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

{- |

Module : ./Comorphisms/CSMOF2CASL.hs

Description : Coding CSMOF into CASL

Copyright : (c) Daniel Calegari Universidad de la Republica, Uruguay 2013

License : GPLv2 or higher, see LICENSE.txt

Maintainer : dcalegar@fing.edu.uy

Stability : provisional

Portability : portable

-}

module Comorphisms.CSMOF2CASL

( CSMOF2CASL (..), mapSign, generateVars

) where

import Logic.Logic

import Logic.Comorphism

import Common.DefaultMorphism

-- CSMOF

import CSMOF.Logic_CSMOF as CSMOF

import CSMOF.As as CSMOFAs

import CSMOF.Sign as CSMOF

-- CASL

import CASL.Logic_CASL

import CASL.AS_Basic_CASL as C

import CASL.Sublogic

import CASL.Sign as C

import CASL.Morphism as C

import Common.AS_Annotation

import Common.GlobalAnnotations

import Common.Id

import Common.ProofTree

import Common.Result

import qualified Common.Lib.Rel as Rel

import qualified Common.Lib.MapSet as MapSet

import qualified Data.Set as Set

import qualified Data.Map as Map

import Data.Maybe (fromMaybe)

-- | lid of the morphism

data CSMOF2CASL = CSMOF2CASL deriving Show

instance Language CSMOF2CASL -- default is ok

instance Comorphism CSMOF2CASL

CSMOF.CSMOF

()

CSMOFAs.Metamodel

CSMOF.Sen

()

()

CSMOF.Sign

CSMOF.Morphism

()

()

()

CASL

CASL_Sublogics

CASLBasicSpec

CASLFORMULA

SYMB_ITEMS

SYMB_MAP_ITEMS

CASLSign

CASLMor

C.Symbol

C.RawSymbol

ProofTree

where

sourceLogic CSMOF2CASL = CSMOF

sourceSublogic CSMOF2CASL = ()

targetLogic CSMOF2CASL = CASL

mapSublogic CSMOF2CASL _ = Just $ caslTop

{ has_part = False

, sub_features = LocFilSub

, cons_features = SortGen True True }

map_theory CSMOF2CASL = mapTheory

map_sentence CSMOF2CASL s = return . mapSen (mapSign s)

map_morphism CSMOF2CASL = mapMor

-- map_symbol CSMOF2CASL _ = Set.singleton . mapSym

is_model_transportable CSMOF2CASL = True

has_model_expansion CSMOF2CASL = True

is_weakly_amalgamable CSMOF2CASL = True

isInclusionComorphism CSMOF2CASL = True

mapTheory :: (CSMOF.Sign, [Named CSMOF.Sen]) -> Result (CASLSign, [Named CASLFORMULA])

mapTheory (s, ns) = let cs = mapSign s in

return (cs, map (mapNamed $ mapSen cs) ns ++ sentences cs)

mapSign :: CSMOF.Sign -> CASLSign

mapSign s =

let

sorts = getSorts (types s) (typeRel s)

ops = getOperations (instances s)

predd = getPredicates (properties s)

sent = getSentencesRels (links s) (instances s)

sentDisEmb = getSortGen (typeRel s) (abstractClasses s) (types s) (instances s)

noConfBetOps = getNoConfusionBetweenSets (instances s) (typeRel s)

in

C.Sign

{ sortRel = sorts

, revSortRel = Just $ Rel.fromList (map revertOrder (Rel.toList sorts))

, emptySortSet = Set.empty

, opMap = ops

, assocOps = MapSet.empty

, predMap = fst predd

, varMap = Map.empty

, sentences = snd predd ++ sent ++ sentDisEmb ++ noConfBetOps

, declaredSymbols = Set.empty

, envDiags = []

, annoMap = MapSet.empty

, globAnnos = emptyGlobalAnnos

, extendedInfo = ()

}

getSorts :: Set.Set TypeClass -> Rel.Rel TypeClass -> Rel.Rel SORT

getSorts setC relC =

let relS = Set.fold (insertSort . name) Rel.empty setC

in foldr insertPair relS (Rel.toList relC)

insertSort :: String -> Rel.Rel SORT -> Rel.Rel SORT

insertSort s = Rel.insertPair (stringToId s) (stringToId s)

insertPair :: (TypeClass, TypeClass) -> Rel.Rel SORT -> Rel.Rel SORT

insertPair (t1, t2) = Rel.insertPair (stringToId $ name t1) (stringToId $ name t2)

revertOrder :: (SORT, SORT) -> (SORT, SORT)

revertOrder (a, b) = (b, a)

getPredicates :: Set.Set PropertyT -> (PredMap, [Named (FORMULA f)])

getPredicates = Set.fold insertPredicate (MapSet.empty, [])

insertPredicate :: PropertyT -> (PredMap, [Named (FORMULA f)]) -> (PredMap, [Named (FORMULA f)])

insertPredicate prop (predM, form) =

let

sort1 = stringToId $ name $ sourceType prop

sort2 = stringToId $ name $ targetType prop

pname1 = stringToId $ targetRole prop

ptype1 = PredType $ sort1 : [sort2]

pname2 = stringToId $ sourceRole prop

ptype2 = PredType $ sort2 : [sort1]

nam = "equiv_" ++ targetRole prop ++ "_" ++ sourceRole prop

varsD = [Var_decl [mkSimpleId "x"] sort2 nullRange,

Var_decl [mkSimpleId "y"] sort1 nullRange]

sentRel = C.Relation

(C.Predication (C.Qual_pred_name pname2

(Pred_type [sort2, sort1] nullRange) nullRange)

(C.Qual_var (mkSimpleId "x") sort2 nullRange :

[C.Qual_var (mkSimpleId "y") sort1 nullRange]) nullRange)

C.Equivalence

(C.Predication (C.Qual_pred_name pname1

(Pred_type [sort1, sort2] nullRange) nullRange)

(C.Qual_var (mkSimpleId "y") sort1 nullRange :

[C.Qual_var (mkSimpleId "x") sort2 nullRange]) nullRange)

nullRange

sent = Quantification Universal varsD sentRel nullRange

in

{- MapSet does not allows repeated elements, but predicate names can be repeated

(this must be corrected by creating a more complex ID) -}

if sourceRole prop == "_"

then (MapSet.insert pname1 ptype1 predM, form)

else if targetRole prop == "_"

then (MapSet.insert pname2 ptype2 predM, form)

else (MapSet.insert pname1 ptype1 $ MapSet.insert pname2 ptype2 predM,

makeNamed nam sent : form)

getOperations :: Map.Map String TypeClass -> OpMap

getOperations ops = foldr insertOperations MapSet.empty (Map.toList ops)

insertOperations :: (String, TypeClass) -> OpMap -> OpMap

insertOperations (na, tc) opM =

let

opName = stringToId na

opType = OpType Total [] (stringToId $ name tc)

in

MapSet.insert opName opType opM

getSentencesRels :: Set.Set LinkT -> Map.Map String TypeClass ->

[Named CASLFORMULA]

getSentencesRels = completenessOfRelations

completenessOfRelations :: Set.Set LinkT -> Map.Map String TypeClass ->

[Named CASLFORMULA]

completenessOfRelations linkk ops =

let ordLinks = getLinksByProperty linkk

in foldr ((++) . createComplFormula ops) [] (Map.toList ordLinks)

createComplFormula :: Map.Map String TypeClass -> (String, [LinkT]) ->

[Named CASLFORMULA]

createComplFormula ops (nam, linksL) =

let

varA = mkSimpleId "x"

varB = mkSimpleId "y"

in

case linksL of

[] -> []

LinkT _ _ pr : _ ->

let sorA = stringToId $ name $ sourceType pr

sorB = stringToId $ name $ targetType pr

varsD = [Var_decl [varA] sorA nullRange,

Var_decl [varB] sorB nullRange]

sent = C.Relation (C.Predication (C.Qual_pred_name

(stringToId $ targetRole pr) (Pred_type [sorA, sorB] nullRange)

nullRange) (C.Qual_var varA sorA nullRange :

[C.Qual_var varB sorB nullRange]) nullRange)

C.Equivalence (Junction Dis

(foldr ((:) . getPropHold ops varA sorA varB sorB) [] linksL)

nullRange) nullRange

sentQuan = Quantification Universal varsD sent nullRange

in [makeNamed ("compRel_" ++ nam) sentQuan]

getPropHold :: Map.Map String TypeClass -> VAR -> SORT -> VAR -> SORT -> LinkT

-> CASLFORMULA

getPropHold ops varA sorA varB sorB lin =

let

souObj = Map.lookup (sourceVar lin) ops

tarObj = Map.lookup (targetVar lin) ops

typSou = case souObj of

Nothing -> sourceVar lin -- if happens then is an error

Just tSou -> name tSou

typTar = case tarObj of

Nothing -> targetVar lin -- if happens then is an error

Just tTar -> name tTar

eqA = Equation (Qual_var varA sorA nullRange)

Strong

(Application (Qual_op_name (stringToId (sourceVar lin))

(Op_type Total [] (stringToId typSou) nullRange)

nullRange) [] nullRange)

nullRange

eqB = Equation (Qual_var varB sorB nullRange)

Strong

(Application (Qual_op_name (stringToId (targetVar lin))

(Op_type Total [] (stringToId typTar) nullRange)

nullRange) [] nullRange)

nullRange

in

Junction Con (eqA : [eqB]) nullRange

getLinksByProperty :: Set.Set LinkT -> Map.Map String [LinkT]

getLinksByProperty linkk =

let elems = Set.elems linkk

in foldr getByProperty Map.empty elems

getByProperty :: LinkT -> Map.Map String [LinkT] -> Map.Map String [LinkT]

getByProperty lin mapL =

let

prope = CSMOF.property lin

nameLook = sourceRole prope ++ name (sourceType prope) ++ targetRole prope

++ name (targetType prope)

setProp = Map.lookup nameLook mapL

in

case setProp of

Nothing -> Map.insert nameLook [lin] (Map.delete nameLook mapL)

Just s -> Map.insert nameLook (lin : s) (Map.delete nameLook mapL)

getSortGen :: Rel.Rel TypeClass -> Set.Set TypeClass -> Set.Set TypeClass ->

Map.Map String TypeClass -> [Named CASLFORMULA]

getSortGen typpR absCl typCl inst = disjointEmbedding absCl typpR ++

sortGeneration inst ++

sortGenerationNonAbstractSuperClasses typpR typCl absCl inst

-- Free type of non-abstract superclasses

sortGenerationNonAbstractSuperClasses :: Rel.Rel TypeClass -> Set.Set TypeClass

-> Set.Set TypeClass -> Map.Map String TypeClass -> [Named CASLFORMULA]

sortGenerationNonAbstractSuperClasses typpR typCl absCl inst =

let

ordObj = foldr orderByClass Map.empty (Map.toList inst)

nonAbsClasses = getNonAbstractClasess absCl typCl

nonAbsClassesWChilds = filter (not . null . snd)

(Set.fold ((:) . getSubClasses typpR) [] nonAbsClasses)

childObjects = foldr ((:) . getClassSubObjects ordObj)

[] nonAbsClassesWChilds -- [(TypeClass,[String])]

in

foldr ((:) . toSortConstraintNonAbsClass inst) [] childObjects

-- Takes the objects, and a class with its child classes and returns the descendent objects of such class

getClassSubObjects :: Map.Map TypeClass [String] -> (TypeClass, [TypeClass]) ->

(TypeClass, [String])

getClassSubObjects objs (tc, subCl) =

let objTC = findObjectInMap objs tc

in

(tc, objTC ++ foldr ((++) . findObjectInMap objs) [] subCl)

findObjectInMap :: Map.Map TypeClass [String] -> TypeClass -> [String]

findObjectInMap objs tc = fromMaybe [] $ Map.lookup tc objs

getNonAbstractClasess :: Set.Set TypeClass -> Set.Set TypeClass -> Set.Set TypeClass

getNonAbstractClasess absCl classes = Set.difference classes absCl

getSubClasses :: Rel.Rel TypeClass -> TypeClass -> (TypeClass, [TypeClass])

getSubClasses typpR tc =

let subCla = map fst (filter (isParent tc) (Rel.toList typpR))

rec = foldr ((++) . snd . getSubClasses typpR) [] subCla

in (tc, subCla ++ rec)

isParent :: TypeClass -> (TypeClass, TypeClass) -> Bool

isParent tc (_, tc2) = tc == tc2

toSortConstraintNonAbsClass :: Map.Map String TypeClass -> (TypeClass, [String])

-> Named CASLFORMULA

toSortConstraintNonAbsClass inst (tc, lisObj) =

let

sor = stringToId $ name tc

varA = Var_decl [mkSimpleId "x"] sor nullRange

sent = Junction Dis (foldr ((:) . getEqualityVarObject sor inst)

[] lisObj) nullRange

constr = Quantification Universal [varA] sent nullRange

in

makeNamed ("sortGenCon_" ++ name tc) constr

getEqualityVarObject :: SORT -> Map.Map String TypeClass -> String -> CASLFORMULA

getEqualityVarObject sor inst obj =

let oTyp = case Map.lookup obj inst of

Nothing -> stringToId obj -- If happens, there is an error

Just ob -> stringToId $ name ob

in

Equation (Qual_var (mkSimpleId "x") sor nullRange)

Strong

(Application (Qual_op_name (stringToId obj)

(Op_type Total [] oTyp nullRange)

nullRange) [] nullRange)

nullRange

-- Sorts are generated as a free type of object functions

sortGeneration :: Map.Map String TypeClass -> [Named CASLFORMULA]

sortGeneration inst =

let

ordObj = foldr orderByClass Map.empty (Map.toList inst)

noJunk = foldr ((:) . toSortConstraint) [] (Map.toList ordObj)

in

noJunk

mapFilterJust :: [Maybe a] -> [a]

mapFilterJust list =

case list of

[] -> []

a : rest -> case a of

Nothing -> mapFilterJust rest

Just el -> el : mapFilterJust rest

orderByClass :: (String, TypeClass) -> Map.Map TypeClass [String] ->

Map.Map TypeClass [String]

orderByClass (ob, tc) mapTC =

case Map.lookup tc mapTC of

Nothing -> Map.insert tc [ob] mapTC

Just listObj -> Map.insert tc (ob : listObj) (Map.delete tc mapTC)

getNoConfusionBetweenSets :: Map.Map String TypeClass -> Rel.Rel TypeClass ->

[Named CASLFORMULA]

getNoConfusionBetweenSets inst relC =

let ordObj = Map.toList $ foldr orderByClass Map.empty (Map.toList inst)

in mapFilterJust $ foldr ((:) . getNoConfusionBSetsAxiom ordObj relC) [] ordObj

getNoConfusionBSetsAxiom :: [(TypeClass, [String])] -> Rel.Rel TypeClass ->

(TypeClass, [String]) -> Maybe (Named CASLFORMULA)

getNoConfusionBSetsAxiom ordObj relC (tc, lisObj) =

case lisObj of

[] -> Nothing

_ : _ ->

let filteredObj = removeUntilType tc ordObj

diffForm = foldr ((++) . diffOfRestConstants (tc, lisObj) relC)

[] filteredObj in

case diffForm of

[] -> Nothing

_ : _ -> let constr = Junction Con diffForm nullRange

in Just $ makeNamed ("noConfusion_" ++ name tc) constr

removeUntilType :: TypeClass -> [(TypeClass, [String])] -> [(TypeClass, [String])]

removeUntilType tc lis =

case lis of

[] -> []

(tc2, lisObj2) : rest -> if tc == tc2

then (tc2, lisObj2) : rest

else removeUntilType tc rest

diffOfRestConstants :: (TypeClass, [String]) -> Rel.Rel TypeClass ->

(TypeClass, [String]) -> [CASLFORMULA]

diffOfRestConstants (tc1, lisObj1) relC (tc2, lisObj2)

| tc1 == tc2 = foldr ((++) . diffOfRestOps tc1 lisObj1) [] lisObj1

| haveCommonSort tc1 tc2 relC =

concatMap (diffOfRestOpsDiffSort (tc1, lisObj1) tc2) lisObj2

| otherwise = []

haveCommonSort :: TypeClass -> TypeClass -> Rel.Rel TypeClass -> Bool

haveCommonSort t1 t2 relT =

let succT1 = superSorts relT t1

succT2 = superSorts relT t2

in not $ Set.null $ Set.intersection succT1 succT2

-- This is the non exported function reachable in Rel

superSorts :: Rel.Rel TypeClass -> TypeClass -> Set.Set TypeClass

superSorts relT tc = Set.fold reach Set.empty $ Rel.succs relT tc where

reach e s = if Set.member e s then s

else Set.fold reach (Set.insert e s) $ Rel.succs relT e

diffOfRestOpsDiffSort :: (TypeClass, [String]) -> TypeClass -> String -> [CASLFORMULA]

diffOfRestOpsDiffSort (tc1, lisObj1) tc2 objName = concatMap

(diffOpsDiffSorts tc2 objName tc1) lisObj1

diffOpsDiffSorts :: TypeClass -> String -> TypeClass -> String -> [CASLFORMULA]

diffOpsDiffSorts tc2 objName2 tc1 objName1 =

[Negation (Equation (Application (Qual_op_name (stringToId objName1)

(Op_type Total [] (stringToId $ name tc1) nullRange) nullRange) [] nullRange)

Strong (Application (Qual_op_name (stringToId objName2)

(Op_type Total [] (stringToId $ name tc2) nullRange)

nullRange) [] nullRange) nullRange) nullRange]

diffOfRestOps :: TypeClass -> [String] -> String -> [CASLFORMULA]

diffOfRestOps tc lisObj objName =

let lis = removeUntil lisObj objName

in concatMap (diffOps tc objName) lis

removeUntil :: [String] -> String -> [String]

removeUntil lis str =

case lis of

[] -> []

a : rest -> if a == str

then rest

else removeUntil rest str

diffOps :: TypeClass -> String -> String -> [CASLFORMULA]

diffOps tc objName1 objName2 =

[Negation (Equation

(Application (Qual_op_name (stringToId objName1)

(Op_type Total [] (stringToId $ name tc) nullRange)

nullRange) [] nullRange)

Strong

(Application (Qual_op_name (stringToId objName2)

(Op_type Total [] (stringToId $ name tc) nullRange)

nullRange) [] nullRange)

nullRange)

nullRange | objName1 /= objName2]

toSortConstraint :: (TypeClass, [String]) -> Named CASLFORMULA

toSortConstraint (tc, lisObj) =

let

sor = stringToId $ name tc

simplCon = Constraint sor (foldr ((:) . toConstraint sor) [] lisObj) sor

constr = mkSort_gen_ax [simplCon] True

in

makeNamed ("sortGenCon_" ++ name tc) constr

toConstraint :: Id -> String -> (OP_SYMB, [Int])

toConstraint sor obName =

let obj = stringToId obName

in

(Qual_op_name obj (Op_type Total [] sor nullRange) nullRange, [])

-- Each abstract class is the disjoint embedding of it subsorts

disjointEmbedding :: Set.Set TypeClass -> Rel.Rel TypeClass ->

[Named CASLFORMULA]

disjointEmbedding absCl rel =

let

injSyms = map (\ (s, t) -> (Qual_op_name

(mkUniqueInjName (stringToId $ name s) (stringToId $ name t))

(Op_type Total [stringToId $ name s]

(stringToId $ name t) nullRange) nullRange, [])) $ Rel.toList $

Rel.irreflex rel

resType _ (Op_name _, _) = False

resType s (Qual_op_name _ t _, _) = res_OP_TYPE t == s

collectOps s = Constraint (stringToId $ name s)

(filter (resType (stringToId $ name s)) injSyms) (stringToId $ name s)

sortList = Set.toList absCl

constrs = map collectOps sortList

in

[makeNamed "disjEmbedd" (Sort_gen_ax constrs True)]

mapSen :: CASLSign -> CSMOF.Sen -> CASLFORMULA

mapSen sig (Sen con car cot) = -- trueForm

case cot of

EQUAL -> let

minC = minConstraint con car (predMap sig)

maxC = maxConstraint con car (predMap sig)

in

Junction Con (minC : [maxC]) nullRange

LEQ -> maxConstraint con car (predMap sig)

GEQ -> minConstraint con car (predMap sig)

minConstraint :: MultConstr -> Integer -> PredMap -> CASLFORMULA

minConstraint con int predM =

let

predTypes = MapSet.lookup (stringToId $ getRole con) predM -- Set PredType

souVars = generateVars "x" 1

tarVars = generateVars "y" int

correctPredType = Set.fold (getCorrectPredType con) [] predTypes

souVarDec = Var_decl souVars (head (predArgs (head correctPredType))) nullRange

tarVarDec = Var_decl tarVars (last (predArgs (head correctPredType))) nullRange

in

if int > 1

then Quantification Universal [souVarDec] (Quantification

Existential [tarVarDec] (Junction Con (generateVarDiff tarVarDec :

[generateProp souVarDec tarVarDec (stringToId $ getRole con)])

nullRange) nullRange) nullRange

else Quantification Universal [souVarDec] (Quantification

Existential [tarVarDec] (generateProp souVarDec tarVarDec

(stringToId $ getRole con)) nullRange) nullRange

getCorrectPredType :: MultConstr -> PredType -> [PredType] -> [PredType]

getCorrectPredType con pt ptLis =

if stringToId (name (CSMOF.getType con)) == head (predArgs pt)

then pt : ptLis else ptLis

generateVars :: String -> Integer -> [VAR]

generateVars varRoot int =

case int of

1 -> [mkSimpleId (varRoot ++ "_" ++ show int)]

n -> mkSimpleId (varRoot ++ "_" ++ show int) : generateVars varRoot (n - 1)

generateVarDiff :: VAR_DECL -> CASLFORMULA

generateVarDiff (Var_decl vars sor _) = Junction Con

(foldr ((++) . diffOfRest sor vars) [] vars) nullRange

diffOfRest :: SORT -> [VAR] -> VAR -> [CASLFORMULA]

diffOfRest sor vars var = map (diffVar sor var) vars

diffVar :: SORT -> VAR -> VAR -> CASLFORMULA

diffVar sor var1 var2 =

if var1 /= var2

then Negation (Equation

(Qual_var var1 sor nullRange)

Strong

(Qual_var var2 sor nullRange)

nullRange)

nullRange

else trueForm

generateProp :: VAR_DECL -> VAR_DECL -> Id -> CASLFORMULA

generateProp (Var_decl varD sort _) (Var_decl varD2 sort2 _) rol =

Junction Con (map (createPropRel (head varD) sort rol sort2) varD2) nullRange

createPropRel :: VAR -> SORT -> Id -> SORT -> VAR -> CASLFORMULA

createPropRel souVar sor rol sor2 tarVar =

Predication (C.Qual_pred_name rol (Pred_type [sor, sor2] nullRange) nullRange)

(Qual_var souVar sor nullRange : [Qual_var tarVar sor2 nullRange]) nullRange

maxConstraint :: MultConstr -> Integer -> PredMap -> CASLFORMULA

maxConstraint con int predM =

let

predTypes = MapSet.lookup (stringToId $ getRole con) predM -- Set PredType

souVars = generateVars "x" 1

tarVars = generateVars "y" (int + 1)

correctPredType = Set.fold (getCorrectPredType con) [] predTypes

souVarDec = Var_decl souVars (head (predArgs (head correctPredType))) nullRange

tarVarDec = Var_decl tarVars (last (predArgs (head correctPredType))) nullRange

in

Quantification Universal (souVarDec : [tarVarDec])

(Relation

(Junction Con [generateProp souVarDec tarVarDec (stringToId $ getRole con)] nullRange)

Implication

(Junction Dis (generateExEqual tarVarDec) nullRange)

nullRange)

nullRange

generateExEqual :: VAR_DECL -> [CASLFORMULA]

generateExEqual (Var_decl varD sor _) = generateExEqualList varD sor

generateExEqualList :: [VAR] -> SORT -> [CASLFORMULA]

generateExEqualList vars sor =

case vars of

[] -> []

v : rest -> generateExEqualVar rest sor v ++ generateExEqualList rest sor

generateExEqualVar :: [VAR] -> SORT -> VAR -> [CASLFORMULA]

generateExEqualVar vars sor var =

foldr ((++) . (\ el -> if el == var

then []

else [Equation (Qual_var var sor nullRange) Strong

(Qual_var el sor nullRange) nullRange]))

[] vars

-- | Translation of morphisms

mapMor :: CSMOF.Morphism -> Result CASLMor

mapMor m = return C.Morphism

{ msource = mapSign $ domOfDefaultMorphism m

, mtarget = mapSign $ codOfDefaultMorphism m

, sort_map = Map.empty

, op_map = Map.empty

, pred_map = Map.empty

, extended_map = ()

}

-- mapSym :: CSMOF.Symbol -> C.Symbol