{- |

Module : $Header$

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

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

Maintainer : maeder@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.Unify

import HasCASL.Symbol

import HasCASL.MapTerm

import HasCASL.AsUtils

import Common.Id

import Common.Keywords

import Common.Result

import Common.PrettyPrint

import Common.Lib.Pretty

import qualified Common.Lib.Map as Map

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 =

let tm = typeIdMap m

fm = funMap m

ds = Map.foldWithKey ( \ (i, TySc s) (j, TySc t) l ->

(printText0 ga i <+> colon <+> printText0 ga s

<+> text mapsTo <+>

printText0 ga j <+> colon <+> printText0 ga t) : l)

[] fm

in (if Map.isEmpty tm then empty

else text (typeS ++ sS) <+> printText0 ga tm)

$$ (if Map.isEmpty fm then empty

else text (opS ++ sS) <+> fsep (punctuate comma ds))

$$ nest 1 colon <+> braces (printText0 ga $ msource m)

$$ nest 1 (text mapsTo)

<+> braces (printText0 ga $ mtarget m)

mapTypeScheme :: IdMap -> TypeScheme -> TypeScheme

-- rename clashing type arguments later

mapTypeScheme = mapTypeOfScheme . mapType

mapTySc :: TypeMap -> IdMap -> TySc -> TySc

mapTySc tm im (TySc s1) =

TySc $ mapTypeOfScheme (expandAlias tm . mapType im) s1

mapSen :: Morphism -> Term -> Term

mapSen m = let im = typeIdMap m in

mapTerm (mapFunSym (typeMap $ mtarget m) im (funMap m), mapType im)

mapDataEntry :: Morphism -> DataEntry -> DataEntry

mapDataEntry m (DataEntry tm i k args alts) =

let tim = compIdMap tm $ typeIdMap m

in DataEntry tim i k args $ map

(mapAlt m tim args $

typeIdToType (Map.findWithDefault i i tim)

args star) alts

mapAlt :: Morphism -> IdMap -> [TypeArg] -> Type -> AltDefn -> AltDefn

mapAlt m tm args dt c@(Construct mi ts p sels) =

case mi of

Just i ->

let sc = TypeScheme args

([] :=> getConstrType dt p (map (mapType tm) ts)) []

(j, TypeScheme _ (_ :=> ty) _) =

mapFunSym (typeMap $ mtarget m) (typeIdMap m) (funMap m) (i, sc)

in Construct (Just j) ts (getPartiality ts ty) sels

-- do not change (unused) selectors

Nothing -> c

mapSentence :: Morphism -> Sentence -> Result Sentence

mapSentence m s = return $ case s of

Formula t -> Formula $ mapSen m t

DatatypeSen td -> DatatypeSen $ map (mapDataEntry m) td

ProgEqSen i sc pe ->

let tm = typeIdMap m

fm = funMap m

f = mapFunSym (typeMap $ mtarget m) tm fm

(ni, nsc) = f (i, sc)

in ProgEqSen ni nsc $ mapEq (f, mapType tm) pe

mapFunSym :: TypeMap -> IdMap -> FunMap -> (Id, TypeScheme) -> (Id, TypeScheme)

mapFunSym tm im fm (i, sc) =

let (j, TySc s) = mapFunEntry tm im fm (i, TySc sc) in (j, s)

mapFunEntry :: TypeMap -> IdMap -> FunMap -> (Id, TySc) -> (Id, TySc)

mapFunEntry tm im fm p@(i, sc) =

if Map.isEmpty im && Map.isEmpty fm then p else

Map.findWithDefault (i, mapTySc tm im sc) (i, sc) fm

mkMorphism :: Env -> Env -> Morphism

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

embedMorphism :: Env -> Env -> Morphism

embedMorphism = mkMorphism

ideMor :: Env -> Morphism

ideMor e = embedMorphism e e

compIdMap :: IdMap -> IdMap -> IdMap

compIdMap im1 im2 = Map.foldWithKey ( \ i j ->

Map.insert i $ Map.findWithDefault j j im2)

im2 $ im1

compMor :: Morphism -> Morphism -> Maybe Morphism

compMor m1 m2 =

if isSubEnv (mtarget m1) (msource m2) then

let tm2 = typeIdMap m2

fm2 = funMap m2 in Just

(mkMorphism (msource m1) (mtarget m2))

{ classIdMap = compIdMap (classIdMap m1) $ classIdMap m2

, typeIdMap = compIdMap (typeIdMap m1) tm2

, funMap = Map.foldWithKey ( \ p1 p2 ->

Map.insert p1

$ mapFunEntry (typeMap $ mtarget m2)

tm2 fm2 p2) fm2 $ 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:"

$$ ptext "Signature 1:" $$ printText e1

$$ ptext "Signature 2:" $$ 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 <- merge (msource m1) $ msource m2

t <- merge (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 &&

asSchemes 0 (equalSubs $ typeMap t) 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 = typeIdMap mor

typeSymMap = Map.foldWithKey ( \ i ti ->

let j = Map.findWithDefault i i tm

k = typeKind ti

in Map.insert (idToTypeSymbol src i k)

$ idToTypeSymbol tar j k) Map.empty $ typeMap src

in Map.foldWithKey

( \ i (OpInfos l) m ->

foldr ( \ oi ->

let ty = opType oi

(j, TySc t2) = mapFunEntry (typeMap tar)

tm (funMap mor) (i, TySc ty)

in Map.insert (idToOpSymbol src i ty)

(idToOpSymbol tar j t2)) m l)

typeSymMap $ assumps src