{- |

Module : $Header$

Copyright : (c) Paolo Torrini and 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 Haskell to Isabelle-HOLCF.

-}

{- todo

use hana to look at outcome of Haskell files

type is in: Haskell.Hatchet.MultiModuleBasics -- main datatype

Haskell.Hatchet.Representation - types, kinds, schemes

Haskell.Hatchet.Env -- environments

look at Isabelle.IsaSign.hs

write function transSignature below,

test it with

hets -g file.hs

click at node, select "Translate theory" or "Prove"

select Haskell2IsabelleHOLCF

write function transSentence below

-}

module Comorphisms.HasCASL2IsabelleHOLCF 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)

import Debug.Trace

-- HasCASL

import Haskell.Hatchet.HsSyn

import Haskell.Hatchet.MultiModuleBasics (ModuleInfo,

emptyModuleInfo,

joinModuleInfo)

import Haskell.Hatchet.AnnotatedHsSyn (AHsDecl)

-- Isabelle

import Isabelle.IsaSign as IsaSign

import Isabelle.Logic_Isabelle

import Isabelle.IsaPrint

-- | The identity of the comorphism

data Haskell2IsabelleHOLCF = Haskell2IsabelleHOLCF deriving (Show)

instance Language Haskell2IsabelleHOLCF -- default definition is okay

{-

instance Comorphism Haskell2IsabelleHOLCF

Haskell Haskell_Sublogics

BasicSpec Le.Sentence SymbItems SymbMapItems

Env Morphism

Symbol RawSymbol ()

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

IsaSign.Sign

() () () () where

sourceLogic _ = Haskell

sourceSublogic _ = Haskell_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 = False,

has_type_constructors = False,

which_logic = HOL

}

targetLogic _ = Isabelle

targetSublogic _ = ()

map_sign _ = transSignature

--map_morphism _ morphism1 -> Maybe morphism2

map_sentence _ sign phi =

Just $ Sentence {senTerm = (transSentence sign phi)}

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

-}

---------------------------- Signature -----------------------------

-- data Sign = Sign { baseSig :: String, -- like Pure, HOL etc.

-- tsig :: TypeSig,

-- constTab :: Map.Map String Typ,

-- syn :: Syntax

-- }

transSignature :: ModuleInfo

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

-- see Common/Result.hs

-- needs to be done! Below, just the HasCASL code!!!

transSignature sign =

Just(IsaSign.Sign{

baseSig = "MainHC",

tsig = emptyTypeSig

{tycons = Map.foldWithKey extractTypeName

Map.empty

(typeMap sign)},

constTab = Map.foldWithKey insertOps

Map.empty

(assumps sign),

dataTypeTab = transDatatype (typeMap sign),

syn = (),

showLemmas = False },

[] ) -- for now, no sentences

where

extractTypeName typeId typeInfo m = if isDatatypeDefn typeInfo then m

else Map.insert (showIsa typeId) 0 m

isDatatypeDefn t = case typeDefn t of

DatatypeDefn _ -> True

_ -> False

insertOps opName opInfs m =

let opIs = opInfos opInfs

in if (length opIs) == 1 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])

transOpInfo :: OpInfo -> Maybe Typ

transOpInfo (OpInfo opT _ opDef) =

case opDef of

NoOpDefn Pred -> Just (transPredType opT)

NoOpDefn _ -> Just (transOpType opT)

ConstructData _ -> Nothing

_ -> error "[Comorphims.Haskell2IsabelleHOLCF] Not supported operation declaration and/or definition"

transOpType :: TypeScheme -> Typ

transOpType (TypeScheme _ op _) = transType op

transPredType :: TypeScheme -> Typ

transPredType (TypeScheme _ pre _) =

case pre of

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

_ ->

error "[Comorphims.Haskell2IsabelleHOLCF] Wrong predicate type"

transType :: Type -> Typ

transType (TypeName typeId _ i) = if i == 0 then Type(showIsa typeId,[])

else TVar((showIsa typeId,0),[])

transType (ProductType types _) = foldl1 IsaSign.mkProductType

(map transType types)

transType (FunType type1 arr type2 _) =

case arr of

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

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

_ ->

error "[Comorphims.Haskell2IsabelleHOLCF] Not supported function type"

transType (TypeAppl type1 type2) = Type("typeAppl", [transType type1] ++ [transType type2])

transType _ = error "[Comorphims.Haskell2IsabelleHOLCF] Not supported type"

transDatatype :: TypeMap -> DataTypeTab

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

extractDataypes :: TypeInfo -> [DataEntry] -> [DataEntry]

extractDataypes ti des = case typeDefn ti of

DatatypeDefn de -> des++[de]

_ -> des

transDataEntry :: DataEntry -> DataTypeTabEntry

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

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

transDataEntry _ =

error "[Comorphims.Haskell2IsabelleHOLCF] Not supported datatype definition"

mkDName :: TypeId -> [TypeArg] -> Typ

mkDName tyId tyArgs = Type(showIsa tyId,(map transTypeArg tyArgs)) --Type("typeAppl",(Type(showIsa tyId,[])):(map transTypeArg tyArgs)) --

transTypeArg :: TypeArg -> Typ

transTypeArg (TypeArg tyId _ _ _) = TVar((showIsa tyId,0),[])

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 (Construct _ _ Partial _) = error "[Comorphims.Haskell2IsabelleHOLCF] Not supported alternative definition in (free) datatype"

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

transVar :: Var -> String

transVar = showIsa

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

transSentence e s = case s of

Le.Formula t -> transTerm e t

DatatypeSen l -> con "Ich bin gar kein richtiges Axiom..." -- transDataEntryAx (head l)

ProgEqSen _ _ _pe ->

error "[Comorphims.Haskell2IsabelleHOLCF] transSentence: program"

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

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

let tp = transType typ

otp = tp --> mkOptionType tp

in (conSomeT otp) `App` IsaSign.Free(transVar var, tp)

transTerm _ (QualOp _ (InstOpId opId _ _) _ _)

| opId == trueId = con "True"

| opId == falseId = con "False"

| otherwise = conSome `App` con (getNameOfOpId opId)

transTerm sign (ApplTerm term1 term2 _) =

testTerm term1

where

-- trace ("Constructors?? "++ show (ApplTerm term1 term2 p) ++ "\n")

testTerm t =

case t of

QualOp Fun (InstOpId opId _ _) _ _ -> transLog sign opId term1 term2

QualOp Pred _ _ _ -> con "pApp"

`App` (transTerm sign term1)

`App` (transTerm sign term2)

QualOp Op _ typeScheme _ -> if isPart typeScheme then mkApp "app"

else mkApp "apt"

ApplTerm t1 _ _ -> testTerm t1

_ -> mkApp "app"

where mkApp s = con s

`App` (transTerm sign term1)

`App` (transTerm sign term2)

isPart (TypeScheme _ op _) =

case op of

FunType _ PFunArr _ _ -> True

FunType _ FunArr _ _ -> False

_ ->

error "[Comorphims.Haskell2IsabelleHOLCF] Wrong operation type"

transTerm sign (QuantifiedTerm quan varDecls phi _) =

foldr (quantify quan)

(transTerm sign phi)

(map toPair varDecls)

transTerm sign (TypedTerm term _ _ _) = transTerm sign term

transTerm sign (LambdaTerm pats part body _) =

case part of

Partial -> lambdaAbs transTerm

Total -> lambdaAbs transTotalLambda

where

lambdaAbs f =

if (null pats) then conSome

`App` Abs(IsaSign.Free("dummyVar",dummyT),

dummyT,

(f sign body))

else conSome `App` (foldr (abstraction sign)

(f sign body)

pats)

transTerm sign (LetTerm Let eqs body _) =

transTerm sign (foldr let2lambda body eqs)

transTerm sign (TupleTerm terms _) =

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

transTerm sign (CaseTerm term pEqs _) =

-- trace ("pEqs " ++ show pEqs ++ "\n")

let alts = arangeCaseAlts sign pEqs

in

case term of

QualVar (VarDecl decl _ _ _) -> Case (IsaSign.Free(transVar decl, dummyT), alts)

_ ->

Case (transTerm sign term,

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

[(conSome `App` IsaSign.Free("caseVar", dummyT),

Case (IsaSign.Free("caseVar", dummyT), alts))])

transTerm _ _ =

error "[Comorphims.Haskell2IsabelleHOLCF] Not supported (abstract) syntax."

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

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

IsaSign.Free(transVar var, transType typ)

transTotalLambda _ (QualOp _ (InstOpId opId _ _) _ _)

| opId == trueId = con "True"

| opId == falseId = con "False"

| otherwise = con (getNameOfOpId opId)

transTotalLambda sign (ApplTerm term1 term2 _) = (transTotalLambda sign term1) `App` (transTotalLambda sign term2)

-- testTerm term1

-- where

-- -- trace ("Constructors?? "++ show (ApplTerm term1 term2 p) ++ "\n")

-- testTerm t =

-- case t of

-- QualOp Fun (InstOpId opId _ _) _ _ -> transLog sign opId term1 term2

-- QualOp Pred _ _ _ -> con "pApp"

-- `App` (transTerm sign term1)

-- `App` (transTerm sign term2)

-- QualOp Op _ typeScheme _ -> if isPart typeScheme then mkApp "app"

-- else mkApp "apt"

-- ApplTerm t1 _ _ -> testTerm t1

-- _ -> mkApp "app"

-- where mkApp s = con s

-- `App` (transTerm sign term1)

-- `App` (transTerm sign term2)

-- isPart (TypeScheme _ op _) =

-- case op of

-- FunType _ PFunArr _ _ -> True

-- FunType _ FunArr _ _ -> False

-- _ ->

-- error "[Comorphims.Haskell2IsabelleHOLCF] Wrong operation type"

-- transTerm sign (QuantifiedTerm quan varDecls phi _) =

-- foldr (quantify quan)

-- (transTerm sign phi)

-- (map toPair varDecls)

transTotalLambda sign (TypedTerm term _ _ _) = transTotalLambda sign term

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",dummyT),

dummyT,

(f sign body))

else (foldr (abstraction sign)

(f sign body)

pats)

transTotalLambda sign (LetTerm Let eqs body _) =

transTotalLambda sign (foldr let2lambda body eqs)

transTotalLambda sign (TupleTerm terms _) =

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

transTotalLambda sign (CaseTerm term pEqs _) =

-- trace ("pEqs " ++ show pEqs ++ "\n")

Case (transTotalLambda sign term, map transCaseAltTotal pEqs)

where transCaseAltTotal (ProgEq pat term _) =

(transPat sign pat, transTotalLambda sign term)

transTotalLambda _ _ =

error "[Comorphims.Haskell2IsabelleHOLCF] Not supported (abstract) syntax."

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

transCaseEx sign term =

case term of

QualVar (VarDecl decl _ _ _) -> IsaSign.Free(transVar decl, dummyT)

_ -> transTerm sign term

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

arangeCaseAlts sign pEqs =

let pats = map stripProgEq pEqs

in

case pats of

(QualVar _):[] -> map (transCaseAlt sign) pEqs

_ -> sortCaseAlts sign pEqs

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

sortCaseAlts sign pEqs =

concat (map (unfoldCons sign) (map (groupCons pEqs)

(getCons sign (getName (head pEqs)))))

getName :: ProgEq -> TypeId

getName (ProgEq pat _ _) =

getTypeName pat

where getTypeName pat = case pat of

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

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

TypedTerm _ _ typ _ -> name typ

ApplTerm t _ _ -> getTypeName t

-- TupleTerm

name t = case t of

TypeName tyId _ 0 -> tyId

TypeAppl t _ -> name t

-- FunType t1 _ t2 ->

-- ProductType

_ ->

error "[Comorphims.Haskell2IsabelleHOLCF] Not supported type"

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

getCons sign tId =

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

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

catMaybes (map ll altDefns)

ll (Construct i _ _ _) = i

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 t2 _ -> hsn t1

TypedTerm t _ _ _ -> hsn t

-- TupleTerm

_ -> False

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

unfoldCons sign pEqs =

let pats = map stripProgEq pEqs

in

if and (map noArgs pats) || and (map argIsVar pats)

then map (transCaseAlt sign) pEqs

else substArg sign pEqs

where noArgs t = case t of

QualOp _ _ _ _ -> True

QualVar _ -> True

_ -> False

argIsVar pat = case pat of

ApplTerm _ t _ -> case t of

QualVar _ -> True

ApplTerm _ t _ -> argIsVar t

_ -> False

QualVar _ -> True

TypedTerm t _ _ _ -> argIsVar t

-- TupleTerm

_ -> False

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

substArg sign pEqs =

let frontCons = transPat sign (getFrontCons pEqs)

varName = "consVar" ++ show (length pEqs)

newPat = frontCons `App` IsaSign.Free(varName, dummyT)

varId = (mkId [(mkSimpleId varName)])

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

newTerm = transTerm sign (CaseTerm newVar newPEqs [])

newPEqs = map getNewPEqs pEqs

in

[(newPat, newTerm)]

where getFrontCons ((ProgEq pat _ _):pEqs) =

case pat of

ApplTerm t _ _ -> t

_ -> pat

getNewPEqs (ProgEq pat term p) =

case pat of

ApplTerm _ t _ -> ProgEq t term p

_ -> ProgEq pat term p

-- VarDecl Var Type SeparatorKind [Pos]

stripProgEq :: ProgEq -> Pattern

stripProgEq (ProgEq pat t pos) = case pat of

TypedTerm p _ _ _ -> stripProgEq (ProgEq p t pos)

-- TupleTerm ->

_ -> pat

-- -- grep the names of all constructors

-- grepCons :: [Pattern] -> [InstOpId]

-- grepCons pats =

-- nub (catMaybes (map allCons pats))

-- where allCons pat =

-- case pat of

-- QualOp _ name _ _ -> Just (name)

-- ApplTerm t1 t2 _ -> allCons t1

-- TypedTerm t _ _ _ -> allCons t

-- QualVar _ -> Nothing

-- -- TupleTerm

-- _ ->

-- error "[Comorphims.Haskell2IsabelleHOLCF] Illegal case pattern."

{- 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

-}

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

transCaseAlt sign (ProgEq pat term _) =

(transPat sign pat, transTerm sign term)

--Abs (transTerm sign pat, dummyT, transTerm sign term)

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

transPat _ (QualVar (VarDecl var _ _ _)) = IsaSign.Free(transVar var, dummyT)

transPat sign (ApplTerm term1 term2 _) =

(transPat sign term1) `App` (transPat sign term2)

transPat sign (TypedTerm term _ _ _) = transPat sign term

-- transPat sign (LambdaTerm pats Partial body _) =

-- if (null pats) then Abs(IsaSign.Free("dummyVar",dummyT),

-- dummyT,

-- (transPat sign body))

-- else foldr (abstraction sign)

-- (transPat sign body)

-- pats

-- transPat sign (LetTerm Let eqs body _) =

-- transPat sign (foldr let2lambda body eqs)

transPat sign (TupleTerm terms _) =

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

transPat _ (QualOp _ (InstOpId id _ _) _ _) = con (getNameOfOpId id)

transPat _ _ = error "[Comorphims.Haskell2IsabelleHOLCF] Not supported (abstract) syntax."

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

let2lambda (ProgEq pat term _) body =

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

getType :: As.Term -> Typ

getType term = case term of

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

TypedTerm _ _ typ _ -> transType typ

TupleTerm terms _ -> evalTupleType terms

_ -> error "[Comorphims.Haskell2IsabelleHOLCF] Illegal pattern in lambda abstraction"

where evalTupleType t = foldr1 IsaSign.mkProductType

(map getType t)

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

transLog sign opId opTerm term

| 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 = (con "Not") `App` (transTerm sign term)

| opId == defId = defOp `App` (transTerm sign term)

| opId == exEq =

binConst conj

(binConst conj

(binConst eq (transTerm sign t1)

(transTerm sign t2))

(defOp `App` (transTerm sign t1)))

(defOp `App` (transTerm sign t2))

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

(transTerm sign t2)

| otherwise = (transTerm sign opTerm) `App` (transTerm sign term)

where ts = getTerms term

t1 = head ts

t2 = last ts

getTerms (TupleTerm terms _) = terms

getTerms _ = error "[Comorphims.Haskell2IsabelleHOLCF] Incorrect formula coding in abstract syntax"

quantify :: Quantifier -> (Var,Type) -> IsaSign.Term -> IsaSign.Term

quantify q (v,t) phi =

con (qname q) `App` Abs (con (transVar v), transType t, phi)

where

qname Universal = "All"

qname Existential = "Ex"

qname Unique = "Ex1"

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

abstraction sign pat body = Abs((transTermAbs sign pat), getType pat, body)

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

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

IsaSign.Free(transVar var, transType typ)

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

(map (transTermAbs sign) terms)

transTermAbs _ (QualOp _ (InstOpId opId _ _) _ _) = con (getNameOfOpId opId)

transTermAbs sign term = transTerm sign term

getNameOfOpId :: Id -> String

getNameOfOpId (Id [] _ _) = error "[Comorphims.Haskell2IsabelleHOLCF] Operation without name"

getNameOfOpId (Id (tok:toks) a b) =

if (tokStr tok) == "__" then getNameOfOpId (Id toks a b)

else tokStr tok

-- isLogId :: Id -> Bool

-- isLogId i = (i == andId)

-- || (i == orId)

-- || (i == implId)

-- || (i == eqvId)

-- || (i == notId)

-- || (i == defId)

-- || (i == exEq)

-- || (i == eqId)

toPair :: GenVarDecl -> (Var,Type)

toPair (GenVarDecl (VarDecl var typ _ _)) = (var,typ)

toPair _ = error "[Comorphims.Haskell2IsabelleHOLCF] Not supported GenVarDecl"

binConst :: String -> IsaSign.Term -> IsaSign.Term -> IsaSign.Term

binConst s t1 t2 = termAppl (termAppl (con s) t1) t2

termAppl :: IsaSign.Term -> IsaSign.Term -> IsaSign.Term

termAppl t1 t2 = t1 `App` t2

con :: String -> IsaSign.Term

con s = Const(s, dummyT)

conSome :: IsaSign.Term

conSome = con "Some"

conSomeT :: Typ -> IsaSign.Term

conSomeT t = Const("Some", t)

defOp :: IsaSign.Term

defOp = con "defOp"

conj :: String

conj = "op &"

disj :: String

disj = "op |"

impl :: String

impl = "op -->"

eqv :: String

eqv = "op <=>"

eq :: String

eq = "op ="

pairC :: String

pairC = "pair"

isaPair :: String

isaPair = "Pair"

some :: String

some = "Some"