{- |

Module : $Header$

Description : analysis of data type declarations

Copyright : (c) Christian Maeder and Uni Bremen 2002-2005

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

Maintainer : Christian.Maeder@dfki.de

Stability : provisional

Portability : portable

analyse alternatives of data types

-}

module HasCASL.DataAna

( DataPat(..)

, toDataPat

, getConstrScheme

, getSelScheme

, anaAlts

, makeDataSelEqs

, inductionScheme

) where

import Data.Maybe

import qualified Data.Map as Map

import qualified Data.Set as Set

import Common.Id

import Common.Result

import Common.AS_Annotation

import HasCASL.As

import HasCASL.Le

import HasCASL.TypeAna

import HasCASL.AsUtils

import HasCASL.Builtin

import HasCASL.Unify

-- | description of polymorphic data types

data DataPat = DataPat Id [TypeArg] RawKind Type

mkVarDecl :: Id -> Type -> VarDecl

mkVarDecl i t = VarDecl i t Other nullRange

mkSelId :: Range -> String -> Int -> Int -> Id

mkSelId p str n m = mkId

[Token (str ++ "_" ++ (if n < 1 then "" else show n ++ "_") ++ show m) p]

mkSelVar :: Int -> Int -> Type -> VarDecl

mkSelVar n m ty = mkVarDecl (mkSelId (getRange ty) "x" n m) ty

genTuple :: Int -> Int -> [Selector] -> [VarDecl]

genTuple _ _ [] = []

genTuple n m (Select _ ty _ : sels) =

mkSelVar n m ty : genTuple n (m + 1) sels

genSelVars :: Int -> [[Selector]] -> [[VarDecl]]

genSelVars n sels = case sels of

[ts] -> [genTuple 0 1 ts]

_ -> if all (\ l -> not (null l) && null (tail l)) sels

then map (: []) $ genTuple 0 1 $ map head sels

else genSelVarsAux n sels

genSelVarsAux :: Int -> [[Selector]] -> [[VarDecl]]

genSelVarsAux _ [] = []

genSelVarsAux n (ts : sels) =

genTuple n 1 ts : genSelVarsAux (n + 1) sels

makeSelTupleEqs :: DataPat -> Term -> Int -> Int -> [Selector] -> [Named Term]

makeSelTupleEqs dt ct n m (Select mi ty p : sels) =

let sc = getSelScheme dt p ty

in (case mi of

Just i -> let

vt = QualVar $ mkSelVar n m ty

eq = mkEqTerm eqId ty nullRange

(mkApplTerm (mkOpTerm i sc) [ct]) vt

in [makeNamed ("ga_select_" ++ show i) eq]

_ -> [])

++ makeSelTupleEqs dt ct n (m + 1) sels

makeSelTupleEqs _ _ _ _ [] = []

makeSelEqs :: DataPat -> Term -> Int -> [[Selector]] -> [Named Term]

makeSelEqs dt ct n (sel:sels) =

makeSelTupleEqs dt ct n 1 sel

++ makeSelEqs dt ct (n + 1) sels

makeSelEqs _ _ _ _ = []

makeAltSelEqs :: DataPat -> AltDefn -> [Named Term]

makeAltSelEqs dt@(DataPat _ iargs _ _) (Construct mc ts p sels) =

case mc of

Nothing -> []

Just c -> let

vars = genSelVars 1 sels

ars = mkSelArgs vars

ct = mkApplTerm (mkOpTerm c $ getConstrScheme dt p ts) ars

in map (mapNamed (mkForall (map GenTypeVarDecl iargs

++ map GenVarDecl (concat vars)))) $ makeSelEqs dt ct 1 sels

mkSelArgs :: [[VarDecl]] -> [Term]

mkSelArgs = map (\ vs -> mkTupleTerm (map QualVar vs) nullRange)

getConstrScheme :: DataPat -> Partiality -> [Type] -> TypeScheme

getConstrScheme (DataPat _ args _ rt) p ts =

TypeScheme args (getFunType rt p ts) nullRange

getSelScheme :: DataPat -> Partiality -> Type -> TypeScheme

getSelScheme (DataPat _ args _ rt) p t =

TypeScheme args (getSelType rt p t) nullRange

-- | remove variances from generalized type arguments

toDataPat :: DataEntry -> DataPat

toDataPat (DataEntry im i _ args rk _) = let j = Map.findWithDefault i i im in

DataPat j (map nonVarTypeArg args) rk $ patToType j args rk

-- | create selector equations for a data type

makeDataSelEqs :: DataPat -> [AltDefn] -> [Named Sentence]

makeDataSelEqs dp = map (mapNamed Formula) . concatMap (makeAltSelEqs dp)

-- | analyse the alternatives of a data type

anaAlts :: [DataPat] -> DataPat -> [Alternative] -> Env -> Result [AltDefn]

anaAlts tys dt alts te =

do l <- mapM (anaAlt tys dt te) alts

Result (checkUniqueness $ catMaybes $

map ( \ (Construct i _ _ _) -> i) l) $ Just ()

return l

anaAlt :: [DataPat] -> DataPat -> Env -> Alternative

-> Result AltDefn

anaAlt _ _ te (Subtype ts _) =

do l <- mapM ( \ t -> anaStarTypeM t te) ts

return $ Construct Nothing (Set.toList $ Set.fromList $ map snd l)

Partial []

anaAlt tys dt te (Constructor i cs p _) =

do newCs <- mapM (anaComps tys dt te) cs

let sels = map snd newCs

Result (checkUniqueness $ catMaybes $

map ( \ (Select s _ _) -> s ) $ concat sels) $ Just ()

return $ Construct (Just i) (map fst newCs) p sels

anaComps :: [DataPat] -> DataPat -> Env -> [Component]

-> Result (Type, [Selector])

anaComps tys rt te cs =

do newCs <- mapM (anaComp tys rt te) cs

return (mkProductType $ map fst newCs, map snd newCs)

anaComp :: [DataPat] -> DataPat -> Env -> Component

-> Result (Type, Selector)

anaComp tys rt te (Selector s _ t _ _) =

do ct <- anaCompType tys rt t te

let (p, nct) = case getTypeAppl ct of

(TypeName i _ _, [lt]) | i == lazyTypeId -> (Partial, lt)

_ -> (Total, ct)

return (nct, Select (Just s) nct p)

anaComp tys rt te (NoSelector t) =

do ct <- anaCompType tys rt t te

return (ct, Select Nothing ct Partial)

anaCompType :: [DataPat] -> DataPat -> Type -> Env -> Result Type

anaCompType tys (DataPat _ tArgs _ _) t te = do

(_, ct) <- anaStarTypeM t te

let ds = unboundTypevars True tArgs ct

if null ds then return () else Result ds Nothing

mapM_ (checkMonomorphRecursion ct te) tys

return $ generalize tArgs ct

checkMonomorphRecursion :: Type -> Env -> DataPat -> Result ()

checkMonomorphRecursion t te (DataPat i _ _ rt) =

case filter (\ ty -> not (lesserType te ty rt || lesserType te rt ty))

$ findSubTypes (typeMap te) i t of

[] -> return ()

ty : _ -> Result [Diag Error ("illegal polymorphic recursion"

++ expected rt ty) $ getRange ty] Nothing

findSubTypes :: TypeMap -> Id -> Type -> [Type]

findSubTypes tm i t = case getTypeAppl t of

(TypeName j _ _, args) -> if relatedTypeIds tm i j then [t]

else concatMap (findSubTypes tm i) args

(topTy, args) -> concatMap (findSubTypes tm i) $ topTy : args

relatedTypeIds :: TypeMap -> Id -> Id -> Bool

relatedTypeIds tm i1 i2 =

not $ Set.null $ Set.intersection (allRelIds tm i1) $ allRelIds tm i2

allRelIds :: TypeMap -> Id -> Set.Set Id

allRelIds tm i = Set.union (superIds tm i) $ subIds tm i

subIds :: TypeMap -> Id -> Set.Set Id

subIds tm i = foldr ( \ j s ->

if Set.member i $ superIds tm j then

Set.insert j s else s) Set.empty $ Map.keys tm

mkPredVar :: DataPat -> VarDecl

mkPredVar (DataPat i _ _ rt) = let ps = posOfId i in

mkVarDecl (if isSimpleId i then mkId [mkSimpleId $ "p_" ++ show i]

else Id [mkSimpleId "p"] [i] ps) (predType ps rt)

mkPredAppl :: DataPat -> Term -> Term

mkPredAppl dp t = mkApplTerm (QualVar $ mkPredVar dp) [t]

mkPredToVarAppl :: DataPat -> VarDecl -> Term

mkPredToVarAppl dp = mkPredAppl dp . QualVar

mkConclusion :: DataPat -> Term

mkConclusion dp@(DataPat _ _ _ ty) =

let v = mkVarDecl (mkId [mkSimpleId "x"]) ty

in mkForall [GenVarDecl v] $ mkPredToVarAppl dp v

mkPremise :: Map.Map Type DataPat -> DataPat -> AltDefn -> [Term]

mkPremise m dp (Construct mc ts p sels) =

case mc of

Nothing -> []

Just c -> let

vars = genSelVars 1 sels

findHypo vd@(VarDecl _ ty _ _) =

fmap (flip mkPredToVarAppl vd) $ Map.lookup ty m

flatVars = concat vars

indHypos = catMaybes $ map findHypo flatVars

indConcl = mkPredAppl dp

$ mkApplTerm (mkOpTerm c $ getConstrScheme dp p ts)

$ mkSelArgs vars

in [mkForall (map GenVarDecl flatVars) $

if null indHypos then indConcl else

mkLogTerm implId nullRange (mkConjunct indHypos) indConcl]

mkConjunct :: [Term] -> Term

mkConjunct ts = if null ts then error "HasCASL.DataAna.mkConjunct" else

toBinJunctor andId ts nullRange

mkPremises :: Map.Map Type DataPat -> DataEntry -> [Term]

mkPremises m de@(DataEntry _ _ _ _ _ alts) =

concatMap (mkPremise m $ toDataPat de) $ Set.toList alts

joinTypeArgs :: [DataPat] -> Map.Map Id TypeArg

joinTypeArgs = foldr (\ (DataPat _ iargs _ _) m ->

foldr (\ ta -> Map.insert (getTypeVar ta) ta) m iargs) Map.empty

inductionScheme :: [DataEntry] -> Term

inductionScheme des =

let dps = map toDataPat des

m = Map.fromList $ map (\ dp@(DataPat _ _ _ ty) -> (ty, dp)) dps

in mkForall (map GenTypeVarDecl (Map.elems $ joinTypeArgs dps)

++ map (GenVarDecl . mkPredVar) dps)

$ mkLogTerm implId nullRange

(mkConjunct $ concatMap (mkPremises m) des)

$ mkConjunct $ map mkConclusion dps