{- |

Module : $Header$

Copyright : (c) Christian Maeder and Uni Bremen 2002-2003

Licence : similar to LGPL, see HetCATS/LICENCE.txt or LIZENZ.txt

Maintainer : hets@tzi.de

Stability : provisional

Portability : portable

Morphism on 'Env' (as for CASL)

-}

module HasCASL.Morphism where

import HasCASL.Le

import HasCASL.HToken

import HasCASL.As

import HasCASL.AsToLe

import HasCASL.TypeCheck

import HasCASL.PrintAs

import HasCASL.PrintLe

import HasCASL.Unify

import HasCASL.Merge

import HasCASL.Symbol

import Common.Id

import Common.Keywords

import Common.Result

import Common.PrettyPrint

import Common.Lib.Pretty

import Common.Lib.State

import qualified Common.Lib.Map as Map

import qualified Common.Lib.Set as Set

import Data.List(partition)

-- new type to defined a different Eq and Ord instance

data TySc = TySc TypeScheme deriving Show

instance Eq TySc where

TySc sc1 == TySc sc2 =

let Result _ ms = mergeScheme Map.empty 0 sc1 sc2

in maybe False (const True) ms

instance Ord TySc where

-- this does not match with Eq TypeScheme!

TySc sc1 <= TySc sc2 =

TySc sc1 == TySc sc2 ||

let (t1, c) = runState (freshInst sc1) 1

t2 = evalState (freshInst sc2) c

v1 = varsOf t1

v2 = varsOf t2

in case compare (Set.size v1) $ Set.size v2 of

LT -> True

EQ -> t1 <= subst (Map.fromAscList $

zipWith (\ v (TypeArg i k _ _) ->

(v, TypeName i k 1))

(Set.toList v1) $ Set.toList v2) t2

GT -> False

data SymbolType = OpAsItemType TySc

| TypeAsItemType Kind

| ClassAsItemType Kind

deriving (Show, Eq, Ord)

instance PrettyPrint SymbolType where

printText0 ga t = case t of

OpAsItemType (TySc sc) -> printText0 ga sc

TypeAsItemType k -> printText0 ga k

ClassAsItemType k -> printText0 ga k

data Symbol = Symbol {symName :: Id, symbType :: SymbolType}

deriving (Show, Eq, Ord)

data RawSymbol = ASymbol Symbol | AnID Id | AKindedId SymbKind Id

deriving (Show, Eq, Ord)

type SymbolMap = Map.Map Symbol Symbol

type RawSymbolMap = Map.Map RawSymbol RawSymbol

type SymbolSet = Set.Set Symbol

idToTypeSymbol :: Id -> Kind -> Symbol

idToTypeSymbol idt k = Symbol idt $ TypeAsItemType k

idToClassSymbol :: Id -> Kind -> Symbol

idToClassSymbol idt k = Symbol idt $ ClassAsItemType k

idToOpSymbol :: Id -> TySc -> Symbol

idToOpSymbol idt typ = Symbol idt $ OpAsItemType typ

idToRaw :: Id -> RawSymbol

idToRaw x = AnID x

rawSymName :: RawSymbol -> Id

rawSymName (ASymbol sym) = symName sym

rawSymName (AnID i) = i

rawSymName (AKindedId _ i) = i

symbTypeToKind :: SymbolType -> SymbKind

symbTypeToKind (OpAsItemType _) = SK_op

symbTypeToKind (TypeAsItemType _) = SK_type

symbTypeToKind (ClassAsItemType _) = SK_class

symbolToRaw :: Symbol -> RawSymbol

symbolToRaw sym = ASymbol sym

symOf :: Env -> SymbolSet

symOf sigma =

let classes = Map.foldWithKey ( \ i ks s ->

Set.insert (Symbol i $ ClassAsItemType $

Intersection (classKinds ks) []) s)

Set.empty $ classMap sigma

types = Map.foldWithKey ( \ i ti s ->

Set.insert (Symbol i $ TypeAsItemType $

typeKind ti) s)

classes $ typeMap sigma

ops = Map.foldWithKey ( \ i ts s0 ->

foldr ( \ t s1 ->

Set.insert (Symbol i $ OpAsItemType $ TySc $

opType t) s1) s0 $ opInfos ts)

types $ assumps sigma

in ops

statSymbMapItems :: [SymbMapItems] -> Result RawSymbolMap

statSymbMapItems sl = do

rs <- mapM ( \ (SymbMapItems kind l _ _)

-> mapM (symbOrMapToRaw kind) l) sl

foldr ( \ (r1, r2) mm -> do

m <- mm

if Map.member r1 m then do

Result [Diag Error ("duplicate mapping for: " ++

showPretty r1 "\n ignoring: " ++ showPretty r2 "")

$ posOfId $ rawSymName r2] $ Just ()

return m

else return $ Map.insert r1 r2 m)

(return Map.empty) $ concat rs

symbOrMapToRaw :: SymbKind -> SymbOrMap -> Result (RawSymbol, RawSymbol)

symbOrMapToRaw k (SymbOrMap s mt _) = do

s1 <- symbToRaw k s

s2 <- symbToRaw k $ case mt of Nothing -> s

Just t -> t

return (s1, s2)

statSymbItems :: [SymbItems] -> Result [RawSymbol]

statSymbItems sl = do rs <- mapM (\ (SymbItems kind l _ _)

-> mapM (symbToRaw kind) l) sl

return $ concat rs

symbToRaw :: SymbKind -> Symb -> Result RawSymbol

symbToRaw k (Symb idt mt _) = case mt of

Nothing -> return $ symbKindToRaw k idt

Just (SymbType sc@(TypeScheme vs (_ :=> t) _)) ->

let r = return $ ASymbol $ idToOpSymbol idt (TySc sc)

rk = if null vs then Nothing else

convertTypeToKind t

rrk = maybeToResult (getMyPos t)

("not a kind: " ++ showPretty t "") rk

in case k of

SK_op -> r

SK_fun -> r

SK_pred -> return $ ASymbol $ idToOpSymbol idt $

TySc $ predTypeScheme sc

SK_class -> do ck <- rrk

return $ ASymbol $ idToClassSymbol idt ck

_ -> do ck <- rrk

return $ ASymbol $ idToTypeSymbol idt ck

convertTypeToKind :: Type -> Maybe Kind

convertTypeToKind (FunType t1 FunArr t2 ps) =

do k1 <- convertTypeToKind t1

k2 <- convertTypeToKind t2

case k2 of

ExtKind _ _ _ -> Nothing

_ -> Just $ FunKind k1 k2 ps

convertTypeToKind (BracketType Parens [] _) =

Nothing

convertTypeToKind (BracketType Parens [t] _) =

convertTypeToKind t

convertTypeToKind (BracketType Parens ts ps) =

do ks <- mapM convertTypeToKind ts

Just $ Intersection ks ps

convertTypeToKind (MixfixType [t1, TypeToken t]) =

let s = tokStr t

v = case s of

"+" -> CoVar

"-" -> ContraVar

_ -> InVar

in case v of

InVar -> Nothing

_ -> do k1 <- convertTypeToKind t1

Just $ ExtKind k1 v [tokPos t]

convertTypeToKind(TypeToken t) =

if tokStr t == "Type" then Just $ Universe [tokPos t] else

let ci = simpleIdToId t in

Just $ ClassKind ci MissingKind

convertTypeToKind _ = Nothing

symbKindToRaw :: SymbKind -> Id -> RawSymbol

symbKindToRaw Implicit = AnID

symbKindToRaw sk = AKindedId $ case sk of

SK_pred -> SK_op

SK_fun -> SK_op

SK_sort -> SK_type

_ -> sk

matchSymb :: Symbol -> RawSymbol -> Bool

matchSymb x (ASymbol y) = x==y

matchSymb (Symbol idt _) (AnID di) = idt==di

matchSymb (Symbol idt (OpAsItemType _)) (AKindedId SK_op di) = idt==di

matchSymb (Symbol idt (OpAsItemType _)) (AKindedId SK_fun di) = idt==di

matchSymb (Symbol idt (OpAsItemType _)) (AKindedId SK_pred di) = idt==di

matchSymb (Symbol idt (TypeAsItemType _)) (AKindedId SK_type di) = idt==di

matchSymb (Symbol idt (TypeAsItemType _)) (AKindedId SK_sort di) = idt==di

matchSymb (Symbol idt (ClassAsItemType _))(AKindedId SK_class di)= idt==di

matchSymb _ _ = False

type IdMap = Map.Map Id Id

mapType :: IdMap -> Type -> Type

-- include classIdMap later

mapType m t = case t of

TypeName i k n ->

if n == 0 then

case Map.lookup i m of

Just j -> TypeName j k 0

_ -> t

else t

TypeAppl t1 t2 ->

TypeAppl (mapType m t1) (mapType m t2)

TypeToken _ -> t

BracketType b l ps ->

BracketType b (map (mapType m) l) ps

KindedType tk k ps ->

KindedType (mapType m tk) k ps

MixfixType l -> MixfixType $ map (mapType m) l

LazyType tl ps -> LazyType (mapType m tl) ps

ProductType l ps -> ProductType (map (mapType m) l) ps

FunType t1 a t2 ps -> FunType (mapType m t1) a (mapType m t2) ps

mapTypeScheme :: IdMap -> TypeScheme -> TypeScheme

-- rename clashing type arguments later

mapTypeScheme m (TypeScheme args (q :=> t) ps) =

TypeScheme args (q :=> mapType m t) ps

mapTySc :: IdMap -> TySc -> TySc

mapTySc m (TySc s1) = TySc (mapTypeScheme m s1)

type FunMap = Map.Map (Id, TySc) (Id, TySc)

mapFunSym :: IdMap -> FunMap -> (Id, TySc) -> Maybe (Id, TySc)

mapFunSym tm fm (i, sc) = do

(newI, _sc1) <- Map.lookup (i, sc) fm

let sc2 = mapTySc tm sc

-- unify sc2 with sc1 later

return (newI, sc2)

mergeOpInfos :: TypeMap -> Int -> OpInfos -> OpInfos -> Result OpInfos

mergeOpInfos tm c (OpInfos l1) (OpInfos l2) =

do l <- mergeOps tm c l1 l2

return $ OpInfos l

-- trace (showPretty l1 "\n+ " ++ showPretty l2 "\n 0" ++ showPretty l "") l

mergeOps :: TypeMap -> Int -> [OpInfo] -> [OpInfo] -> Result [OpInfo]

mergeOps _ _ [] l = return l

mergeOps tm c (o:os) l2 = do

let (es, us) = partition (isUnifiable (addUnit tm) c

(opType o) . opType) l2

l1 <- mergeOps tm c os us

if null es then return (o : l1)

else do r <- mergeOpInfo tm c o $ head es

return (r : l1)

mergeEnv :: Env -> Env -> Result Env

mergeEnv e1 e2 =

do cMap <- merge (classMap e1) $ classMap e2

let m = max (counter e1) $ counter e2

tMap <- mergeMap (mergeTypeInfo Map.empty 0)

(typeMap e1) $ typeMap e2

as <- mergeMap (mergeOpInfos tMap m)

(assumps e1) $ assumps e2

return initialEnv { classMap = cMap

, typeMap = tMap

, assumps = as }

data Morphism = Morphism { msource :: Env

, mtarget :: Env

, classIdMap :: IdMap -- ignore

, typeIdMap :: IdMap

, funMap :: FunMap }

deriving (Eq, Show)

mkMorphism :: Env -> Env -> Morphism

mkMorphism e1 e2 = Morphism e1 e2 Map.empty Map.empty Map.empty

embedMorphism :: Env -> Env -> Morphism

embedMorphism a b =

(mkMorphism a b)

{ typeIdMap = foldr (\x -> Map.insert x x) Map.empty

$ Map.keys $ typeMap a

, funMap = Map.foldWithKey

( \ i (OpInfos ts) m -> foldr

(\ oi -> let v = (i, TySc $ opType oi) in

Map.insert v v) m ts)

Map.empty $ assumps a

}

ideMor :: Env -> Morphism

ideMor e = embedMorphism e e

compMor :: Morphism -> Morphism -> Maybe Morphism

compMor m1 m2 =

if isSubEnv (mtarget m1) (msource m2) then Just

(mkMorphism (msource m1) (mtarget m2))

{ typeIdMap = Map.map ( \ i -> Map.findWithDefault i i $ typeIdMap m2)

$ typeIdMap m1

, funMap = Map.foldWithKey ( \ (i1, sc1) (i2, sc2) m ->

Map.insert (i1, sc1)

(Map.findWithDefault (i2, sc2) (i2, sc2) $

funMap m2) m) Map.empty $ funMap m1

}

else Nothing

inclusionMor :: Env -> Env -> Result Morphism

inclusionMor e1 e2 =

if isSubEnv e1 e2

then return (embedMorphism e1 e2)

else pplain_error (ideMor initialEnv)

(ptext "Attempt to construct inclusion between non-subsignatures:"

$$ ptext "Singature 1:" $$ printText e1

$$ ptext "Singature 2:" $$ printText e2)

nullPos

symbMapToMorphism :: Env -> Env -> SymbolMap -> Result Morphism

symbMapToMorphism sigma1 sigma2 smap = do

type_map1 <- Map.foldWithKey myIdMap (return Map.empty) $ typeMap sigma1

fun_map1 <- Map.foldWithKey myAsMap (return Map.empty) $ assumps sigma1

return (mkMorphism sigma1 sigma2)

{ typeIdMap = type_map1

, funMap = fun_map1}

where

myIdMap i k m = do

m1 <- m

sym <- maybeToResult nullPos

("symbMapToMorphism - Could not map sort "++showId i "")

$ Map.lookup (Symbol { symName = i

, symbType = TypeAsItemType

$ typeKind k}) smap

return (Map.insert i (symName sym) m1)

myAsMap i (OpInfos ots) m = foldr (insFun i) m ots

insFun i ot m = do

let osc = TySc $ opType ot

m1 <- m

sym <- maybeToResult nullPos

("symbMapToMorphism - Could not map op "++showId i "")

$ Map.lookup (Symbol { symName = i

, symbType = OpAsItemType osc}) smap

k <- case symbType sym of

OpAsItemType sc -> return sc

_ -> plain_error osc

("symbMapToMorphism - Wrong result symbol type for op"

++showId i "") nullPos

return (Map.insert (i, osc) (symName sym,k) m1)

legalEnv :: Env -> Bool

legalEnv _ = True -- maybe a closure test?

legalMor :: Morphism -> Bool

legalMor m = let s = msource m

t = mtarget m

ts = typeIdMap m

fs = funMap m

in

all (`elem` (Map.keys $ typeMap s))

(Map.keys ts)

&& all (`elem` (Map.keys $ typeMap t))

(Map.elems ts)

&& all ((`elem` (Map.keys $ assumps s)) . fst)

(Map.keys fs)

&& all ((`elem` (Map.keys $ assumps t)) . fst)

(Map.elems fs)

morphismUnion :: Morphism -> Morphism -> Result Morphism

morphismUnion m1 m2 =

do s <- mergeEnv (msource m1) $ msource m2

t <- mergeEnv (mtarget m1) $ mtarget m2

tm <- foldr ( \ (i, j) rm ->

do m <- rm

case Map.lookup i m of

Nothing -> return $ Map.insert i j m

Just k -> if j == k then return m

else do

Result [Diag Error

("incompatible mapping of type id: " ++

showId i " to: " ++ showId j " and: "

++ showId k "") $ posOfId i] $ Just ()

return m)

(return $ typeIdMap m1) $ Map.toList $ typeIdMap m2

fm <- foldr ( \ (isc@(i, _), jsc@(j, TySc sc1)) rm -> do

m <- rm

case Map.lookup isc m of

Nothing -> return $ Map.insert isc jsc m

Just ksc@(k, TySc sc2) -> if j == k &&

isUnifiable (typeMap t) 0 sc1 sc2

then return m

else do

Result [Diag Error

("incompatible mapping of op: " ++

showFun isc " to: " ++ showFun jsc " and: "

++ showFun ksc "") $ posOfId i] $ Just ()

return m)

(return $ funMap m1) $ Map.toList $ funMap m2

return (mkMorphism s t)

{ typeIdMap = tm

, funMap = fm }

showFun :: (Id, TySc) -> ShowS

showFun (i, TySc ty) = showId i . (" : " ++) . showPretty ty

morphismToSymbMap :: Morphism -> SymbolMap

morphismToSymbMap mor =

let

tm = typeMap $ msource mor

typeSymMap =

Map.foldWithKey

( \ s1 s2 m -> let k = typeKind $

Map.findWithDefault starTypeInfo s1 tm

in Map.insert (idToTypeSymbol s1 k) (idToTypeSymbol s2 k) m)

Map.empty $

typeIdMap mor

in Map.foldWithKey

( \ (id1,t1) (id2,t2) m ->

Map.insert (idToOpSymbol id1 t1)

(idToOpSymbol id2 t2) m)

typeSymMap $ funMap mor

instance PrettyPrint Morphism where

printText0 ga m = braces (printText0 ga (msource m))

$$ text mapsTo

<+> braces (printText0 ga (mtarget m))

instance PrettyPrint Symbol where

printText0 ga s = text (case symbType s of

OpAsItemType _ -> opS

TypeAsItemType _ -> typeS

ClassAsItemType _ -> classS) <+>

printText0 ga (symName s) <+> text colonS <+>

printText0 ga (symbType s)

instance PrettyPrint RawSymbol where

printText0 ga rs = case rs of

ASymbol s -> printText0 ga s

AnID i -> printText0 ga i

AKindedId k i -> text (case k of

SK_type -> typeS

SK_sort -> sortS

SK_op -> opS

SK_fun -> funS

SK_pred -> predS

SK_class -> classS

Implicit -> "") <+> printText0 ga i