{- |

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 CoCASL to Isabelle-HOL.

-}

{- todo:

encoding of cofreeness

modal formulas

-}

module Comorphisms.CoCASL2IsabelleHOL where

import Logic.Logic

import Logic.Comorphism

import Data.List as List

import Data.Maybe

import Data.Char

import Debug.Trace

-- CoCASL

import CoCASL.Logic_CoCASL

import CoCASL.CoCASLSign

import CoCASL.AS_CoCASL

import CoCASL.StatAna

import CASL.AS_Basic_CASL

import CASL.Morphism

import Comorphisms.CASL2IsabelleHOL

-- Isabelle

import Isabelle.IsaSign as IsaSign

import Isabelle.Logic_Isabelle

-- | The identity of the comorphism

data CoCASL2IsabelleHOL = CoCASL2IsabelleHOL deriving (Show)

instance Language CoCASL2IsabelleHOL -- default definition is okay

instance Comorphism CoCASL2IsabelleHOL

CoCASL ()

C_BASIC_SPEC CoCASLFORMULA SYMB_ITEMS SYMB_MAP_ITEMS

CSign

CoCASLMor

CASL.Morphism.Symbol CASL.Morphism.RawSymbol ()

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

IsaSign.Sign

() () () () where

sourceLogic _ = CoCASL

sourceSublogic _ = ()

targetLogic _ = Isabelle

targetSublogic _ = ()

map_theory _ = transTheory sigTrCoCASL formTrCoCASL

--map_morphism _ morphism1 -> Maybe morphism2

map_sentence _ sign =

Just . mapSen formTrCoCASL sign

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

-- | extended signature translation for CoCASL

sigTrCoCASL :: SignTranslator C_FORMULA CoCASLSign

sigTrCoCASL _ _ = id

-- | extended formula translation for CoCASL

formTrCoCASL :: FormulaTranslator C_FORMULA CoCASLSign

formTrCoCASL sign (CoSort_gen_ax sorts ops _) =

foldr (quantifyIsa "All") phi (predDecls++[("u",ts),("v",ts)])

where

ts = transSort $ head sorts

-- phi expresses: all bisimulations are the equality

phi = prems `binImpl` concls

-- indices and predicates for all involved sorts

indices = [0..length sorts - 1]

predDecls = zip [rvar i | i<-indices] (map binPred sorts)

binPred s = let s' = transSort s in mkCurryFunType [s',s'] boolType

-- premises: all relations are bisimulations

prems = conj (map prem (zip sorts indices))

{- generate premise for s, where s is the i-th sort

for all x,y of that sort,

if all sel_j(x) R_j sel_j(y), where sel_j ranges over the selectors for s

then x R y

here, R_i is the relation for the result type of sel_j, or the equality

-}

prem (s::SORT,i) =

let -- get all selectors with first argument sort s

sels = List.filter isSelForS ops

isSelForS (Qual_op_name _ t _) = case (args_OP_TYPE t) of

(s1:_) -> s1 == s

_ -> False

isSelForS _ = False

premSel opsymb@(Qual_op_name n t _) =

let -- get extra parameters of the selectors

args = tail $ args_OP_TYPE t

indicesArgs = [1..length args]

res = res_OP_TYPE t

-- variables for the extra parameters

varDecls = zip [xvar i | i<-indicesArgs] (map transSort args)

-- the selector ...

top = Const (transOP_SYMB sign opsymb) noType isaTerm

-- applied to x and extra parameter vars

appFold = foldl ( \ t1 t2 -> App t1 t2 IsCont)

rhs = appFold (App top (var "x") IsCont)

(map (var . xvar) indicesArgs)

-- applied to y and extra parameter vars

lhs = appFold (App top (var "y") IsCont)

(map (var . xvar) indicesArgs)

chi = -- is the result of selector non-observable?

if res `elem` sorts

-- then apply corresponding relation

then App (App (var $

rvar (fromJust (findIndex (==res) sorts)))

rhs NotCont) lhs NotCont

-- else use equality

else binEq rhs lhs

in foldr (quantifyIsa "All") chi varDecls

prem1 = conj (map premSel sels)

concl1 = App (App (var $ rvar i) (var "x") NotCont) (var "y") NotCont

psi = concl1 `binImpl` prem1

typS = transSort s

in foldr (quantifyIsa "All") psi [("x",typS),("y",typS)]

-- conclusion: all relations are the equality

concls = conj (map concl (zip sorts indices))

concl (s,i::Int) = binImpl (App (App (var $ rvar i) (var "u") NotCont)

(var "v") NotCont)

(binEq (var "u") (var "v"))

formTrCoCASL sign (Box mod phi _) =

trace "WARNING: ignoring modal forumla"

$ true

formTrCoCASL sign (Diamond mod phi _) =

trace "WARNING: ignoring modal forumla"

$ true