mikrokosmos (empty) → 0.1.0
raw patch · 10 files changed
+1609/−0 lines, 10 filesdep +HUnitdep +ansi-terminaldep +basesetup-changed
Dependencies added: HUnit, ansi-terminal, base, containers, haskeline, mtl, multimap, parsec
Files
- Format.hs +103/−0
- LICENSE +674/−0
- Lambda.hs +130/−0
- Main.hs +266/−0
- MultiBimap.hs +52/−0
- NamedLambda.hs +78/−0
- README.md +70/−0
- Setup.hs +2/−0
- mikrokosmos.cabal +42/−0
- std.mkr +192/−0
+ Format.hs view
@@ -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<expression>\t evaluates the expression",+ "\t:quit \t quits the interpreter",+ "\t:load <file>\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+ ]
+ LICENSE view
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If not, see <http://www.gnu.org/licenses/>.++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:++ <program> Copyright (C) <year> <name of author>+ 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+<http://www.gnu.org/licenses/>.++ 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+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+ Lambda.hs view
@@ -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
+ Main.hs view
@@ -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))))
+ MultiBimap.hs view
@@ -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:+<https://hackage.haskell.org/package/bimap-0.3.2/docs/Data-Bimap.html>+-}+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
+ NamedLambda.hs view
@@ -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++
+ README.md view
@@ -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:++++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:++++## 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:++++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.++++## 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:++++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)
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ mikrokosmos.cabal view
@@ -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+++
+ std.mkr view
@@ -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