-- |

{-# LANGUAGE DeriveDataTypeable #-}

module Language.PureScript.Types where

import Data.Data

import Data.List (nub)

import Control.Monad.Unify

import Control.Arrow (second)

import Control.Applicative

import Control.Monad ((<=<))

import Language.PureScript.Names

import Language.PureScript.Kinds

import Language.PureScript.Traversals

-- |

newtype SkolemScope = SkolemScope { runSkolemScope :: Int } deriving (Show, Eq, Ord, Data, Typeable)

-- |

data Type

-- |

-- A unification variable of type Type

--

= TUnknown Unknown

-- |

-- A named type variable

--

| TypeVar String

-- |

-- A type wildcard, as would appear in a partial type synonym

--

| TypeWildcard

-- |

-- A type constructor

--

| TypeConstructor (Qualified ProperName)

-- |

-- A type application

--

| TypeApp Type Type

-- |

-- A type synonym which is \"saturated\", i.e. fully applied

--

| SaturatedTypeSynonym (Qualified ProperName) [Type]

-- |

-- Forall quantifier

--

| ForAll String Type (Maybe SkolemScope)

-- |

-- A type with a set of type class constraints

--

| ConstrainedType [Constraint] Type

-- |

-- A skolem constant

--

| Skolem String Int SkolemScope

-- |

-- An empty row

--

| REmpty

-- |

-- A non-empty row

--

| RCons String Type Type

-- |

-- A type with a kind annotation

--

| KindedType Type Kind

--

-- |

-- A placeholder used in pretty printing

--

| PrettyPrintFunction Type Type

-- |

-- A placeholder used in pretty printing

--

| PrettyPrintObject Type

-- |

-- A placeholder used in pretty printing

--

| PrettyPrintForAll [String] Type deriving (Show, Eq, Data, Typeable)

-- |

type Constraint = (Qualified ProperName, [Type])

-- |

rowToList :: Type -> ([(String, Type)], Type)

rowToList (RCons name ty row) = let (tys, rest) = rowToList row

in ((name, ty):tys, rest)

rowToList r = ([], r)

-- |

rowFromList :: ([(String, Type)], Type) -> Type

rowFromList ([], r) = r

rowFromList ((name, t):ts, r) = RCons name t (rowFromList (ts, r))

-- |

isMonoType :: Type -> Bool

isMonoType ForAll{} = False

isMonoType _ = True

-- |

mkForAll :: [String] -> Type -> Type

mkForAll args ty = foldl (\t arg -> ForAll arg t Nothing) ty args

-- |

replaceTypeVars :: String -> Type -> Type -> Type

replaceTypeVars v r = replaceAllTypeVars [(v, r)]

-- |

replaceAllTypeVars :: [(String, Type)] -> Type -> Type

replaceAllTypeVars = go []

where

go :: [String] -> [(String, Type)] -> Type -> Type

go _ m (TypeVar v) =

case v `lookup` m of

Just r -> r

Nothing -> TypeVar v

go bs m (TypeApp t1 t2) = TypeApp (go bs m t1) (go bs m t2)

go bs m (SaturatedTypeSynonym name' ts) = SaturatedTypeSynonym name' $ map (go bs m) ts

go bs m f@(ForAll v t sco) | v `elem` keys = go bs (filter ((/= v) . fst) m) f

| v `elem` usedVars =

let v' = genName v (keys ++ bs ++ usedVars)

t' = go bs [(v, TypeVar v')] t

in ForAll v' (go (v' : bs) m t') sco

| otherwise = ForAll v (go (v : bs) m t) sco

where

keys = map fst m

usedVars = concatMap (usedTypeVariables . snd) m

go bs m (ConstrainedType cs t) = ConstrainedType (map (second $ map (go bs m)) cs) (go bs m t)

go bs m (RCons name' t r) = RCons name' (go bs m t) (go bs m r)

go bs m (KindedType t k) = KindedType (go bs m t) k

go _ _ ty = ty

genName orig inUse = try 0

where

try :: Integer -> String

try n | (orig ++ show n) `elem` inUse = try (n + 1)

| otherwise = orig ++ show n

-- |

usedTypeVariables :: Type -> [String]

usedTypeVariables = nub . everythingOnTypes (++) go

where

go (TypeVar v) = [v]

go _ = []

-- |

freeTypeVariables :: Type -> [String]

freeTypeVariables = nub . go []

where

go :: [String] -> Type -> [String]

go bound (TypeVar v) | v `notElem` bound = [v]

go bound (TypeApp t1 t2) = go bound t1 ++ go bound t2

go bound (SaturatedTypeSynonym _ ts) = concatMap (go bound) ts

go bound (ForAll v t _) = go (v : bound) t

go bound (ConstrainedType cs t) = concatMap (concatMap (go bound) . snd) cs ++ go bound t

go bound (RCons _ t r) = go bound t ++ go bound r

go bound (KindedType t _) = go bound t

go _ _ = []

-- |

quantify :: Type -> Type

quantify ty = foldr (\arg t -> ForAll arg t Nothing) ty $ freeTypeVariables ty

-- |

moveQuantifiersToFront :: Type -> Type

moveQuantifiersToFront = go [] []

where

go qs cs (ForAll q ty sco) = go ((q, sco) : qs) cs ty

go qs cs (ConstrainedType cs' ty) = go qs (cs ++ cs') ty

go qs cs ty =

let constrained = case cs of

[] -> ty

cs' -> ConstrainedType cs' ty

in case qs of

[] -> constrained

qs' -> foldl (\ty' (q, sco) -> ForAll q ty' sco) constrained qs'

-- |

containsWildcards :: Type -> Bool

containsWildcards = everythingOnTypes (||) go

where

go :: Type -> Bool

go TypeWildcard = True

go _ = False

everywhereOnTypes :: (Type -> Type) -> Type -> Type

everywhereOnTypes f = go

where

go (TypeApp t1 t2) = f (TypeApp (go t1) (go t2))

go (SaturatedTypeSynonym name tys) = f (SaturatedTypeSynonym name (map go tys))

go (ForAll arg ty sco) = f (ForAll arg (go ty) sco)

go (ConstrainedType cs ty) = f (ConstrainedType (map (fmap (map go)) cs) (go ty))

go (RCons name ty rest) = f (RCons name (go ty) (go rest))

go (KindedType ty k) = f (KindedType (go ty) k)

go (PrettyPrintFunction t1 t2) = f (PrettyPrintFunction (go t1) (go t2))

go (PrettyPrintObject t) = f (PrettyPrintObject (go t))

go (PrettyPrintForAll args t) = f (PrettyPrintForAll args (go t))

go other = f other

everywhereOnTypesTopDown :: (Type -> Type) -> Type -> Type

everywhereOnTypesTopDown f = go . f

where

go (TypeApp t1 t2) = TypeApp (go (f t1)) (go (f t2))

go (SaturatedTypeSynonym name tys) = SaturatedTypeSynonym name (map (go . f) tys)

go (ForAll arg ty sco) = ForAll arg (go (f ty)) sco

go (ConstrainedType cs ty) = ConstrainedType (map (fmap (map (go . f))) cs) (go (f ty))

go (RCons name ty rest) = RCons name (go (f ty)) (go (f rest))

go (KindedType ty k) = KindedType (go (f ty)) k

go (PrettyPrintFunction t1 t2) = PrettyPrintFunction (go (f t1)) (go (f t2))

go (PrettyPrintObject t) = PrettyPrintObject (go (f t))

go (PrettyPrintForAll args t) = PrettyPrintForAll args (go (f t))

go other = f other

everywhereOnTypesM :: (Functor m, Applicative m, Monad m) => (Type -> m Type) -> Type -> m Type

everywhereOnTypesM f = go

where

go (TypeApp t1 t2) = (TypeApp <$> go t1 <*> go t2) >>= f

go (SaturatedTypeSynonym name tys) = (SaturatedTypeSynonym name <$> mapM go tys) >>= f

go (ForAll arg ty sco) = (ForAll arg <$> go ty <*> pure sco) >>= f

go (ConstrainedType cs ty) = (ConstrainedType <$> mapM (sndM (mapM go)) cs <*> go ty) >>= f

go (RCons name ty rest) = (RCons name <$> go ty <*> go rest) >>= f

go (KindedType ty k) = (KindedType <$> go ty <*> pure k) >>= f

go (PrettyPrintFunction t1 t2) = (PrettyPrintFunction <$> go t1 <*> go t2) >>= f

go (PrettyPrintObject t) = (PrettyPrintObject <$> go t) >>= f

go (PrettyPrintForAll args t) = (PrettyPrintForAll args <$> go t) >>= f

go other = f other

everywhereOnTypesTopDownM :: (Functor m, Applicative m, Monad m) => (Type -> m Type) -> Type -> m Type

everywhereOnTypesTopDownM f = go <=< f

where

go (TypeApp t1 t2) = TypeApp <$> (f t1 >>= go) <*> (f t2 >>= go)

go (SaturatedTypeSynonym name tys) = SaturatedTypeSynonym name <$> mapM (go <=< f) tys

go (ForAll arg ty sco) = ForAll arg <$> (f ty >>= go) <*> pure sco

go (ConstrainedType cs ty) = ConstrainedType <$> mapM (sndM (mapM (go <=< f))) cs <*> (f ty >>= go)

go (RCons name ty rest) = RCons name <$> (f ty >>= go) <*> (f rest >>= go)

go (KindedType ty k) = KindedType <$> (f ty >>= go) <*> pure k

go (PrettyPrintFunction t1 t2) = PrettyPrintFunction <$> (f t1 >>= go) <*> (f t2 >>= go)

go (PrettyPrintObject t) = PrettyPrintObject <$> (f t >>= go)

go (PrettyPrintForAll args t) = PrettyPrintForAll args <$> (f t >>= go)

go other = f other

everythingOnTypes :: (r -> r -> r) -> (Type -> r) -> Type -> r

everythingOnTypes (<>) f = go

where

go t@(TypeApp t1 t2) = f t <> go t1 <> go t2

go t@(SaturatedTypeSynonym _ tys) = foldl (<>) (f t) (map go tys)

go t@(ForAll _ ty _) = f t <> go ty

go t@(ConstrainedType cs ty) = foldl (<>) (f t) (map go $ concatMap snd cs) <> go ty

go t@(RCons _ ty rest) = f t <> go ty <> go rest

go t@(KindedType ty _) = f t <> go ty

go t@(PrettyPrintFunction t1 t2) = f t <> go t1 <> go t2

go t@(PrettyPrintObject t1) = f t <> go t1

go t@(PrettyPrintForAll _ t1) = f t <> go t1

go other = f other