{- |

Module : $Header$

Copyright : (c) Till Mossakowski and Uni Bremen 2003

Licence : All rights reserved.

Maintainer : hets@tzi.de

Stability : provisional

Portability : non-portable (imports Logic.Logic)

The embedding comorphism from HasCASL to Isabelle-HOL.

-}

module Comorphisms.HasCASL2IsabelleHOL where

import Logic.Logic

import Logic.Comorphism

import Common.Id

import qualified Common.Lib.Map as Map

import Data.List

import Data.Maybe

import Common.AS_Annotation (Named(..))

-- HasCASL

import HasCASL.Logic_HasCASL

import HasCASL.Sublogic

import HasCASL.Le as Le

import HasCASL.As as As

import HasCASL.Builtin

import HasCASL.Morphism

-- Isabelle

import Isabelle.IsaSign as IsaSign

import Isabelle.IsaConsts

import Isabelle.Logic_Isabelle

import Isabelle.Translate

-- | The identity of the comorphism

data HasCASL2IsabelleHOL = HasCASL2IsabelleHOL deriving (Show)

instance Language HasCASL2IsabelleHOL -- default definition is okay

instance Comorphism HasCASL2IsabelleHOL

HasCASL HasCASL_Sublogics

BasicSpec Le.Sentence SymbItems SymbMapItems

Env Morphism

Symbol RawSymbol ()

Isabelle () () IsaSign.Sentence () ()

IsaSign.Sign

() () () () where

sourceLogic _ = HasCASL

sourceSublogic _ = HasCASL_SL

{ has_sub = False, -- subsorting

has_part = True, -- partiality

has_eq = True, -- equality

has_pred = True, -- predicates

has_ho = True, -- higher order

has_type_classes = False,

has_polymorphism = True,

has_type_constructors = True,

which_logic = HOL

}

targetLogic _ = Isabelle

targetSublogic _ = ()

map_sign _ = transSignature

-- map_morphism _ morphism1 -> Maybe morphism2

map_sentence _ sign phi =

case transSentence sign phi of

Nothing -> Nothing

Just (ts) -> Just $ Sentence {senTerm = ts}

-- map_symbol :: cid -> symbol1 -> Set symbol2

-- ============================ Signature ================================== --

transSignature :: Env

-> Maybe (IsaSign.Sign,[Named IsaSign.Sentence])

transSignature sign =

Just (IsaSign.emptySign {

baseSig = "MainHC",

-- translation of typeconstructors

tsig = emptyTypeSig

{ arities = Map.foldWithKey extractTypeName

Map.empty

(typeMap sign) },

-- translation of operation declarations

constTab = Map.foldWithKey insertOps

Map.empty

(assumps sign),

-- translation of datatype declarations

dataTypeTab = transDatatype (typeMap sign),

showLemmas = True },

[] )

where

extractTypeName tId typeInfo m =

if isDatatypeDefn typeInfo then m

else Map.insert (showIsa tId) [(isaTerm, [])] m

-- translate the kind here!

isDatatypeDefn t = case typeDefn t of

DatatypeDefn _ -> True

_ -> False

insertOps opName opInfs m =

let opIs = opInfos opInfs

in if isSingle opIs then

let transOp = transOpInfo (head opIs)

in case transOp of

Just op -> Map.insert (showIsa opName) op m

Nothing -> m

else

let transOps = map transOpInfo opIs

in foldl (\ m1 (transOp,i) ->

case transOp of

Just typ -> Map.insert (showIsaI opName i)

typ m1

Nothing -> m1)

m

(zip transOps [1..length transOps])

---------- translation of a type in an operation declaration ----------

transOpInfo :: OpInfo -> Maybe Typ

transOpInfo (OpInfo opT _ opDef) =

case opDef of

NoOpDefn Pred -> Just (transPredType opT)

NoOpDefn _ -> Just (transOpType opT)

ConstructData _ -> Nothing

Definition _ _ -> Just (transOpType opT)

_ ->

error ("[Comorphisms.HasCASL2IsabelleHOL] Not supported"

++ "operation declaration and/or definition")

-- operation

transOpType :: TypeScheme -> Typ

transOpType (TypeScheme _ op _) = transType op

-- predicate

transPredType :: TypeScheme -> Typ

transPredType (TypeScheme _ pre _) =

case pre of

FunType tp _ _ _ -> mkFunType (transType tp) boolType

_ ->

error "[Comorphisms.HasCASL2IsabelleHOL] Wrong predicate type"

-- types composed of simple types

transType :: Type -> Typ

transType (TypeName tId _ i) =

if i == 0 then Type (showIsa tId) [] [] [] -- translate kind here!!

else TFree (showIsa tId) []

transType (ProductType types _) = foldl1 IsaSign.prodType

(map transType types)

transType (FunType type1 arr type2 _) =

case arr of

PFunArr -> mkFunType (transType type1) (mkOptionType (transType type2))

FunArr -> mkFunType (transType type1) (transType type2)

_ ->

error "[Comorphisms.HasCASL2IsabelleHOL] Not supported function type"

transType (TypeAppl type1 type2) =

mkTypeAppl c (ts ++ [transType type2])

where (c, ts) = stripAppl type1 "" []

stripAppl t c ts =

case t of

TypeAppl t1 t2 -> stripAppl t1 c ((transType t2):ts)

TypeName i _ _ -> (showIsa i, ts)

_ -> error "HasCASL2IsabelleHOL.transType"

transType _ = error "[Comorphisms.HasCASL2IsabelleHOL] Not supported type"

---------- translation of a datatype declaration ----------

transDatatype :: TypeMap -> DataTypeTab

transDatatype tm = map transDataEntry (Map.fold extractDataypes [] tm)

where extractDataypes ti des = case typeDefn ti of

DatatypeDefn de -> des++[de]

_ -> des

-- datatype with name (tyId) + args (tyArgs) and alternatives

transDataEntry :: DataEntry -> DataTypeTabEntry

transDataEntry (DataEntry _ tyId Le.Free tyArgs alts) =

[((mkDName tyId tyArgs), (map mkAltDefn alts))]

where mkDName ti ta = Type (showIsa ti) [] [] (map transTypeArg ta)

transDataEntry _ =

error "[Comorphisms.HasCASL2IsabelleHOL] Not supported datatype definition"

-- arguments of datatype's typeconstructor

transTypeArg :: TypeArg -> Typ

transTypeArg (TypeArg tyId _ _ _) = TFree (showIsa tyId) []

mkAltDefn :: AltDefn -> DataTypeAlt

mkAltDefn (Construct opId types Total _) =

let typs = map transType types

in case opId of

Just opI -> (showIsa opI, typs)

Nothing -> ("", typs)

mkAltDefn _ =

error ("[Comorphisms.HasCASL2IsabelleHOL] Not supported"

++ "alternative definition in (free) datatype")

------------------------------ Formulas ------------------------------

transVar :: Var -> String

transVar = showIsa

transSentence :: Env -> Le.Sentence -> Maybe IsaSign.Term

transSentence e s = case s of

Le.Formula t -> Just (transTerm e t)

DatatypeSen _ -> Nothing

ProgEqSen _ _ _pe -> Nothing

transOpId :: Env -> UninstOpId -> TypeScheme -> String

transOpId sign op ts =

case (do ops <- Map.lookup op (assumps sign)

if isSingle (opInfos ops) then return $ showIsa op

else do i <- elemIndex ts (map opType (opInfos ops))

return $ showIsaI op (i+1)) of

Just str -> str

Nothing -> showIsa op

transTerm :: Env -> As.Term -> IsaSign.Term

transTerm _ (QualVar (VarDecl var typ _ _)) =

let tp = transType typ

otp = mkFunType tp $ mkOptionType tp

in termAppl (conSomeT otp) (IsaSign.Free (transVar var) tp isaTerm)

transTerm sign (QualOp _ (InstOpId opId _ _) ts _)

| opId == trueId = con "True"

| opId == falseId = con "False"

| otherwise = termAppl conSome (con (transOpId sign opId ts))

transTerm sign (ApplTerm term1 term2 _) =

transApplTerm term1

where

transApplTerm t =

case t of

QualOp Fun (InstOpId opId _ _) _ _ ->

if opId == whenElse then transWhenElse sign term2

else transLog sign opId term1 term2

QualOp Pred _ _ _ ->

termAppl (termAppl (con "pApp") (transTerm sign term1))

(transTerm sign term2)

QualOp Op _ typeScheme _ ->

if isPart typeScheme then mkApp "app"

else mkApp "apt"

ApplTerm t' _ _ -> transApplTerm t'

TypedTerm t' _ _ _ -> transApplTerm t'

_ -> mkApp "app"

mkApp s = termAppl (termAppl (con s) (transTerm sign term1))

(transTerm sign term2)

isPart (TypeScheme _ op _) =

case op of

FunType _ PFunArr _ _ -> True

FunType _ FunArr _ _ -> False

_ ->

error "[Comorphisms.HasCASL2IsabelleHOL] Wrong operation type"

transTerm sign (QuantifiedTerm quan varDecls phi' _) =

foldr (quantify quan) (transTerm sign phi') varDecls

where

quantify q gvd phi =

case gvd of

(GenVarDecl (VarDecl var typ _ _)) ->

termAppl (con $ qname q) (Abs (con $ transVar var)

(transType typ) phi NotCont)

(GenTypeVarDecl (TypeArg _ _ _ _)) -> phi

qname Universal = allS

qname Existential = exS

qname Unique = ex1S

transTerm sign (TypedTerm t _ _ _) = transTerm sign t

transTerm sign (LambdaTerm pats part body _) =

case part of

Partial -> lambdaAbs transTerm

Total -> lambdaAbs transTotalLambda

where

lambdaAbs f =

if (null pats) then termAppl conSome

(Abs (IsaSign.Free "dummyVar" noType isaTerm)

noType (f sign body) IsCont)

else termAppl conSome (foldr (abstraction sign)

(f sign body)

pats)

transTerm sign (LetTerm As.Let eqs body _) =

IsaSign.Let (map transPEq eqs) (transTerm sign body) IsCont

where

transPEq (ProgEq pat t _) =

(transPattern sign pat, transPattern sign t)

transTerm sign (TupleTerm terms _) =

foldl1 (binConst pairC) (map (transTerm sign) terms)

transTerm sign (CaseTerm t pEqs _) =

let alts = arangeCaseAlts sign pEqs

in

case t of

QualVar (VarDecl decl _ _ _) ->

Case (IsaSign.Free (transVar decl) noType isaTerm) alts IsCont

_ ->

Case (transTerm sign t)

((con "None", con "None"):

[(App conSome (IsaSign.Free "caseVar" noType isaTerm) IsCont,

Case (IsaSign.Free "caseVar" noType isaTerm) alts IsCont)])

IsCont

transTerm _ _ =

error "[Comorphisms.HasCASL2IsabelleHOL] Not supported (abstract) syntax."

-- translation formulas with logical connectives

transLog :: Env -> Id -> As.Term -> As.Term -> IsaSign.Term

transLog sign opId opTerm t

| opId == andId = foldl1 (binConst conj)

(map (transTerm sign) ts)

| opId == orId = foldl1 (binConst disj)

(map (transTerm sign) ts)

| opId == implId = binConst impl (transTerm sign t1)

(transTerm sign t2)

| opId == eqvId = binConst eqv (transTerm sign t1)

(transTerm sign t2)

| opId == notId = termAppl notOp (transTerm sign t)

| opId == defId = termAppl defOp (transTerm sign t)

| opId == exEq =

binConst conj

(binConst conj

(binConst eq (transTerm sign t1)

(transTerm sign t2))

(termAppl defOp (transTerm sign t1)))

(termAppl defOp (transTerm sign t2))

| opId == eqId = binConst eq (transTerm sign t1)

(transTerm sign t2)

| otherwise = termAppl (transTerm sign opTerm) (transTerm sign t)

where ts = getTerms t

t1 = head ts

t2 = last ts

getTerms (TupleTerm terms _) = terms

getTerms _ =

error ("[Comorphisms.HasCASL2IsabelleHOL] Incorrect"

++ "formula coding in abstract syntax")

----------------- translation of lambda-things -----------------

-- form Abs(...)

abstraction :: Env -> As.Term -> IsaSign.Term -> IsaSign.Term

abstraction sign pat body =

Abs (transPattern sign pat) (getType pat) body IsCont where

getType t =

case t of

QualVar (VarDecl _ typ _ _) -> transType typ

TypedTerm _ _ typ _ -> transType typ

TupleTerm terms _ -> evalTupleType terms

_ ->

error "HasCASL2IsabelleHOL.abstraction"

evalTupleType t = foldr1 IsaSign.prodType (map getType t)

{- translation of lambda patterns --> without constant:t

-> Some constant:t option -}

transPattern :: Env -> As.Term -> IsaSign.Term

transPattern _ (QualVar (VarDecl var typ _ _)) =

IsaSign.Free (transVar var) (transType typ) isaTerm

transPattern sign (TupleTerm terms _) = foldl1 (binConst isaPair)

(map (transPattern sign) terms)

transPattern _ (QualOp _ (InstOpId opId _ _) _ _) = con (showIsa opId)

transPattern sign (TypedTerm t _ _ _) = transPattern sign t

transPattern sign (ApplTerm t1 t2 _) = App (transPattern sign t1) (transPattern sign t2) IsCont

transPattern sign t = transTerm sign t

-- translation of bodies of total lambda abstractions

transTotalLambda :: Env -> As.Term -> IsaSign.Term

transTotalLambda _ (QualVar (VarDecl var typ _ _)) =

IsaSign.Free(transVar var) (transType typ) isaTerm

transTotalLambda sign t@(QualOp _ (InstOpId opId _ _) _ _) =

if (opId == trueId) || (opId == falseId) then transTerm sign t

else con (showIsa opId)

transTotalLambda sign (ApplTerm term1 term2 _) =

termAppl (transTotalLambda sign term1) (transTotalLambda sign term2)

transTotalLambda sign (TypedTerm t _ _ _) = transTotalLambda sign t

transTotalLambda sign (LambdaTerm pats part body _) =

case part of

Partial -> lambdaAbs transTerm

Total -> lambdaAbs transTotalLambda

where

lambdaAbs f =

if (null pats) then Abs(IsaSign.Free "dummyVar" noType isaTerm)

noType (f sign body) IsCont

else (foldr (abstraction sign)

(f sign body)

pats)

transTotalLambda sign (TupleTerm terms _) =

foldl1 (binConst isaPair) (map (transTotalLambda sign) terms)

transTotalLambda sign (CaseTerm t pEqs _) =

Case (transTotalLambda sign t) (map transCaseAltTotal pEqs) IsCont

where transCaseAltTotal (ProgEq pat trm _) =

(transPat sign pat, transTotalLambda sign trm)

transTotalLambda sign t = transTerm sign t

transWhenElse :: Env -> As.Term -> IsaSign.Term

transWhenElse sign t =

case t of

TupleTerm terms _ ->

let ts = (map (transTerm sign) terms)

in

if (length ts) == 3

then If (head $ tail ts) (head ts) (last ts) NotCont

else error

"[Comorphisms.HasCASL2IsabelleHOL] Wrong when-else definition"

_ ->

error "[Comorphisms.HasCASL2IsabelleHOL] Wrong when-else definition"

let2lambda :: ProgEq -> As.Term -> As.Term

let2lambda (ProgEq pat t _) body =

ApplTerm (LambdaTerm [pat] Partial body [nullPos]) t [nullPos]

transLetPat :: Env -> As.Term -> IsaSign.Term

transLetPat sign t@(QualVar (VarDecl _var _typ _ _)) = transPattern sign t

transLetPat sign t@(TupleTerm _terms _) = transPattern sign t

transLetPat sign t@(QualOp _ (InstOpId _opId _ _) _ _) = transPattern sign t

transLetPat sign t = transTerm sign t

{- todo

nested case patterns:

1. check if set of patterns is

1a. one pattern consisting of a variable => we are done

1b. set of constructor patterns

1b1. sort patterns according to leading constructor

1b2. for each group of patterns with the same leading constructor

1b2a. for each argument position, call 1. recursively

-}

{- Annotation concerning Patterns:

Following the HasCASL-Summary and the limits of this encoding

patterns may take the form:

QualVar, QualOp, ApplTerm, TupleTerm and TypedTerm

-}

-- Input: List of case alternative one pattern per term

-- Functionality: Tests wheter pattern is a variable -> case alternative are

-- translated

arangeCaseAlts :: Env -> [ProgEq]-> [(IsaSign.Term, IsaSign.Term)]

arangeCaseAlts sign pEqs

| and (map patIsVar pEqs) = map (transCaseAlt sign) pEqs

| otherwise = sortCaseAlts sign pEqs

-- Input: List of case alternatives, that patterns does consist of datatype constructors

-- (with arguments) or tupels

-- Functionality: Groups case alternatives by leading pattern-constructor

-- each pattern group is 'unfolded'

-- !! Von hier an hat man es nur mit EINER Art von leading constructor zu tun!!

sortCaseAlts :: Env -> [ProgEq]-> [(IsaSign.Term, IsaSign.Term)]

sortCaseAlts sign pEqs =

let consList

| null pEqs = error "No case alternatives."

| otherwise = getCons sign (getName (head pEqs))

groupedByCons = Data.List.nub (map (groupCons pEqs) consList)

in map (flattenPattern sign) groupedByCons

-- Returns a list of the constructors of the used datatype

getCons :: Env -> TypeId -> [UninstOpId]

getCons sign tId =

extractIds (typeDefn (Map.find tId (typeMap sign)))

where extractIds (DatatypeDefn (DataEntry _ _ _ _ altDefns)) =

catMaybes (map stripConstruct altDefns)

extractIds _ = error "HasCASL2Isabelle.extractIds"

stripConstruct (Construct i _ _ _) = i

-- Extracts the type of the used datatype in case patterns

getName :: ProgEq -> TypeId

getName (ProgEq pat _ _) = (getTypeName pat)

getTypeName p =

case p of

QualVar (VarDecl _ typ _ _) -> name typ

QualOp _ _ (TypeScheme _ typ _) _ -> name typ

TypedTerm _ _ typ _ -> name typ

ApplTerm t _ _ -> getTypeName t

TupleTerm ts _ -> getTypeName (head ts)

_ -> error "HasCASL2IsabelleHOL.getTypeName"

where name tp = case tp of

TypeName tyId _ 0 -> tyId

TypeAppl tp' _ -> name tp'

FunType _ _ tp' _ -> name tp'

ProductType (tp':tps) _ -> name tp'

_ ->

error "HasCASL2IsabelleHOL.name (of type)"

-- Input: Case alternatives and name of one constructor

-- Functionality: Filters case alternatives by constructor's name

groupCons :: [ProgEq] -> UninstOpId -> [ProgEq]

groupCons pEqs name = filter hasSameName pEqs

where hasSameName (ProgEq pat _ _) =

hsn pat

hsn pat =

case pat of

QualOp _ (InstOpId n _ _) _ _ -> n == name

ApplTerm t1 _ _ -> hsn t1

TypedTerm t _ _ _ -> hsn t

TupleTerm _ _ -> True

_ -> False

-- Input: List of case alternatives with same leading constructor

-- Functionality: Tests whether the constructor has no arguments, if so

-- translates case alternatives

-- if not

flattenPattern :: Env -> [ProgEq] -> (IsaSign.Term, IsaSign.Term)

flattenPattern sign pEqs

| null pEqs = error "Missing constructor alternative in case pattern."

| isSingle pEqs = (transCaseAlt sign) (head pEqs)

-- at this stage there are patterns left which use 'ApplTerm' or 'TupleTerm'

-- or the 'TypedTerm' variant of one of them

| otherwise = let m = concentrate (matricize pEqs) sign

in

transCaseAlt sign (ProgEq (shrinkPat m) (term m) nullPos)

{- First of all a matrix is allocated (matriArg) with the arguments of a

constructor resp. of a tuple. They're binded with the term, that would

be executed if the pattern matched. Then the resulting list of

matrices is grouped by the leading argument. (groupArgs) Afterwards -

if a list of grouped arguments has more than one element - the last

pattern argument (in the list 'patterns') is ... -}

data CaseMatrix = CaseMatrix { patBrand :: PatBrand,

cons :: Maybe As.Term,

args :: [Pattern],

newArgs :: [Pattern],

term :: As.Term } deriving (Show)

data PatBrand = Appl | Tuple | QuOp | QuVar deriving (Eq, Show)

instance Eq CaseMatrix where

(==) cmx cmx' = (patBrand cmx == patBrand cmx')

&& (args cmx == args cmx')

&& (term cmx == term cmx')

&& (cons cmx == cons cmx')

&& (newArgs cmx == newArgs cmx')

-- Input: List with CaseMatrix of same leading constructor pattern

-- Functionality: First: Groups CMs so that these CMs are in one list

-- that only differ in their last argument

-- then: reduces list of every CMslist to one CM

-- if there's only one CM left ->

--

concentrate :: [CaseMatrix] -> Env -> CaseMatrix

concentrate cmxs sign

| isSingle cmsWithSubstitutedLastArg = head cmsWithSubstitutedLastArg

| otherwise = concentrate cmsWithSubstitutedLastArg sign

where cmll = Data.List.nub (map (groupByArgs cmxs) [0..(length cmxs-1)])

cmsWithSubstitutedLastArg = map (redArgs sign) cmll

groupByArgs :: [CaseMatrix] -> Int -> [CaseMatrix]

groupByArgs cmxs i

| and (map null (map args cmxs)) = cmxs

| otherwise = (filter equalPat cmxs)

where patE = init (args (cmxs !! i))

equalPat cmx = isSingle (args cmx) || init (args cmx) == patE

-- Functionality: turns ProgEq into CaseMatrix

matricize :: [ProgEq] -> [CaseMatrix]

matricize = map matriPEq

matriPEq :: ProgEq -> CaseMatrix

matriPEq (ProgEq pat altTerm _) = matriArg pat altTerm

matriArg :: Pattern -> As.Term -> CaseMatrix

matriArg pat cTerm =

case pat of

ApplTerm t1 t2 _ -> let (c, p) = stripAppl t1 (Nothing, [])

in

CaseMatrix { patBrand = Appl,

cons = c,

args = p ++ [t2],

newArgs = [],

term = cTerm }

TupleTerm ts _ -> CaseMatrix { patBrand = Tuple,

cons = Nothing,

args = ts,

newArgs = [],

term = cTerm }

TypedTerm t _ _ _ -> matriArg t cTerm

qv@(QualVar _) -> CaseMatrix { patBrand = QuVar,

cons = Nothing,

args = [qv],

newArgs = [],

term = cTerm }

qo@(QualOp _ _ _ _) -> CaseMatrix { patBrand = QuOp,

cons = Nothing,

args = [qo],

newArgs = [],

term = cTerm }

_ -> error "HasCASL2IsabelleHOL.matriArg"

-- Assumption: The innermost term of a case-pattern consisting of a ApplTerm

-- is a QualOp, that is a datatype constructor

where stripAppl ct tp =

(case ct of

TypedTerm (ApplTerm q@(QualOp _ _ _ _) t' _) _ _ _ -> (Just q, [t'] ++ snd tp)

TypedTerm (ApplTerm (TypedTerm

q@(QualOp _ _ _ _) _ _ _) t' _) _ _ _ -> (Just q, [t'] ++ snd tp)

TypedTerm (ApplTerm t' t'' _) _ _ _ ->

stripAppl t' (fst tp, [t''] ++ snd tp)

ApplTerm q@(QualOp _ _ _ _) t' _ -> (Just q, [t'] ++ snd tp)

ApplTerm (TypedTerm

q@(QualOp _ _ _ _) _ _ _) t' _ -> (Just q, [t'])

ApplTerm t' t'' _ ->

stripAppl t' (fst tp, [t''] ++ snd tp)

-- TypedTerm t' _ _ _ -> stripAppl t' tp

q@(QualOp _ _ _ _) -> (Just q, snd tp)

_ -> (Nothing, [ct] ++ snd tp))

redArgs :: Env -> [CaseMatrix] -> CaseMatrix

redArgs sign caMas

| and (map (testPatBrand Appl) caMas) = redAppl caMas sign

| and (map (testPatBrand Tuple) caMas) = redAppl caMas sign

| isSingle caMas = head caMas

| otherwise = head caMas

where testPatBrand pb cm = pb == patBrand cm

-- Input: List of CMs thats leading constructor and arguments except the last one are equal

-- Functionality: Reduces n CMs to one with same last argument in pattern

redAppl :: [CaseMatrix] -> Env -> CaseMatrix

redAppl caMas sign

| and (map null (map args caMas)) = head caMas

| isSingle caMas =

hCaMas { args = init (args hCaMas),

newArgs = (last (args hCaMas)):(newArgs hCaMas) }

| and (map termIsVar lastArgs) = substVar (head caMas)

| otherwise = substTerm (head caMas)

where terms = map term caMas

hCaMas = head caMas

lastArgs = map last (map args caMas)

varName = "caseVar" ++ show (length (args (head caMas)))

varId = (mkId [(mkSimpleId varName)])

newVar = QualVar (VarDecl varId (TypeName varId MissingKind 1) Other [])

newPEqs = (map newPE (zip lastArgs terms))

newPEqs' = recArgs sign newPEqs

substVar caMa

| null (args caMa) = caMa

| isSingle (args caMa) =

caMa { args = [],

newArgs = last(args caMa) : (newArgs caMa) }

| otherwise =

caMa { args = init (args caMa),

newArgs = last(args caMa) : (newArgs caMa) }

substTerm caMa

| null (args caMa) = caMa

| isSingle (args caMa) =

caMa { args = [],

newArgs = newVar : (newArgs caMa),

term = CaseTerm newVar newPEqs' [] }

| otherwise =

caMa { args = init(args caMa),

newArgs = newVar : (newArgs caMa),

term = CaseTerm newVar newPEqs' [] }

recArgs :: Env -> [ProgEq] -> [ProgEq]

recArgs sign newPEqs

| isSingle groupedByCons

|| null groupedByCons = []

| otherwise = doPEQ groupedByCons []

where consList

| null newPEqs = error "No case alternatives."

| otherwise = getCons sign (getName (head newPEqs))

groupedByCons = map (groupCons newPEqs) consList

doPEQ [] res = res

doPEQ (g:gByCs) res

| isSingle g = doPEQ gByCs (res ++ g)

| otherwise = doPEQ gByCs (res ++ [(toPEQ (testPEQs sign g))])

toPEQ cmx = ProgEq (shrinkPat cmx) (term cmx) nullPos

testPEQs :: Env -> [ProgEq] -> CaseMatrix

testPEQs sign pEqs

| null pEqs = error "HasCASL2IsabelleHOL.testPEQs"

| otherwise = concentrate (matricize pEqs) sign

newPE (p, t) = ProgEq p t nullPos

newPEq cm = ProgEq (head (args cm)) (term cm) nullPos

shrinkPat :: CaseMatrix -> As.Term

shrinkPat caMa =

case patBrand caMa of

Appl -> case cons caMa of

Just c -> foldl mkApplT c ((args caMa) ++ (newArgs caMa))

Nothing -> error "HasCASL2IsabelleHOL.shrinkPat"

Tuple -> TupleTerm ((args caMa) ++ (newArgs caMa)) []

QuOp -> head (args caMa)

_ -> head (newArgs caMa)

where mkApplT t1 t2 = ApplTerm t1 t2 []

patIsVar :: ProgEq -> Bool

patIsVar (ProgEq pat _ _) = termIsVar pat

termIsVar :: As.Term -> Bool

termIsVar t = case t of

QualVar _ -> True

TypedTerm tr _ _ _ -> termIsVar tr

TupleTerm ts _ -> and (map termIsVar ts)

_ -> False

patHasNoArg :: ProgEq -> Bool

patHasNoArg (ProgEq pat _ _) = termHasNoArg pat

termHasNoArg :: As.Term -> Bool

termHasNoArg t = case t of

QualOp _ _ _ _ -> True

TypedTerm tr _ _ _ -> termHasNoArg tr

_ -> False

transCaseAlt :: Env -> ProgEq -> (IsaSign.Term, IsaSign.Term)

transCaseAlt sign (ProgEq pat trm _) =

(transPat sign pat, (transTerm sign trm))

transPat :: Env -> As.Term -> IsaSign.Term

transPat _ (QualVar (VarDecl var _ _ _)) =

IsaSign.Free (transVar var) noType isaTerm

transPat sign (ApplTerm term1 term2 _) =

termAppl (transPat sign term1) (transPat sign term2)

transPat sign (TypedTerm trm _ _ _) = transPat sign trm

transPat sign (TupleTerm terms _) =

foldl1 (binConst isaPair) (map (transPat sign) terms)

transPat _ (QualOp _ (InstOpId i _ _) _ _) = con (showIsa i)

transPat _ _ = error "HasCASL2IsabelleHOL.transPat"

showPEQ peqs = "PEQ-Liste: "++show (map spe peqs) ++"\n\n"

spe (ProgEq pat term _) = "PEQ Pattern: " ++ sT pat++" "++"Term: "++sT term++"\n"

sT (QualVar (VarDecl v _ _ _)) = show v

sT (QualOp _ (InstOpId i _ _) _ _) = show i

sT (ApplTerm t1 t2 _) = "ApplT ("++sT t1++") ("++sT t2++")"

sT (TupleTerm ts _) = "TupleT "++concat (map sT ts)

sT (TypedTerm t _ _ _) = "Typed "++sT t

sT (CaseTerm t peqs _) = "Case "++sT t++" "-- ++showPEQ peqs

sT t = show t

-- showCM cm = "MATRIX -+- Cons: PB: "++show (patBrand cm)++" Pats: "++concat (map sT (args cm))++" newArgs: "++concat (map sT (newArgs cm))++" term: "++sT (term cm)