215 lines
7.5 KiB
Haskell
215 lines
7.5 KiB
Haskell
import Data.List
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import Data.Maybe
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import Text.ParserCombinators.ReadP
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{-
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- The Expression type
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-}
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data Expression s = ESymbol s
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| EReference Int
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| EExpr (Expression s) (Expression s)
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| ELambda s (Expression s)
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-- list of names -> name -> unique name
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-- Find a unique name not in the list of names.
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-- Appends apostrophes until name is unique.
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makeUnique :: [String] -> String -> String
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makeUnique context s =
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let apostrophes = iterate ('\'' :) ""
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modified = zipWith (++) (repeat s) apostrophes
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available = filter (not . (`elem` context)) modified
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in head available -- list of available names is infinite
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-- Expression -> Expression with unique symbol names
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renameUniquely :: (Show s) => Expression s -> Expression String
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renameUniquely = rename_ []
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-- rename_ :: (Show s) => [String] -> Expression s -> Expression String
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where rename_ c (EReference r) = EReference r
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rename_ c (ESymbol s) = ESymbol . makeUnique c . show $ s
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rename_ c (EExpr a b) = EExpr (rename_ c a) (rename_ c b)
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rename_ c (ELambda s e) = let name = makeUnique c . show $ s
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in ELambda name (rename_ (name : c) e)
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instance (Show s) => Show (Expression s) where
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show = show_ [] . renameUniquely
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-- show_ :: Expression String -> String
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where show_ c (EReference n)
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| n >= 0 && n < length c = c !! n
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| otherwise = "ERR" -- TODO: Deal with errors properly?
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show_ c (ESymbol s) = s
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show_ c (ELambda s e) = "\\" ++ s ++ "." ++ show_ (s : c) e
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show_ c (EExpr a@(ELambda _ _) b@(ELambda _ _)) = "(" ++ show_ c a ++ ") (" ++ show_ c b ++ ")"
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show_ c (EExpr a@(ELambda _ _) b@(EExpr _ _)) = "(" ++ show_ c a ++ ") (" ++ show_ c b ++ ")"
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show_ c (EExpr a@(ELambda _ _) b ) = "(" ++ show_ c a ++ ") " ++ show_ c b
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show_ c (EExpr a b@(ELambda _ _)) = show_ c a ++ " (" ++ show_ c b ++ ")"
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show_ c (EExpr a b@(EExpr _ _)) = show_ c a ++ " (" ++ show_ c b ++ ")"
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show_ c (EExpr a b) = show_ c a ++ " " ++ show_ c b
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instance (Eq s) => Eq (Expression s) where
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(ESymbol a) == (ESymbol b) = a == b
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(EReference a) == (EReference b) = a == b
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(EExpr a b) == (EExpr c d) = a == c && b == d
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(ELambda _ a) == (ELambda _ b) = a == b
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_ == _ = False
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instance Functor Expression where
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fmap f (EReference n) = EReference n
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fmap f (ESymbol a) = ESymbol (f a)
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fmap f (ELambda s e) = ELambda (f s) (fmap f e)
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fmap f (EExpr a b) = EExpr (fmap f a) (fmap f b)
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{-
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- Evaluating expressions
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-}
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-- Expression to be inserted -> Expression to be inserted into -> result
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-- TODO: Make clearer what insert does - better description, ...
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insertExpr :: Int -> Expression s -> Expression s -> Expression s
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insertExpr level replace ref@(EReference n)
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| n == level = replace
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| otherwise = ref
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insertExpr level replace (EExpr a b) = EExpr (insertExpr level replace a)
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(insertExpr level replace b)
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insertExpr level replace (ELambda s e) = ELambda s (insertExpr (level + 1) replace e)
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insertExpr _ _ symbol = symbol
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apply :: Expression s -> Expression s
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apply (EExpr l@(ELambda s e) b) = insertExpr 0 b e
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apply (EExpr e@(EExpr _ _) b) = EExpr (apply e) b
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apply e = e
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takeWhileUnique :: (Eq a) => [a] -> [a]
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takeWhileUnique l = map fst
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$ takeWhile (\a -> not $ fst a `elem` snd a)
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$ zip l (inits l)
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evaluate :: (Eq s) => Expression s -> [Expression s]
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evaluate = takeWhileUnique . iterate apply
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{-
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- Parsing expressions
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-}
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parens :: [(Char, Char)]
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parens = [('(',')'),('[',']'),('{','}')]
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isOpeningParen :: Char -> Bool
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isOpeningParen a = isJust $ lookup a parens
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-- Pointfree alternative:
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-- isOpeningParen = isJust . flip lookup parens
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isClosingParen :: Char -> Char -> Bool
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isClosingParen a b = fromMaybe False $ (==b) <$> lookup a parens
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-- And as monad:
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-- isClosingParen a b = fromMaybe False $ do
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-- closing <- lookup a parens
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-- return $ closing == b
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-- And again as a monad:
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-- isClosingParen a b = fromMaybe False $ lookup a parens >>= return . (==b)
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parenthesize :: ReadP a -> ReadP a
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parenthesize parser = do
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paren <- satisfy isOpeningParen
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result <- parser
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satisfy $ isClosingParen paren
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return result
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parseSymbol :: ReadP (Expression String)
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parseSymbol = do
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a <- munch1 (`elem` ['a'..'z'])
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b <- munch (=='\'')
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return $ ESymbol (a ++ b)
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parseLambda :: ReadP (Expression String)
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parseLambda = do
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char '\\' +++ char 'λ'
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(ESymbol s) <- parseSymbol
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char '.'
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e <- parseExpr
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return $ ELambda s e
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parseExpr :: ReadP (Expression String)
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parseExpr =
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let options = parseSymbol
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+++ parseLambda
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+++ parenthesize parseExpr
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-- let options = choice [parseSymbol
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-- ,parseLambda
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-- ,parenthesize parseExpr
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-- ]
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parse = between skipSpaces skipSpaces options
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in chainl1 parse (return EExpr)
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findReferences :: (Eq s) => Expression s -> Expression s
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findReferences = find_ []
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where find_ context sym@(ESymbol s) = fromMaybe sym $ EReference <$> elemIndex s context
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find_ context ref@(EReference _) = ref
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find_ context (ELambda s e) = ELambda s $ find_ (s:context) e
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find_ context (EExpr a b) = EExpr (find_ context a) (find_ context b)
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removeApostrophes :: String -> String
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removeApostrophes = reverse . dropWhile (=='\'') . reverse
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maybeParseExpression :: String -> Maybe (Expression String)
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maybeParseExpression s = do
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let results = readP_to_S parseExpr s
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(expr, _) <- safeLast results
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return . fmap removeApostrophes . findReferences $ expr
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where safeLast [] = Nothing
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safeLast xs = Just $ last xs
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{-
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- Testing output
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-}
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-- Helper type for using arbitrary strings as symbols
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newtype StrSymbol = StrSymbol String
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instance Show StrSymbol where
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show (StrSymbol s) = s
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instance Eq StrSymbol where
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(StrSymbol a) == (StrSymbol b) = a == b
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_s = ESymbol
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_e = EExpr
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_r = EReference
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_l = ELambda
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_ss = StrSymbol
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main = do
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putStrLn "Test nested expressions and parentheses"
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print (_e (_e (_s 1) (_s 2)) (_e (_s 3) (_s 4)))
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print (_e (_e (_s 1) (_e (_s 2) (_s 3))) (_s 4))
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print (_e (_e (_l 1 (_r 0)) (_e (_l 2 (_r 0)) (_l 3 (_r 0)))) (_l 4 (_r 0)))
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putStrLn "Test references and symbols in lambda expressions"
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print (_l 5 (_l 2 (_e (_s 3) (_r 0))))
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print (_l 5 (_l 2 (_e (_s 3) (_r 1))))
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print (_l 5 (_l 2 (_e (_s 3) (_r 2)))) -- should fail in some way
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putStrLn "More reference tests"
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print (_l 1 (_e (_l 2 (_r 0)) (_l 3 (_r 1))))
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print ((_r 0) :: Expression Int) -- should also fail in some way
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putStrLn "Test insertion"
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putStrLn "Testing Ints as symbols..."
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let t = (_l 1 (_l 2 (_r 1)))
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f = (_l 1 (_l 2 (_r 0)))
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n = (_l 1 (_e (_e (_r 0) f) t))
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print t
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print f
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print n
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putStrLn "Evaluating... N T"
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mapM_ print . evaluate $ (_e n t)
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putStrLn "Evaluating... N F"
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mapM_ print . evaluate $ (_e n f)
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putStrLn "Testing StrSymbols as symbols..."
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let st = (_l (_ss "a") (_l (_ss "b") (_r 1)))
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sf = (_l (_ss "a") (_l (_ss "b") (_r 0)))
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sn = (_l (_ss "n") (_e (_e (_r 0) sf) st))
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print st
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print sf
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print sn
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putStrLn "Evaluating... N T"
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mapM_ print . evaluate $ (_e sn st)
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putStrLn "Evaluating... N F"
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mapM_ print . evaluate $ (_e sn sf)
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