{- |

Module : $Header$

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

License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

Maintainer : maeder@tzi.de

Stability : experimental

Portability : portable

analyse types

-}

module HasCASL.TypeAna where

import HasCASL.As

import HasCASL.AsUtils

import HasCASL.Le

import HasCASL.ClassAna

import HasCASL.TypeMixAna

import qualified Common.Lib.Map as Map

import qualified Common.Lib.Set as Set

import Common.Id

import Common.Result

import Common.PrettyPrint

import Data.List as List

import Data.Maybe

import Control.Exception(assert)

-- * infer kind

-- | inspect types and classes only

type TypeEnv = Env

-- | extract kinds of type identifier

getIdKind :: TypeEnv -> Id -> Result ((RawKind, [Kind]), Type)

getIdKind te i =

case Map.lookup i $ localTypeVars te of

Nothing -> case Map.lookup i $ typeMap te of

Nothing -> mkError "unknown type" i

Just (TypeInfo rk l _ _) -> return ((rk, l), TypeName i rk 0)

Just (TypeVarDefn rk vk c) -> assert (c > 0) $

return ((rk, [toKind vk]), TypeName i rk c)

-- | extract kinds of co- or invariant type identifiers

getCoVarKind :: Maybe Bool -> TypeEnv -> Id -> Result ((RawKind, [Kind]), Type)

getCoVarKind b te i = do

((rk, l), ty) <- getIdKind te i

case (rk, b) of

(ExtKind ek ContraVar _, Just True) -> Result

[mkDiag Hint "wrong contravariance of" i] $ Just ((ek, []), ty)

(ExtKind ek CoVar _, Just False) -> Result

[mkDiag Hint "wrong covariance of" i] $ Just ((ek, []), ty)

_ -> return ((invertKindVariance False rk,

map (invertKindVariance False) $

keepMinKinds (classMap te) l), ty)

-- | check if there is at least one solution

subKinds :: DiagKind -> ClassMap -> Type -> Kind -> [Kind] -> [Kind]

-> Result [Kind]

subKinds dk cm ty sk ks res =

if any ( \ k -> lesserKind cm k sk) ks then return res

else Result [Diag dk

("no kind found for '" ++ showPretty ty "'" ++

if null ks then "" else expected sk $ head ks)

$ posOfType ty] $ Just []

-- | infer all minimal kinds

inferKinds :: Maybe Bool -> Type -> TypeEnv -> Result ((RawKind, [Kind]), Type)

inferKinds b ty te@Env{classMap = cm} = let

resu = case ty of

TypeName i _ _ -> getCoVarKind b te i

TypeAppl t1 t2 -> do

((rk, ks), t3) <- inferKinds b t1 te

case rk of

FunKind rarg rr _ -> do

((_, l), t4) <- case rarg of

ExtKind _ ContraVar _ ->

inferKinds (fmap not b) t2 te

ExtKind _ CoVar _ ->

inferKinds b t2 te

_ -> inferKinds Nothing t2 te

kks <- mapM (getFunKinds cm) ks

rs <- mapM ( \ fk -> case fk of

FunKind arg res _ -> do

let ek = case arg of

ExtKind k _ _ -> k

_ -> arg

subKinds Hint cm t2 ek l [res]

_ -> error "inferKinds: no function kind"

) $ keepMinKinds cm $ concat kks

return ((rr, keepMinKinds cm $ concat rs), TypeAppl t3 t4)

_ -> mkError "unexpected type argument" t2

KindedType kt kind ps -> do

let Result ds _ = anaKindM kind cm

k <- if null ds then return kind else Result ds Nothing

((rk, ks), t) <- inferKinds b kt te

l <- subKinds Hint cm kt k ks [k]

return ((rk, l), KindedType t k ps)

ProductType ts ps -> do

l <- mapM ( \ t -> inferKinds b t te) ts

let res@(Result _ mk) = inferKinds b (convertType ty) te

case mk of

Just (kp, _) -> return (kp, ProductType (map snd l) ps)

Nothing -> res

LazyType t ps -> do

(kp, nt) <- inferKinds b t te

return (kp, LazyType nt ps)

FunType t1 a t2 ps -> do

(_, t3) <- inferKinds (fmap not b) t1 te

(_, t4) <- inferKinds b t2 te

let res@(Result _ mk) = inferKinds b (convertType ty) te

case mk of

Just (kp, _) -> return (kp, FunType t3 a t4 ps)

Nothing -> res

ExpandedType t1 t2 -> do

let Result _ mk = inferKinds b t1 te

(kp, t4) <- inferKinds b t2 te

return (kp, case mk of

Just (_, t3) -> ExpandedType t3 t4

Nothing -> t4)

_ -> error "inferKinds"

in -- trace (showPretty ty " : " ++ showPretty resu "")

resu

-- * converting type terms

-- | change lazy, product and fun types to type constructor name with arguments

getTypeAppl :: Type -> (Type, [Type])

getTypeAppl ty = let (t, args) = getTyAppl ty in

(t, reverse args) where

getTyAppl typ = case typ of

TypeName _ _ _ -> (typ, [])

TypeAppl t1 t2 -> let (t, args) = getTyAppl t1 in (t, t2 : args)

ExpandedType _ t -> getTyAppl t

LazyType t ps -> getTyAppl $ liftType t ps

KindedType t _ _ -> getTyAppl t

ProductType ts _ -> let n = length ts in

(TypeName (productId n) (prodKind n) 0, reverse ts)

FunType t1 a t2 _ -> (TypeName (arrowId a) funKind 0, [t2, t1])

_ -> error "getTypeAppl: unresolved type"

-- | change lazy, product and fun types to uniform applications

convertType :: Type -> Type

convertType ty = let (c, args) = getTypeAppl ty in mkTypeAppl c args

-- * subtyping relation

-- | extract the raw kind from a type term

rawKindOfType :: Type -> RawKind

rawKindOfType ty = case ty of

TypeName _ k _ -> k

TypeAppl t1 _ -> case rawKindOfType t1 of

FunKind _ rk _ -> rk

_ -> error "rawKindOfType"

_ -> rawKindOfType $ convertType ty

-- | subtyping relation

lesserType :: TypeEnv -> Type -> Type -> Bool

lesserType te t1 t2 = case (t1, t2) of

(TypeAppl c1 a1, TypeAppl c2 a2) ->

let b1 = lesserType te a1 a2

b2 = lesserType te a2 a1

b = b1 && b2

in (case (rawKindOfType c1, rawKindOfType c2) of

(FunKind ak1 _ _, FunKind ak2 _ _) ->

case (ak1, ak2) of

(ExtKind _ v1 _, ExtKind _ v2 _) ->

if v1 == v2 then case v1 of

CoVar -> b1

ContraVar -> b2

else b

_ -> b

_ -> error "lesserType: no FunKind") && lesserType te c1 c2

(TypeName i1 _ _, TypeName i2 _ _) | i1 == i2 -> True

(TypeName i _ _, _) -> case Map.lookup i $ localTypeVars te of

Nothing -> case Map.lookup i $ typeMap te of

Nothing -> False

Just ti -> any ( \ t -> lesserType te t t2) $ superTypes ti

Just (TypeVarDefn _ vk _) -> case vk of

Downset t -> lesserType te t t2

_ -> False

(TypeAppl _ _, TypeName _ _ _) -> False

_ -> lesserType te (convertType t1) $ convertType t2

-- * leaves of types and substitution

-- | the type name components of a type

leaves :: (Int -> Bool) -> Type -> [(Int, (Id, RawKind))]

leaves b t =

case t of

TypeName j k i -> if b(i)

then [(i, (j, k))]

else []

TypeAppl t1 t2 -> leaves b t1 `List.union` leaves b t2

ExpandedType _ t2 -> leaves b t2

KindedType tk _ _ -> leaves b tk

LazyType tl _ -> leaves b tl

ProductType l _ -> foldl List.union [] $ map (leaves b) l

FunType t1 _ t2 _ -> leaves b t1 `List.union` leaves b t2

_ -> error ("leaves: " ++ show t)

-- | type identifiers of a type

idsOf :: (Int -> Bool) -> Type -> Set.Set TypeId

idsOf b = Set.fromList . map (fst . snd) . leaves b

-- | replace some type names with types

repl :: Map.Map Id Type -> Type -> Type

repl m = rename ( \ i k n ->

case Map.lookup i m of

Just s -> s

Nothing -> TypeName i k n)

-- * super type ids

-- | compute super type ids of one type id

superIds :: TypeMap -> Id -> Set.Set Id

superIds tm = supIds tm Set.empty . Set.singleton

-- | compute all super type ids for several type ids given as second argument

supIds :: TypeMap -> Set.Set Id -> Set.Set Id -> Set.Set Id

supIds tm known new =

if Set.null new then known else

let more = Set.unions $ map superTypeToId $

concatMap ( \ i -> superTypes

$ Map.findWithDefault starTypeInfo i tm)

$ Set.toList new

newKnown = Set.union known new

in supIds tm newKnown (more Set.\\ newKnown)

-- | extract super type ids from a type

superTypeToId :: Type -> Set.Set Id

superTypeToId t =

case t of

TypeName i _ _ -> Set.singleton i

_ -> Set.empty

-- * expand alias types

-- | expand aliases in a type scheme

expand :: TypeMap -> TypeScheme -> TypeScheme

expand = mapTypeOfScheme . expandAlias

-- | expand aliases in a type

expandAlias :: TypeMap -> Type -> Type

expandAlias tm t =

let (ps, ts, ta, b) = expandAliases tm t in

if b && length ps == length ts then

ExpandedType t $ repl (Map.fromList (zip

(map getTypeVar ps) $ reverse ts)) ta

else ta

{- | Collect formal and actual parameters of the first argument of a

type application. -}

expandAliases :: TypeMap -> Type -> ([TypeArg], [Type], Type, Bool)

expandAliases tm t = case t of

TypeName i _ _ -> case Map.lookup i tm of

Just ti -> case typeDefn ti of

AliasTypeDefn (TypeScheme l ty _) ->

(l, [], ty, True)

Supertype _ (TypeScheme l ty _) _ ->

case ty of

TypeName _ _ _ -> wrap t

_ -> (l, [], ty, True)

_ -> wrap t

_ -> wrap t

TypeAppl t1 t2 ->

let (ps, ts, ta, b) = expandAliases tm t1

t3 = expandAlias tm t2

in if b then

(ps, t3 : ts, ta, b) -- reverse later on

else wrap $ TypeAppl t1 t3

FunType t1 a t2 ps ->

wrap $ FunType (expandAlias tm t1) a (expandAlias tm t2) ps

ProductType ts ps -> wrap $ ProductType (map (expandAlias tm) ts) ps

LazyType ty ps -> wrap $ LazyType (expandAlias tm ty) ps

ExpandedType t1 t2 -> wrap $ ExpandedType t1 $ expandAlias tm t2

KindedType ty k ps -> wrap $ KindedType (expandAlias tm ty) k ps

_ -> wrap t

where wrap ty = ([], [], ty, False)

-- | find unexpanded alias identifier

hasAlias :: TypeMap -> Type -> [Diagnosis]

hasAlias tm t =

map ( \ i -> mkDiag Error ("unexpanded alias '" ++ showId i "' in") t)

$ filter ( \ i -> case Map.lookup i tm of

Just ti -> case typeDefn ti of

AliasTypeDefn _ -> True

_ -> False

_ -> False) $ Set.toList $ idsOf (const True) t

-- * resolve and analyse types

-- | resolve type and infer minimal kinds

anaTypeM :: (Maybe Kind, Type) -> TypeEnv -> Result ((RawKind, [Kind]), Type)

anaTypeM (mk, parsedType) te =

do resolvedType <- mkTypeConstrAppl parsedType

let tm = typeMap te

expandedType = expandAlias tm resolvedType

cm = classMap te

((rk, ks), checkedType) <- inferKinds (Just True) expandedType te

l <- case mk of

Nothing -> subKinds Error cm parsedType

(if null ks then rk else head ks)

ks ks

Just k -> subKinds Error cm parsedType k ks $

filter ( \ j -> lesserKind cm j k) ks

Result (hasAlias tm checkedType) $ Just ()

return ((rk, l), checkedType)

-- | resolve the type and check if it is of the universe class

anaStarTypeM :: Type -> TypeEnv -> Result ((RawKind, [Kind]), Type)

anaStarTypeM t = anaTypeM (Just star, t)

-- * misc functions on types

-- | check if an id occurs in a type

cyclicType :: Id -> Type -> Bool

cyclicType i ty = Set.member i $ idsOf (==0) ty

-- | check for unbound (or too many) type variables

unboundTypevars :: Bool -> [TypeArg] -> Type -> [Diagnosis]

unboundTypevars b args ty =

let fvs = map (fst . snd) (leaves (> 0) ty)

argIds = map getTypeVar args

restVars1 = fvs List.\\ argIds

restVars2 = argIds List.\\ fvs

in (if null restVars1 then []

else [mkDiag Error ("unbound type variable(s)\n "

++ showSepList ("," ++) showId

restVars1 " in") ty])

++ if b || null restVars2 then [] else

[mkDiag Warning ("ignoring unused variable(s)\n "

++ showSepList ("," ++) showId

restVars2 " in") ty]

generalizable :: TypeScheme -> [Diagnosis]

generalizable (TypeScheme args ty _) =

(if null args then [] else unboundTypevars False args ty)

++ checkUniqueTypevars args

-- | check uniqueness of type variables

checkUniqueTypevars :: [TypeArg] -> [Diagnosis]

checkUniqueTypevars = checkUniqueness . map getTypeVar