{- |

Module : ./HasCASL/Unify.hs

Description : generalized unification of types

Copyright : (c) Christian Maeder and Uni Bremen 2003-2005

License : GPLv2 or higher, see LICENSE.txt

Maintainer : Christian.Maeder@dfki.de

Stability : experimental

Portability : portable

substitution and unification of types

-}

module HasCASL.Unify where

import HasCASL.As

import HasCASL.FoldType

import HasCASL.AsUtils

import HasCASL.PrintAs ()

import HasCASL.ClassAna

import HasCASL.TypeAna

import HasCASL.Le

import qualified Data.Map as Map

import qualified Data.Set as Set

import Common.DocUtils

import Common.Id

import Common.Lib.State

import Common.Result

import Data.List as List

import Data.Maybe

-- | composition (reversed: first substitution first!)

compSubst :: Subst -> Subst -> Subst

compSubst s1 s2 = Map.union (Map.map (subst s2) s1) s2

-- | test if second scheme is a substitution instance

instScheme :: TypeMap -> Int -> TypeScheme -> TypeScheme -> Bool

instScheme tm c = asSchemes c (subsume tm)

specializedScheme :: ClassMap -> [TypeArg] -> [TypeArg] -> Bool

specializedScheme cm args1 args2 = length args1 == length args2 && and

(zipWith (\ (TypeArg _ v1 vk1 _ _ _ _) (TypeArg _ v2 vk2 _ _ _ _) ->

(v1 == v2 || v1 == NonVar) && case (vk1, vk2) of

(VarKind k1, VarKind k2) -> lesserKind cm k1 k2

_ -> vk1 == vk2) args1 args2)

-- | lift 'State' Int to 'State' Env

toEnvState :: State Int a -> State Env a

toEnvState p = do

s <- get

let (r, c) = runState p $ counter s

put s { counter = c }

return r

toSchemes :: (Type -> Type -> a) -> TypeScheme -> TypeScheme -> State Int a

toSchemes f sc1 sc2 = do

(t1, _) <- freshInst sc1

(t2, _) <- freshInst sc2

return $ f t1 t2

asSchemes :: Int -> (Type -> Type -> a) -> TypeScheme -> TypeScheme -> a

asSchemes c f sc1 sc2 = evalState (toSchemes f sc1 sc2) c

substTypeArg :: Subst -> TypeArg -> VarKind

substTypeArg s (TypeArg _ _ vk _ _ _ _) = case vk of

Downset super -> Downset $ substGen s super

_ -> vk

mapArgs :: Subst -> [(Id, Type)] -> [TypeArg] -> [(Type, VarKind)]

mapArgs s ts = foldr ( \ ta l ->

maybe l ( \ (_, t) -> (t, substTypeArg s ta) : l) $

find ( \ (j, _) -> getTypeVar ta == j) ts) []

freshInst :: TypeScheme -> State Int (Type, [(Type, VarKind)])

freshInst (TypeScheme tArgs t _) = do

let ls = leaves (< 0) t -- generic vars

vs = map snd ls

ts <- mkSubst vs

let s = Map.fromList $ zip (map fst ls) ts

return (substGen s t, mapArgs s (zip (map fst vs) ts) tArgs)

inc :: State Int Int

inc = do

c <- get

put (c + 1)

return c

freshVar :: Id -> State Int (Id, Int)

freshVar i@(Id ts _ _) = do

c <- inc

return (Id [mkSimpleId $ "_v" ++ show c ++ case ts of

[t] -> '_' : dropWhile (== '_') (tokStr t)

_ -> ""] [] $ posOfId i, c)

mkSingleSubst :: (Id, RawKind) -> State Int Type

mkSingleSubst (i, rk) = do

(ty, c) <- freshVar i

return $ TypeName ty rk c

mkSubst :: [(Id, RawKind)] -> State Int [Type]

mkSubst = mapM mkSingleSubst

type Subst = Map.Map Int Type

eps :: Subst

eps = Map.empty

flatKind :: Type -> RawKind

flatKind = nonVarRawKind . rawKindOfType

noAbs :: Type -> Bool

noAbs t = case t of

TypeAbs {} -> False

_ -> True

match :: TypeMap -> (Id -> Id -> Bool)

-> (Bool, Type) -> (Bool, Type) -> Result Subst

match tm rel p1@(b1, ty1) p2@(b2, ty2) =

if flatKind ty1 == flatKind ty2 then case (ty1, ty2) of

(_, ExpandedType _ t2) | noAbs t2 -> match tm rel p1 (b2, t2)

(ExpandedType _ t1, _) | noAbs t1 -> match tm rel (b1, t1) p2

(_, TypeAppl (TypeName l _ _) t2) | l == lazyTypeId ->

match tm rel p1 (b2, t2)

(TypeAppl (TypeName l _ _) t1, _) | l == lazyTypeId ->

match tm rel (b1, t1) p2

(_, KindedType t2 _ _) -> match tm rel p1 (b2, t2)

(KindedType t1 _ _, _) -> match tm rel (b1, t1) p2

(TypeName i1 _k1 v1, TypeName i2 _k2 v2)

| rel i1 i2 && v1 == v2 -> return eps

| v1 > 0 && b1 -> return $ Map.singleton v1 ty2

| v2 > 0 && b2 -> return $ Map.singleton v2 ty1

{- the following two conditions only guarantee that instScheme also matches for

a partial function that is mapped to a total one.

Maybe a subtype condition is better. -}

| not b1 && b2 && v1 == 0 && v2 == 0 && Set.member i1 (superIds tm i2) ||

b1 && not b2 && v1 == 0 && v2 == 0 && Set.member i2 (superIds tm i1)

-> return eps

| otherwise -> uniResult "typename" ty1

"is not unifiable with typename" ty2

(TypeName _ _ v1, _) -> case redStep ty2 of

Just ry2 -> match tm rel p1 (b2, ry2)

Nothing ->

if v1 > 0 && b1 then

if null $ leaves (== v1) ty2 then

return $ Map.singleton v1 ty2

else uniResult "var" ty1 "occurs in" ty2

else uniResult "typename" ty1

"is not unifiable with type" ty2

(_, TypeName {}) -> match tm rel p2 p1

(TypeAppl f1 a1, TypeAppl f2 a2) -> case redStep ty1 of

Just ry1 -> match tm rel (b1, ry1) p2

Nothing -> case redStep ty2 of

Just ry2 -> match tm rel p1 (b2, ry2)

Nothing -> do

s1 <- match tm rel (b1, f1) (b2, f2)

s2 <- match tm rel (b1, if b1 then subst s1 a1 else a1)

(b2, if b2 then subst s1 a2 else a2)

return $ compSubst s1 s2

_ -> if ty1 == ty2 then return eps else

uniResult "type" ty1 "is not unifiable with type" ty2

else uniResult "type" ty1 "is not unifiable with differently kinded type" ty2

shapeMatch :: TypeMap -> Type -> Type -> Result Subst

shapeMatch tm a b = match tm (const $ const True) (True, a) (True, b)

subsume :: TypeMap -> Type -> Type -> Bool

subsume tm a b =

isJust $ maybeResult $ match tm (==) (False, a) (True, b)

-- | substitute generic variables with negative index

substGen :: Subst -> Type -> Type

substGen m = foldType mapTypeRec

{ foldTypeName = \ t _ _ n -> if n >= 0 then t

else Data.Maybe.fromMaybe t (Map.lookup n m)

, foldTypeAbs = \ t v1@(TypeArg _ _ _ _ c _ _) ty p ->

if Map.member c m then substGen (Map.delete c m) t else TypeAbs v1 ty p }

getTypeOf :: Monad m => Term -> m Type

getTypeOf trm = case trm of

TypedTerm _ q t _ -> return $ case q of

InType -> unitType

_ -> t

QualVar (VarDecl _ t _ _) -> return t

QualOp _ _ (TypeScheme _ t _) is _ _ -> return $

substGen (Map.fromList $ zip [-1, -2 ..] is) t

TupleTerm ts ps -> if null ts then return unitType else do

tys <- mapM getTypeOf ts

return $ mkProductTypeWithRange tys ps

QuantifiedTerm _ _ t _ -> getTypeOf t

LetTerm _ _ t _ -> getTypeOf t

AsPattern _ p _ -> getTypeOf p

_ -> fail $ "getTypeOf: " ++ showDoc trm ""

-- | substitute variables with positive index

subst :: Subst -> Type -> Type

subst m = if Map.null m then id else foldType mapTypeRec

{ foldTypeName = \ t _ _ n -> if n <= 0 then t

else Data.Maybe.fromMaybe t (Map.lookup n m) }

showDocWithPos :: Type -> ShowS

showDocWithPos a = let p = getRange a in

showChar '\'' . showDoc a . showChar '\''

. noShow (isNullRange p) (showChar ' ' .

showParen True (showPos $ maximum (rangeToList p)))

uniResult :: String -> Type -> String -> Type -> Result Subst

uniResult s1 a s2 b = Result [Diag Hint ("in type\n" ++ " " ++ s1 ++ " " ++

showDocWithPos a "\n " ++ s2 ++ " " ++

showDocWithPos b "") nullRange] Nothing

-- | make representation of bound variables unique

generalize :: [TypeArg] -> Type -> Type

generalize tArgs = subst $ Map.fromList $ zipWith

( \ (TypeArg i _ _ rk c _ _) n -> (c, TypeName i rk n)) tArgs [-1, -2 ..]

genTypeArgs :: [TypeArg] -> [TypeArg]

genTypeArgs tArgs = snd $ mapAccumL ( \ n (TypeArg i v vk rk _ s ps) ->

(n - 1, TypeArg i v (case vk of

Downset t -> Downset $ generalize tArgs t

_ -> vk) rk n s ps)) (-1) tArgs