{- |

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.As

import HasCASL.AsToLe

import HasCASL.TypeCheck

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 qualified Common.Lib.Map as Map

import Data.List(partition)

type IdMap = Map.Map Id Id

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

data Morphism = Morphism { msource :: Env

, mtarget :: Env

, classIdMap :: IdMap -- ignore

, typeIdMap :: IdMap

, funMap :: FunMap }

deriving (Eq, Show)

instance PrettyPrint Morphism where

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

$$ text mapsTo

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

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)

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 }

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

, symType = TypeAsItemType

$ typeKind k

, symEnv = sigma1 }) 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 = opType ot

m1 <- m

sym <- maybeToResult nullPos

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

$ Map.lookup (Symbol { symName = i

, symType = OpAsItemType osc

, symEnv = sigma1 }) smap

k <- case symType sym of

OpAsItemType sc -> return $ TySc sc

_ -> plain_error (TySc osc)

("symbMapToMorphism - Wrong result symbol type for op"

++showId i "") nullPos

return (Map.insert (i, TySc 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

src = msource mor

tar = mtarget mor

tm = typeMap src

typeSymMap =

Map.foldWithKey

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

Map.findWithDefault starTypeInfo s1 tm

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

Map.empty $

typeIdMap mor

in Map.foldWithKey

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

Map.insert (idToOpSymbol src id1 t1)

(idToOpSymbol tar id2 t2) m)

typeSymMap $ funMap mor