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

{- |

Module : $Header$

Description : translating from HolLight to Isabelle

Copyright : (c) Jonathan von Schroeder and M. Codescu, DFKI 2010

License : GPLv2 or higher, see LICENSE.txt

Maintainer : jonathan.von_schroeder@dfki.de

Stability : provisional

Portability : non-portable (imports Logic.Logic)

-}

module Comorphisms.HolLight2Isabelle where

import Logic.Comorphism

import Logic.Logic

import qualified Isabelle.IsaSign as IsaSign

import Isabelle.Logic_Isabelle

import Isabelle.IsaConsts as IsaConsts

import Isabelle.Translate

import Common.Result

import Common.AS_Annotation

import qualified Data.Map as Map

import qualified Data.Set as Set

import Data.List ((\\))

import HolLight.Sign

import HolLight.Sentence

import HolLight.Term

import HolLight.Logic_HolLight

import HolLight.Sublogic

import HolLight.Helper

data HolLight2Isabelle = HolLight2Isabelle deriving Show

instance Language HolLight2Isabelle

instance Comorphism HolLight2Isabelle

HolLight

HolLightSL -- sublogic

() -- basic_spec

Sentence -- sentence

() -- symb_items

() -- symb_map_items

Sign -- sign

HolLightMorphism -- morphism

() -- symbol

() -- raw_symbol

() -- proof_tree

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

IsaSign.Sign

IsabelleMorphism () () () where

sourceLogic _ = HolLight

sourceSublogic _ = Top

targetLogic _ = Isabelle

mapSublogic _ _ = Just ()

map_theory HolLight2Isabelle = mapTheory

map_morphism = mapDefaultMorphism

map_sentence HolLight2Isabelle = mapSentence

-- mapping sentences

mapSentence :: Sign -> Sentence -> Result IsaSign.Sentence

mapSentence _ s = return $ mapHolSen s

mapHolSen :: Sentence -> IsaSign.Sentence

mapHolSen (Sentence t _) = IsaSign.Sentence {

IsaSign.isSimp = False

, IsaSign.isRefuteAux = False

, IsaSign.metaTerm =

IsaSign.Term $ translateTerm t

, IsaSign.thmProof = Nothing

}

tp2DTyp :: HolType -> IsaSign.DTyp

tp2DTyp tp = IsaSign.Hide {

IsaSign.typ = tp2Typ tp,

IsaSign.kon = IsaSign.TCon,

IsaSign.arit = Nothing

}

constMap :: Map.Map String IsaSign.VName

constMap = Map.fromList [("+", IsaConsts.plusV)

, ("-", IsaConsts.minusV)

, ("*", IsaConsts.timesV)

, ("!", IsaSign.mkVName IsaConsts.allS)

, ("?", IsaSign.mkVName IsaConsts.exS)

, ("?!", IsaSign.mkVName IsaConsts.ex1S)

, ("=", IsaConsts.eqV)

, ("<=>", IsaConsts.eqV)

, ("/\\", IsaConsts.conjV)

, ("\\/", IsaConsts.disjV)

, ("==>", IsaConsts.implV)

, ("~", IsaConsts.notV)

, ("F", IsaSign.mkVName IsaConsts.cTrue)

, ("T", IsaSign.mkVName IsaConsts.cFalse)

]

notIgnore :: [String]

notIgnore = ["+", "-", "*"]

ignore :: [String]

ignore = (map fst $ Map.toList constMap) \\ notIgnore

transConstS :: String -> HolType -> IsaSign.VName

transConstS s t = case (Map.lookup s constMap, elem s notIgnore) of

(Just v, False) -> v

(_, _) -> IsaSign.mkVName $ typedName s t

typedName :: String -> HolType -> String

typedName s t = transConstStringT bs $ s ++ "_" ++ (show $ pp_print_type t)

unpack_gabs :: Term -> (IsaSign.Term, [IsaSign.Term], IsaSign.Term, IsaSign.Term)

unpack_gabs t = case unpack_gabs' t [] of

Just (q, vs, tm) ->

let (pat, res) = case tm of

Comb (Comb (Const "GEQ" _ _)

(Comb (Var "f" _ _) pat1)) res1 -> (pat1, res1)

_ -> error "unpack_gabs failed"

in (q, vs, translateTerm pat, translateTerm res)

Nothing -> error "unpack_gabs' failed"

unpack_gabs' :: Term -> [IsaSign.Term] -> Maybe (IsaSign.Term, [IsaSign.Term], Term)

unpack_gabs' (Comb c@(Const "!" _ _) (Abs v@(Var _ _ _) tm)) vs =

case unpack_gabs' tm ((translateTerm v) : vs) of

Just r -> Just r

Nothing -> Just (translateTerm c, (translateTerm v) : vs, tm)

unpack_gabs' _ _ = Nothing

makeForAll :: IsaSign.Term -> [IsaSign.Term] -> IsaSign.Term -> IsaSign.Term

makeForAll _ [] t = t

makeForAll q (v : vs) t = IsaSign.App q

(IsaSign.Abs v

(makeForAll q vs t)

IsaSign.NotCont)

IsaSign.NotCont

handleGabs :: Bool -> Term -> IsaSign.Term

handleGabs b t = case t of

(Comb (Const "GABS" _ _) (Abs (Var "f" _ _) tm)) ->

let (q, vars, pat, res) = unpack_gabs tm in

let n = IsaSign.Free $ IsaSign.mkVName "p" in

let t1 = IsaSign.Abs n

(IsaSign.Case n [(pat, res)])

IsaSign.NotCont

in if b then makeForAll q vars (IsaSign.App q t1

IsaSign.NotCont)

else t1

_ -> error "handleGabs failed"

mkAbs :: Term -> IsaSign.Term

mkAbs t = IsaSign.Abs

(IsaSign.Free (IsaSign.mkVName "y"))

(IsaSign.App (translateTerm t)

(IsaSign.Free (IsaSign.mkVName "y"))

IsaSign.NotCont)

IsaSign.NotCont

mkQuantifier :: Term -> IsaSign.Term

mkQuantifier t = IsaSign.Abs

(IsaSign.Free (IsaSign.mkVName "y"))

(IsaSign.App (translateTerm t)

(IsaSign.Abs

(IsaSign.Free (IsaSign.mkVName "y"))

(IsaSign.Free (IsaSign.mkVName "y"))

IsaSign.NotCont)

IsaSign.NotCont)

IsaSign.NotCont

isAppT :: HolType -> Bool

isAppT (TyApp _ _) = True

isAppT _ = False

isQuantifier :: Term -> Bool

isQuantifier (Const c _ _) = elem c ["!", "?", "?!"]

isQuantifier _ = False

translateTerm :: Term -> IsaSign.Term

translateTerm (Comb (Comb (Const "," _ _) a) b) = IsaSign.Tuplex [translateTerm a, translateTerm b] IsaSign.NotCont

translateTerm (Var s tp _) = IsaSign.Free $ (transConstS s tp)

translateTerm (Const s tp _) = IsaSign.Const (transConstS s tp) $ tp2DTyp tp

translateTerm (Comb (Const "!" _ _) t@(Comb (Const "GABS" _ _) _)) = handleGabs True t

translateTerm t@(Comb (Const "GABS" _ _) (Abs (Var "f" _ _) _)) = handleGabs False t

translateTerm (Comb (Comb (Comb (Const "COND" _ _) i) t) e) = IsaSign.If

(translateTerm i)

(translateTerm t)

(translateTerm e)

IsaSign.NotCont

translateTerm (Comb c1@(Const c tp _) t) = if (is_abs t) || ((isAppT tp) && not (isQuantifier t) && not (isQuantifier c1) && c /= "@")

then IsaSign.App

(translateTerm c1)

(translateTerm t)

IsaSign.NotCont

else IsaSign.App (translateTerm c1)

(if isQuantifier t

then (mkQuantifier t)

else (mkAbs t))

IsaSign.NotCont

translateTerm (Comb tm1 tm2) = IsaSign.App (translateTerm tm1)

(translateTerm tm2)

IsaSign.NotCont

translateTerm (Abs tm1 tm2) = IsaSign.Abs (translateTerm tm1)

(translateTerm tm2)

IsaSign.NotCont

-- mapping theories

mapTheory :: (Sign, [Named Sentence]) ->

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

mapTheory (sig, n_sens) = let

sig' = mapSign sig

n_sens' = map mapNamedSen n_sens

in return (sig', n_sens')

bs :: IsaSign.BaseSig

bs = IsaSign.MainHC_thy

mapSign :: Sign -> IsaSign.Sign

mapSign (Sign t o) = IsaSign.emptySign {

IsaSign.baseSig = IsaSign.MainHC_thy,

IsaSign.constTab = mapOps o,

IsaSign.tsig = mapTypes t

}

mapOps :: Map.Map String (Set.Set HolType) -> IsaSign.ConstTab

mapOps f = Map.fromList

$ map (\ (x, y) -> (transConstS x y, tp2Typ y))

$ concatMap (\ (x, s) -> Set.toList $ Set.map (\ a -> (x, a)) s)

$ Map.toList (foldl (\ m i -> Map.delete i m) f ignore)

tp2Typ :: HolType -> IsaSign.Typ

tp2Typ (TyVar s) = IsaSign.Type (transTypeStringT bs s) holType []

tp2Typ (TyApp s tps) = case tps of

[a1, a2] | s == "fun" -> mkFunType (tp2Typ a1) (tp2Typ a2)

[] | s == "bool" -> boolType

_ -> IsaSign.Type (transTypeStringT bs s) holType $ map tp2Typ tps

arity2tp :: Int -> [(IsaSign.IsaClass, [(IsaSign.Typ, IsaSign.Sort)])]

arity2tp i = [(isaTerm, map (\ k -> (IsaSign.TFree ("'a" ++ show (k)) [], [isaTerm]))

[1 .. i])]

mapTypes :: Map.Map String Int -> IsaSign.TypeSig

mapTypes tps = IsaSign.emptyTypeSig {

IsaSign.arities = Map.fromList $ map extractTypeName

$ Map.toList $ foldr Map.delete tps

["bool", "fun", "prod"] }

where

extractTypeName (s, arity) = (transTypeStringT bs s, arity2tp arity)

mapNamedSen :: Named Sentence -> Named IsaSign.Sentence

mapNamedSen n_sen = let

sen = sentence n_sen

trans = mapHolSen sen

in

n_sen {sentence = trans}