module HM
( -- * Types
Type(..)
- , Term
+ , TypeScheme(..)
+ , Term(..)
+ , TypedTerm(..)
-- * Type inference
, algW
) where
+import Control.Monad.State
+
import HM.Term
import HM.Parser
type Substitution = TypeScheme -> TypeScheme
+type VarS a = State Int a
fresh :: TypeVarName
fresh = undefined
+--fresh = do
+-- n <- get
+-- "a" ++ show n
+
substitute :: TypeScheme -> TypeVarName -> TypeScheme -> TypeScheme
substitute = undefined
unify (TScheme (TypeVar a)) (TScheme (TypeVar b)) | a == b = Right id
unify a b = Left $ "cannot unify " ++ show a ++ " with " ++ show b
-algW :: HMTerm -> Either String TypeScheme
-algW (HMTerm (Var _) t) = Right t
-algW (HMTerm (Lambda x t) (TScheme p)) = do
- let v = TScheme (TypeVar fresh)
- np = substitute v x t
- unify p np
-algW (HMTerm (App u v) t) = do
- tu <- algW u
- tv <- algW v
- case tu of
- (TScheme (TypeFunction a b)) -> do
- unify a tv
- return b
- _ -> Left $ "cannot apply " ++ show tu ++ " to " ++ show tv
+algW :: TypedTerm -> Either String TypeScheme
+algW (TTerm (Var _) t) = Right t
+--algW (TTerm (Lam x t) (TScheme p)) = do
+-- let v = TScheme (TypeVar fresh)
+-- np = substitute v x t
+-- unify p np
+--algW (TTerm (App u v) t) = do
+-- tu <- algW u
+-- tv <- algW v
+-- case tu of
+-- (TScheme (TypeFunction a b)) -> do
+-- unify a tv
+-- return b
+-- _ -> Left $ "cannot apply " ++ show tu ++ " to " ++ show tv
, parseTerm
) where
+import Data.Char (isAsciiLower, isAsciiUpper)
import Data.Text as T hiding (map)
import Data.Attoparsec.Text
import Control.Applicative
import HM.Term
-import qualified Lambda.Parser.Fancy as Lambda
-import qualified Lambda.Term as Lambda
braced :: String -> String
braced t = "(" ++ t ++ ")"
show (Var x) = x
show (Lam x (NTTerm (Lam y t))) = show (Lam (x ++ " " ++ y) t)
show (Lam x t) = braced $ "λ" ++ x ++ "." ++ show t
- show (App a (NTTerm (App b c))) = show a ++ " " ++ (braced $ show (App b c))
+ show (App a (NTTerm (App b c))) = show a ++ " " ++ braced ( show (App b c))
show (App t r) = show t ++ " " ++ show r
- show (Let x e1 e2) = braced $ "let " ++ x ++ " = " ++ show e1 ++ " in " ++ show e2
+ show (Let x e1 e2) = braced $ "LET " ++ x ++ " = " ++ show e1 ++ " IN " ++ show e2
instance Show TypedTerm where
show (NTTerm t) = show t
show (TScheme t) = show t
show (TSForAll x t) = braced $ "∀" ++ x ++ ": " ++ show t
-tRead :: String -> Term
-tRead = undefined
+tRead :: String -> TypedTerm
+tRead s = case parseOnly (parseTypedTerm <* endOfInput) (T.pack s) of
+ (Right t) -> t
+ (Left e) -> error e
-parseTerm :: Parser TypedTerm
+parseTerm :: Parser Term
parseTerm = parseLet <|>
- (lambdaToHM <$> Lambda.parseTerm)
+ parseApp <|>
+ parseVar <|>
+ parseLambda
-parseLet :: Parser TypedTerm
-parseLet = do
+parseTermNA :: Parser Term
+parseTermNA = parseLet <|>
+ parseVar <|>
+ parseLambda
+
+parseTypeAndTermNA :: Parser TypedTerm
+parseTypeAndTermNA = do
+ term <- parseTermNA
+ string " :: "
+ tp <- parseTypeScheme
+ return $! TTerm term tp
+
+parseTypeAndTerm :: Parser TypedTerm
+parseTypeAndTerm = do
+ term <- parseTerm
+ string " :: "
+ tp <- parseTypeScheme
+ return $! TTerm term tp
+
+parseTypedTermNA :: Parser TypedTerm
+parseTypedTermNA = parseBraces <|>
+ parseTypeAndTermNA <|>
+ (NTTerm <$> parseTerm)
+
+parseTypedTerm :: Parser TypedTerm
+parseTypedTerm = parseBraces <|>
+ parseTypeAndTerm <|>
+ (NTTerm <$> parseTerm)
+
+parseType :: Parser Type
+parseType = parsePrimitive <|>
+ parseTypeVar <|>
+ parseTypeFunction
+
+parsePrimitive :: Parser Type
+parsePrimitive = do
+ x <- many1 $ satisfy isAsciiUpper
+ return $! Primitive x
+
+parseTypeVar :: Parser Type
+parseTypeVar = do
+ x <- many1 $ satisfy isAsciiLower
+ return $! TypeVar x
+
+parseTypeFunction :: Parser Type
+parseTypeFunction = do
+ a <- parseType
+ string " -> "
+ b <- parseType
+ return $! TypeFunction a b
+
+parseTypeScheme :: Parser TypeScheme
+parseTypeScheme = parseForAll <|>
+ (TScheme <$> parseType)
+
+parseForAll :: Parser TypeScheme
+parseForAll = do
+ string "FORALL "
+ (TypeVar x) <- parseTypeVar
+ string "."
+ t <- parseTypeScheme
+ return $! TSForAll x t
+
+parseBraces :: Parser TypedTerm
+parseBraces = do
char '('
- string "let "
- (Lambda.Var x) <- Lambda.parseVar
- string " = "
- e1 <- lambdaToHM <$> Lambda.parseTerm
- string " in "
- e2 <- lambdaToHM <$> Lambda.parseTerm
+ t <- parseTypedTerm
char ')'
- return . NTTerm $ Let x e1 e2
+ return t
+
+parseLet :: Parser Term
+parseLet = do
+ string "LET "
+ (Var x) <- parseVar
+ string " = "
+ e1 <- parseTypedTerm
+ string " IN "
+ e2 <- parseTypedTerm
+ return $! Let x e1 e2
+
+parseVar :: Parser Term
+parseVar = do
+ x <- many1 $ satisfy isAsciiLower
+ return $! Var x
+
+parseLambda :: Parser Term
+parseLambda = do
+ char '\\' <|> char 'λ' <|> char 'L'
+ vars <- sepBy1 parseVar (char ' ')
+ char '.'
+ t <- parseTypedTerm
+ let (NTTerm l) = createLambda vars t
+ return $! l
+
+parseApp :: Parser Term
+parseApp = do
+ aps <- sepBy1 parseTypedTermNA (char ' ')
+ return $! createApp aps
+
+createLambda :: [Term] -> TypedTerm -> TypedTerm
+createLambda (Var x : vs) t = NTTerm . Lam x $ createLambda vs t
+createLambda [] t = t
+createLambda _ _ = error "createLambda failed"
+
+createApp :: [TypedTerm] -> Term
+createApp [t,ts] = App t ts
+createApp (t:ts:tss) = createApp (NTTerm (App t ts) : tss)
+createApp [] = error "empty createApp"
-lambdaToHM :: Lambda.Term -> TypedTerm
-lambdaToHM (Lambda.Var x) = NTTerm $ Var x
-lambdaToHM (Lambda.App t u) = NTTerm $ App (lambdaToHM t) (lambdaToHM u)
-lambdaToHM (Lambda.Lambda x t) = NTTerm $ Lam x (lambdaToHM t)
-- |
-- TODO prop> t == tRead (show (t :: Term))
-
-{-
-tRead :: String -> Term
-tRead s = case parseOnly (parseTerm <* endOfInput) (T.pack s) of
- (Right t) -> t
- (Left e) -> error e
--}