + + default-language: Haskell2010 + ghc-options: -Wall + + + diff --git a/std.mkr b/std.mkr new file mode 100644 --- /dev/null +++ b/std.mkr @@ -0,0 +1,192 @@ +## Standard library ## + +# This is the standard library for the Mikrokosmos untyped lambda calculus +# interpreter. It contains basic logic and arithmetic operations. +# You can read more about Church encoding in its wikipedia page: +# https://en.wikipedia.org/wiki/Church_encoding +# +# This library is licensed under CC0. + + + + +## Logic +# Uses Church Booleans +true = \a.\b.a +false = \a.\b.b + +# Basic logic gates +and = \p.\q.p q p +or = \p.\q.p p q +not = \b.b false true + +# Conditional +ifelse = (\x.x) + + + + +## Arithmethic +# This library uses Church numerals to represent natural numbers +# Succesor of a natural number is defined with 0 +succ = \n.\f.\x.f (n f x) +0 = \f.\x.x + +# Basic operations on natural numbers +plus = \m.\n.\f.\x.m f (n f x) +mult = \m.\n.\f.\x.m (n f) x + +# Substraction +pred = \n.\f.\x.n (\g.(\h.h (g f))) (\u.x) (\u.u) +minus = \m.\n.(n pred) m + +# Predicates on natural numbers +iszero = \n.(n (\x.false) true) +leq = \m.\n.(iszero (minus m n)) +eq = \m.\n.(and (leq m n) (leq n m)) + + + + +## Data structures +# Pairs +pair = \x.\y.\z.z x y +first = \p.p true +second = \p.p false + +# Lists +# Uses the right-fold representation of lists. +# The representation of a list is its foldr function. +cons = \h.\t.\c.\n.(c h (t c n)) +nil = \c.\n.n + +# Folds +foldr = \o.\n.\l.(l o n) +sum = (foldr plus 0) +prod = (foldr mult (succ 0)) +length = (foldr (\h.\t.succ t) 0) + +# Map +# Writes map as a foldr. +map = (\f.(foldr (\h.\t.cons (f h) t) nil)) +filter = \p.(foldr (\h.\t.((p h) (cons h t) t)) nil) + +# Trees +# Uses the fold representation of a binary tree +# Its nil is the same one as the list representation +node = \x.\l.\r.\f.\n.(f x (l f n) (r f n)) + + + + +## Fixpoint operator and recursion +fix != (\f.(\x.f (x x)) (\x.f (x x))) +fact != fix (\f.\n.iszero n (succ 0) (mult n (f (pred n)))) +fib != fix (\f.\n.iszero n 1 (plus (f (pred n)) (f (pred (pred n))))) + + + + +## APPENDIX +## Natural numbers +# List of 100 first natural numbers +1 = succ 0 +2 = succ 1 +3 = succ 2 +4 = succ 3 +5 = succ 4 +6 = succ 5 +7 = succ 6 +8 = succ 7 +9 = succ 8 +10 = succ 9 +11 = succ 10 +12 = succ 11 +13 = succ 12 +14 = succ 13 +15 = succ 14 +16 = succ 15 +17 = succ 16 +18 = succ 17 +19 = succ 18 +20 = succ 19 +21 = succ 20 +22 = succ 21 +23 = succ 22 +24 = succ 23 +25 = succ 24 +26 = succ 25 +27 = succ 26 +28 = succ 27 +29 = succ 28 +30 = succ 29 +31 = succ 30 +32 = succ 31 +33 = succ 32 +34 = succ 33 +35 = succ 34 +36 = succ 35 +37 = succ 36 +38 = succ 37 +39 = succ 38 +40 = succ 39 +41 = succ 40 +42 = succ 41 +43 = succ 42 +44 = succ 43 +45 = succ 44 +46 = succ 45 +47 = succ 46 +48 = succ 47 +49 = succ 48 +50 = succ 49 +51 = succ 50 +52 = succ 51 +53 = succ 52 +54 = succ 53 +55 = succ 54 +56 = succ 55 +57 = succ 56 +58 = succ 57 +59 = succ 58 +60 = succ 59 +61 = succ 60 +62 = succ 61 +63 = succ 62 +64 = succ 63 +65 = succ 64 +66 = succ 65 +67 = succ 66 +68 = succ 67 +69 = succ 68 +70 = succ 69 +71 = succ 70 +72 = succ 71 +73 = succ 72 +74 = succ 73 +75 = succ 74 +76 = succ 75 +77 = succ 76 +78 = succ 77 +79 = succ 78 +80 = succ 79 +81 = succ 80 +82 = succ 81 +83 = succ 82 +84 = succ 83 +85 = succ 84 +86 = succ 85 +87 = succ 86 +88 = succ 87 +89 = succ 88 +90 = succ 89 +91 = succ 90 +92 = succ 91 +93 = succ 92 +94 = succ 93 +95 = succ 94 +96 = succ 95 +97 = succ 96 +98 = succ 97 +99 = succ 98 +100 = succ 99