{-# LANGUAGE MultiParamTypeClasses, TypeSynonymInstances, FlexibleInstances #-}

{- |

Module : ./Comorphisms/CFOL2IsabelleHOL.hs

Description : embedding from CASL (CFOL) to Isabelle-HOL

Copyright : (c) Till Mossakowski and Uni Bremen 2003-2005

License : GPLv2 or higher, see LICENSE.txt

Maintainer : Christian.Maeder@dfki.de

Stability : provisional

Portability : non-portable (imports Logic.Logic)

The embedding comorphism from CASL to Isabelle-HOL.

-}

module Comorphisms.CFOL2IsabelleHOL

( CFOL2IsabelleHOL (..)

, transTheory

, transVar

, typeToks

, mapSen

, IsaTheory

, SignTranslator

, FormulaTranslator

, getAssumpsToks

, formTrCASL

, quantifyIsa

, quantify

, transFORMULA

, transSort

, transRecord

, transOpSymb

) where

import Logic.Logic

import Logic.Comorphism

import CASL.Logic_CASL

import CASL.AS_Basic_CASL

import CASL.Sublogic as SL

import CASL.Sign

import CASL.Morphism

import CASL.Quantification

import CASL.Fold

import CASL.Induction

import CASL.ToDoc

import Isabelle.IsaSign as IsaSign hiding (qname)

import Isabelle.IsaConsts

import Isabelle.Logic_Isabelle

import Isabelle.Translate

import Common.AS_Annotation

import Common.Id

import Common.ProofTree

import Common.Utils

import qualified Common.Lib.MapSet as MapSet

import qualified Data.Map as Map

import qualified Data.Set as Set

import Data.List

-- | The identity of the comorphism

data CFOL2IsabelleHOL = CFOL2IsabelleHOL deriving Show

-- Isabelle theories

type IsaTheory = (IsaSign.Sign, [Named IsaSign.Sentence])

-- extended signature translation

type SignTranslator f e = CASL.Sign.Sign f e -> e -> IsaTheory -> IsaTheory

-- extended signature translation for CASL

sigTrCASL :: SignTranslator () ()

sigTrCASL _ _ = id

-- extended formula translation

type FormulaTranslator f e = CASL.Sign.Sign f e -> Set.Set String -> f -> Term

-- extended formula translation for CASL

formTrCASL :: FormulaTranslator () ()

formTrCASL _ _ = error "CFOL2IsabelleHOL: No extended formulas allowed in CASL"

instance Language CFOL2IsabelleHOL where

language_name CFOL2IsabelleHOL = "CASL2Isabelle"

instance Comorphism CFOL2IsabelleHOL

CASL CASL_Sublogics

CASLBasicSpec CASLFORMULA SYMB_ITEMS SYMB_MAP_ITEMS

CASLSign

CASLMor

Symbol RawSymbol ProofTree

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

IsaSign.Sign

IsabelleMorphism () () () where

sourceLogic CFOL2IsabelleHOL = CASL

sourceSublogic CFOL2IsabelleHOL = SL.cFol

targetLogic CFOL2IsabelleHOL = Isabelle

mapSublogic cid sl = if sl `isSubElem` sourceSublogic cid

then Just () else Nothing

map_theory CFOL2IsabelleHOL = return . transTheory sigTrCASL formTrCASL

map_sentence CFOL2IsabelleHOL sign =

return . mapSen formTrCASL sign (typeToks sign)

has_model_expansion CFOL2IsabelleHOL = True

is_weakly_amalgamable CFOL2IsabelleHOL = True

isInclusionComorphism CFOL2IsabelleHOL = True

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

baseSign :: BaseSig

baseSign = Main_thy

typeToks :: CASL.Sign.Sign f e -> Set.Set String

typeToks = Set.map (`showIsaTypeT` baseSign) . sortSet

transTheory :: FormExtension f => SignTranslator f e ->

FormulaTranslator f e ->

(CASL.Sign.Sign f e, [Named (FORMULA f)])

-> IsaTheory

transTheory trSig trForm (sign, sens) =

trSig sign (extendedInfo sign) (IsaSign.emptySign {

baseSig = baseSign,

tsig = emptyTypeSig {arities =

Set.fold (\ s -> let s1 = showIsaTypeT s baseSign in

Map.insert s1 [(isaTerm, [])])

Map.empty (sortSet sign)},

constTab = Map.foldWithKey insertPreds

(Map.foldWithKey insertOps Map.empty

. MapSet.toMap $ opMap sign) . MapSet.toMap $ predMap sign,

domainTab = dtDefs},

map (\ (s, n) -> makeNamed ("ga_induction_" ++ show n) $ myMapSen s)

(number gens) ++

map (mapNamed myMapSen) real_sens)

-- for now, no new sentences

where

gens =

map (inductionScheme . fst) genTypes

tyToks = typeToks sign

myMapSen = mkSen . transFORMULA sign tyToks trForm (getAssumpsToks sign)

(real_sens, sort_gen_axs) = foldr ( \ s (rs, cs) -> case sentence s of

Sort_gen_ax c b -> (rs, (c, b) : cs)

_ -> (s : rs, cs)) ([], []) sens

unique_sort_gen_axs = nubOrdOn (Set.fromList . map newSort . fst)

sort_gen_axs

(freeTypes, genTypes) = partition snd unique_sort_gen_axs

dtDefs = makeDtDefs sign tyToks $ map fst freeTypes

ga = globAnnos sign

insertOps op ts m = if isSingleton ts then

let t = Set.findMin ts in Map.insert

(mkIsaConstT False ga (length $ opArgs t) op baseSign tyToks)

(transOpType t) m

else foldl (\ m1 (t, i) -> Map.insert

(mkIsaConstIT False ga (length $ opArgs t) op i baseSign tyToks)

(transOpType t) m1) m $ number $ Set.toList ts

insertPreds pre ts m = if isSingleton ts then

let t = Set.findMin ts in Map.insert

(mkIsaConstT True ga (length $ predArgs t) pre baseSign tyToks)

(transPredType t) m

else foldl (\ m1 (t, i) -> Map.insert

(mkIsaConstIT True ga (length $ predArgs t) pre i baseSign tyToks)

(transPredType t) m1) m $ number $ Set.toList ts

makeDtDefs :: CASL.Sign.Sign f e -> Set.Set String -> [[Constraint]]

-> [[(Typ, [(VName, [Typ])])]]

makeDtDefs sign = map . makeDtDef sign

makeDtDef :: CASL.Sign.Sign f e -> Set.Set String -> [Constraint]

-> [(Typ, [(VName, [Typ])])]

makeDtDef sign tyToks constrs = map makeDt srts where

(srts, ops, _maps) = recover_Sort_gen_ax constrs

makeDt s = (transSort s, map makeOp (filter (hasTheSort s) ops))

makeOp opSym = (transOpSymb sign tyToks opSym, transArgs opSym)

hasTheSort s (Qual_op_name _ ot _) = s == res_OP_TYPE ot

hasTheSort _ _ = error "CFOL2IsabelleHOL.hasTheSort"

transArgs (Qual_op_name _ ot _) = map transSort $ args_OP_TYPE ot

transArgs _ = error "CFOL2IsabelleHOL.transArgs"

transSort :: SORT -> Typ

transSort s = Type (showIsaTypeT s baseSign) [] []

transOpType :: OpType -> Typ

transOpType ot = mkCurryFunType (map transSort $ opArgs ot)

$ transSort (opRes ot)

transPredType :: PredType -> Typ

transPredType pt = mkCurryFunType (map transSort $ predArgs pt) boolType

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

getAssumpsToks :: CASL.Sign.Sign f e -> Set.Set String

getAssumpsToks sign = Map.foldWithKey ( \ i ops s ->

Set.union s $ Set.unions

$ map ( \ (_, o) -> getConstIsaToks i o baseSign)

$ number $ Set.toList ops)

(Map.foldWithKey ( \ i prds s ->

Set.union s $ Set.unions

$ map ( \ (_, o) -> getConstIsaToks i o baseSign)

$ number $ Set.toList prds) Set.empty . MapSet.toMap

$ predMap sign)

. MapSet.toMap $ opMap sign

transVar :: Set.Set String -> VAR -> String

transVar toks v = let

s = showIsaConstT (simpleIdToId v) baseSign

renVar t = if Set.member t toks then renVar $ "X_" ++ t else t

in renVar s

quantifyIsa :: String -> (String, Typ) -> Term -> Term

quantifyIsa q (v, _) phi =

termAppl (conDouble q) (Abs (mkFree v) phi NotCont)

quantify :: Set.Set String -> QUANTIFIER -> (VAR, SORT) -> Term -> Term

quantify toks q (v, t) =

quantifyIsa (qname q) (transVar toks v, transSort t)

where

qname Universal = allS

qname Existential = exS

qname Unique_existential = ex1S

transOpSymb :: CASL.Sign.Sign f e -> Set.Set String -> OP_SYMB -> VName

transOpSymb sign tyToks qo = case qo of

Qual_op_name op ot _ -> let

ga = globAnnos sign

l = length $ args_OP_TYPE ot

in case Set.toList . MapSet.lookup op $ opMap sign of

[] -> error $ "CASL2Isabelle unknown op: " ++ show op

[_] -> mkIsaConstT False ga l op baseSign tyToks

ots -> case elemIndex (toOpType ot) ots of

Just i -> mkIsaConstIT False ga l op (i + 1) baseSign tyToks

Nothing -> error $ "CASL2Isabelle unknown type for op: " ++ show op

Op_name op -> error $ "CASL2Isabelle: unqualified op: " ++ show op

transPredSymb :: CASL.Sign.Sign f e -> Set.Set String -> PRED_SYMB -> VName

transPredSymb sign tyToks qp =

let ga = globAnnos sign

d = mkIsaConstT True ga (-1) (predSymbName qp) baseSign tyToks

-- for predicate names in induction schemes

in case qp of

Qual_pred_name p pt@(Pred_type args _) _ -> let

l = length args

in case Set.toList . MapSet.lookup p $ predMap sign of

[] -> d

[_] -> mkIsaConstT True ga l p baseSign tyToks

pts -> case elemIndex (toPredType pt) pts of

Just i -> mkIsaConstIT True ga l p (i + 1) baseSign tyToks

Nothing -> d

Pred_name _ -> d

mapSen :: FormulaTranslator f e -> CASL.Sign.Sign f e -> Set.Set String

-> FORMULA f -> Sentence

mapSen trForm sign tyToks =

mkSen . transFORMULA sign tyToks trForm (getAssumpsToks sign)

transRecord :: CASL.Sign.Sign f e -> Set.Set String -> FormulaTranslator f e

-> Set.Set String -> Record f Term Term

transRecord sign tyToks tr toks = Record

{ foldQuantification = \ _ qu vdecl phi _ ->

foldr (quantify toks qu) phi (flatVAR_DECLs vdecl)

, foldJunction = \ _ j phis _ -> let

(n, op) = case j of

Con -> (true, binConj)

Dis -> (false, binDisj)

in if null phis then n else foldr1 op phis

, foldRelation = \ _ phi1 c phi2 _ -> (if c == Equivalence

then binEqv else binImpl) phi1 phi2

, foldNegation = \ _ phi _ -> termAppl notOp phi

, foldAtom = \ _ b _ -> if b then true else false

, foldPredication = \ _ psymb args _ ->

foldl termAppl (con $ transPredSymb sign tyToks psymb) args

, foldDefinedness = \ _ _ _ -> true -- totality assumed

, foldEquation = \ _ t1 _ t2 _ -> binEq t1 t2 -- equal types assumed

, foldMembership = \ _ _ _ _ -> true -- no subsorting assumed

, foldMixfix_formula = error "transRecord: Mixfix_formula"

, foldSort_gen_ax = error "transRecord: Sort_gen_ax"

, foldQuantOp = error "transRecord: QuantOp"

, foldQuantPred = error "transRecord: QuantPred"

, foldExtFORMULA = \ _ -> tr sign tyToks

, foldQual_var = \ _ v _ _ -> mkFree $ transVar toks v

, foldApplication = \ _ opsymb args _ ->

foldl termAppl (con $ transOpSymb sign tyToks opsymb) args

, foldSorted_term = \ _ t _ _ -> t -- no subsorting assumed

, foldCast = \ _ t _ _ -> t -- no subsorting assumed

, foldConditional = \ _ t1 phi t2 _ -> -- equal types assumed

If phi t1 t2 NotCont

, foldMixfix_qual_pred = error "transRecord: Mixfix_qual_pred"

, foldMixfix_term = error "transRecord: Mixfix_term"

, foldMixfix_token = error "transRecord: Mixfix_token"

, foldMixfix_sorted_term = error "transRecord: Mixfix_sorted_term"

, foldMixfix_cast = error "transRecord: Mixfix_cast"

, foldMixfix_parenthesized = error "transRecord: Mixfix_parenthesized"

, foldMixfix_bracketed = error "transRecord: Mixfix_bracketed"

, foldMixfix_braced = error "transRecord: Mixfix_braced"

, foldExtTERM = error "transRecord: ExtTERM"

}

transFORMULA :: CASL.Sign.Sign f e -> Set.Set String -> FormulaTranslator f e

-> Set.Set String -> FORMULA f -> Term

transFORMULA sign tyToks tr = foldFormula . transRecord sign tyToks tr