{-# LANGUAGE MultiParamTypeClasses, TypeSynonymInstances #-}

{- |

Module : $Header$

Description : Comorphism from OWL 2 to CASL_Dl

Copyright : (c) Francisc-Nicolae Bungiu

License : GPLv2 or higher, see LICENSE.txt

Maintainer : f.bungiu@jacobs-university.de

Stability : provisional

Portability : non-portable (via Logic.Logic)

-}

module OWL2.OWL22CASL (OWL22CASL (..)) where

import Logic.Logic as Logic

import Logic.Comorphism

import Common.AS_Annotation

import Common.Result

import Common.Id

import Control.Monad

import Data.Char

import qualified Data.Set as Set

import qualified Data.Map as Map

import qualified Common.Lib.MapSet as MapSet

import qualified Common.Lib.Rel as Rel

-- the DL with the initial signature for OWL

import CASL_DL.PredefinedCASLAxioms

-- OWL = domain

import OWL2.Logic_OWL2

import OWL2.MS

import OWL2.AS

import OWL2.ProfilesAndSublogics

import OWL2.ManchesterPrint ()

import OWL2.Morphism

import OWL2.Symbols

import qualified OWL2.Sign as OS

-- CASL_DL = codomain

import CASL.Logic_CASL

import CASL.AS_Basic_CASL

import CASL.Sign

import CASL.Morphism

import CASL.Sublogic

import Common.ProofTree

import Data.Maybe

data OWL22CASL = OWL22CASL deriving Show

instance Language OWL22CASL

instance Comorphism

OWL22CASL -- comorphism

OWL2 -- lid domain

ProfSub -- sublogics domain

OntologyDocument -- Basic spec domain

Axiom -- sentence domain

SymbItems -- symbol items domain

SymbMapItems -- symbol map items domain

OS.Sign -- signature domain

OWLMorphism -- morphism domain

Entity -- symbol domain

RawSymb -- rawsymbol domain

ProofTree -- proof tree codomain

CASL -- lid codomain

CASL_Sublogics -- sublogics codomain

CASLBasicSpec -- Basic spec codomain

CASLFORMULA -- sentence codomain

SYMB_ITEMS -- symbol items codomain

SYMB_MAP_ITEMS -- symbol map items codomain

CASLSign -- signature codomain

CASLMor -- morphism codomain

Symbol -- symbol codomain

RawSymbol -- rawsymbol codomain

ProofTree -- proof tree domain

where

sourceLogic OWL22CASL = OWL2

sourceSublogic OWL22CASL = topS

targetLogic OWL22CASL = CASL

mapSublogic OWL22CASL _ = Just $ cFol

{ cons_features = emptyMapConsFeature }

map_theory OWL22CASL = mapTheory

map_morphism OWL22CASL = mapMorphism

isInclusionComorphism OWL22CASL = True

has_model_expansion OWL22CASL = True

-- | Mapping of OWL morphisms to CASL morphisms

mapMorphism :: OWLMorphism -> Result CASLMor

mapMorphism oMor =

do

cdm <- mapSign $ osource oMor

ccd <- mapSign $ otarget oMor

let emap = mmaps oMor

preds = Map.foldWithKey (\ (Entity ty u1) u2 -> let

i1 = uriToId u1

i2 = uriToId u2

in case ty of

Class -> Map.insert (i1, conceptPred) i2

ObjectProperty -> Map.insert (i1, objectPropPred) i2

DataProperty -> Map.insert (i1, dataPropPred) i2

_ -> id) Map.empty emap

ops = Map.foldWithKey (\ (Entity ty u1) u2 -> case ty of

NamedIndividual ->

Map.insert (uriToId u1, indiConst) (uriToId u2, Total)

_ -> id) Map.empty emap

return (embedMorphism () cdm ccd)

{ op_map = ops

, pred_map = preds }

data VarOrIndi = OVar Int | OIndi IRI

objectPropPred :: PredType

objectPropPred = PredType [thing, thing]

dataPropPred :: PredType

dataPropPred = PredType [thing, dataS]

indiConst :: OpType

indiConst = OpType Total [] thing

mapSign :: OS.Sign -- ^ OWL signature

-> Result CASLSign -- ^ CASL signature

mapSign sig =

let conc = OS.concepts sig

cvrt = map uriToId . Set.toList

tMp k = MapSet.fromList . map (\ u -> (u, [k]))

cPreds = thing : nothing : cvrt conc

oPreds = cvrt $ OS.objectProperties sig

dPreds = cvrt $ OS.dataProperties sig

aPreds = foldr MapSet.union MapSet.empty

[ tMp conceptPred cPreds

, tMp objectPropPred oPreds

, tMp dataPropPred dPreds ]

in return $ uniteCASLSign predefSign (emptySign ())

{ predMap = aPreds

, opMap = tMp indiConst . cvrt $ OS.individuals sig

}

loadDataInformation :: ProfSub -> Sign f ()

loadDataInformation _ =

let

dts = Set.fromList $ map stringToId datatypeKeys

in

(emptySign ()) { sortRel = Rel.fromKeysSet dts }

mapTheory :: (OS.Sign, [Named Axiom])

-> Result (CASLSign, [Named CASLFORMULA])

mapTheory (owlSig, owlSens) =

let

sl = topS

in

do

cSig <- mapSign owlSig

let pSig = loadDataInformation sl

(cSens, nSig) <- foldM (\ (x, y) z ->

do

(sen, sig) <- mapSentence y z

return (sen ++ x, uniteCASLSign sig y)

) ([], cSig) owlSens

return (uniteCASLSign nSig pSig, predefinedAxioms ++ cSens)

-- | mapping of OWL to CASL_DL formulae

mapSentence :: CASLSign -- ^ CASL Signature

-> Named Axiom -- ^ OWL2 Sentence

-> Result ([Named CASLFORMULA], CASLSign) -- ^ CASL Sentence

mapSentence cSig inSen = do

(outAx, outSig) <- mapAxioms cSig $ sentence inSen

return (map (flip mapNamed inSen . const) outAx, outSig)

mapAxioms :: CASLSign

-> Axiom

-> Result ([CASLFORMULA], CASLSign)

mapAxioms cSig ax =

case ax of

PlainAxiom ex fb ->

case fb of

ListFrameBit rel lfb ->

mapListFrameBit cSig ex rel lfb

AnnFrameBit _anno afb ->

mapAnnFrameBit cSig ex afb

toIRILst :: EntityType

-> Extended

-> Maybe IRI

toIRILst ty ane = case ane of

SimpleEntity (Entity ty2 iri) | ty == ty2 -> Just iri

_ -> Nothing

-- | Mapping of ListFrameBit

mapListFrameBit :: CASLSign

-> Extended

-> Maybe Relation

-> ListFrameBit

-> Result ([CASLFORMULA], CASLSign)

mapListFrameBit cSig ex rel lfb = case lfb of

AnnotationBit _a -> return ([], cSig)

ExpressionBit cls ->

case ex of

Misc _ -> return ([], cSig)

SimpleEntity (Entity ty iri) ->

case ty of

NamedIndividual | rel == Just Types ->

do

inD <- mapIndivURI cSig iri

ocls <- mapM (\ (_, c) -> mapDescription cSig c 1) cls

return (map (mkForall

[mkVarDecl (mkNName 1) thing] .

mkImpl (mkStEq (toQualVar

(mkVarDecl (mkNName 1) thing)) inD)

) ocls, cSig)

DataProperty | rel == (Just $ DRRelation ADomain) ->

do

oEx <- mapDataProp cSig iri 1 2

odes <- mapM (\ (_, c) -> mapDescription cSig c 1) cls

let vars = (mkNName 1, mkNName 2)

return (map (mkForall

[mkVarDecl (fst vars) thing] .

mkExist

[mkVarDecl (snd vars) dataS] .

mkImpl oEx

) odes, cSig)

_ -> return ([], cSig)

ObjectEntity oe ->

case rel of

Nothing -> return ([], cSig)

Just re ->

case re of

DRRelation r -> do

tobjP <- mapObjProp cSig oe 1 2

tdsc <- mapM (\ (_, c) -> mapDescription cSig c $

case r of

ADomain -> 1

ARange -> 2) cls

let vars = case r of

ADomain -> (mkNName 1, mkNName 2)

ARange -> (mkNName 2, mkNName 1)

return (map (mkForall

[mkVarDecl (fst vars) thing] .

mkExist

[mkVarDecl (snd vars) thing] .

mkImpl tobjP

) tdsc, cSig)

_ -> fail "ObjectEntity Relation nyi"

ClassEntity ce -> do

let map2nd = map snd cls

case rel of

Nothing -> return ([], cSig)

Just r -> case r of

EDRelation re ->

do

decrsS <- mapDescriptionListP cSig 1

$ comPairsaux ce map2nd

let decrsP = map (\ (x, y) -> mkForall

[mkVarDecl (mkNName 1) thing]

(case re of

Equivalent -> mkEqv x y

Disjoint -> mkNeg (conjunct [x, y])

)) decrsS

return (decrsP, cSig)

SubClass ->

do

domT <- mapDescription cSig ce 1

codT <- mapDescriptionList cSig 1 map2nd

return (map (mkForall

[mkVarDecl (mkNName 1) thing] .

mkImpl domT)

codT, cSig)

_ -> fail "ClassEntity Relation nyi"

ObjectBit ol ->

let mol = fmap ObjectProp (toIRILst ObjectProperty ex)

isJ = isJust mol

Just ob = mol

map2nd = map snd ol

in case rel of

Nothing -> return ([], cSig)

Just r -> case r of

EDRelation ed -> do

pairs <- mapComObjectPropsList cSig mol map2nd 1 2

return (map (\ (a, b) -> mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

(case ed of

Equivalent -> mkEqv a b

Disjoint -> mkNeg (conjunct [a, b])

)) pairs, cSig)

SubPropertyOf | isJ -> do

os <- mapM (\ (o1, o2) -> mapSubObjProp cSig o1 o2 3)

$ comPairsaux ob map2nd

return (os, cSig)

InverseOf | isJ ->

do

os1 <- mapM (\ o1 -> mapObjProp cSig o1 1 2) map2nd

o2 <- mapObjProp cSig ob 2 1

return (map (mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

. mkEqv o2

) os1, cSig)

_ -> return ([], cSig)

DataBit db ->

let mol = toIRILst DataProperty ex

isJ = isJust mol

map2nd = map snd db

Just ob = mol

in case rel of

Nothing -> return ([], cSig)

Just r -> case r of

SubPropertyOf | isJ -> do

os1 <- mapM (\ o1 -> mapDataProp cSig o1 1 2) map2nd

o2 <- mapDataProp cSig ob 2 1

return (map (mkForall [mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) dataS]

. mkImpl o2)

os1, cSig)

EDRelation ed -> do

pairs <- mapComDataPropsList cSig map2nd 1 2

return (map (\ (a, b) -> mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

(case ed of

Equivalent -> mkEqv a b

Disjoint -> mkNeg (conjunct [a, b])

)) pairs, cSig)

_ -> return ([], cSig)

IndividualSameOrDifferent al ->

do

let mol = toIRILst NamedIndividual ex

map2nd = map snd al

case rel of

Nothing -> return ([], cSig)

Just r ->

case r of

SDRelation re -> do

fs <- mapComIndivList cSig re mol map2nd

return (fs, cSig)

_ -> return ([], cSig)

DataPropRange dpr ->

case rel of

Nothing -> return ([], cSig)

Just re ->

case re of

DRRelation r ->

case r of

ARange ->

case ex of

SimpleEntity ent ->

case ent of

Entity ty iri ->

case ty of

DataProperty ->

do

oEx <- mapDataProp cSig iri 1 2

odes <- mapM (\ (_, c) ->

mapDataRange cSig c 2) dpr

let vars = (mkNName 1, mkNName 2)

return (map (mkForall [mkVarDecl

(fst vars) thing] .

mkExist [mkVarDecl

(snd vars) thing] .

mkImpl oEx

) odes, cSig)

_ -> fail "DataPropRange EntityType fail"

_ -> fail "DataPropRange Entity fail"

_ -> fail "DataPropRange ADomain ni"

_ -> fail "DataPropRange Relations ni"

IndividualFacts indf ->

let map2nd = map snd indf

in

case map2nd of

[ObjectPropertyFact posneg obe ind] ->

case ex of

SimpleEntity (Entity NamedIndividual siri) ->

do

inS <- mapIndivURI cSig siri

inT <- mapIndivURI cSig ind

oPropH <- mapObjProp cSig obe 1 2

let oProp = case posneg of

Positive -> oPropH

Negative -> Negation oPropH nullRange

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

(mkImpl

(conjunct

[mkStEq (toQualVar

(mkVarDecl (mkNName 1) thing)) inS,

mkStEq (toQualVar

(mkVarDecl (mkNName 2) thing)) inT]

) oProp)]

, cSig)

_ -> fail $ "ObjectPropertyFactsFacts Entity fail: " ++ show ex

[DataPropertyFact posneg dpe lit] ->

case ex of

SimpleEntity (Entity ty iri) ->

case ty of

DataProperty ->

do

inS <- mapIndivURI cSig iri

inT <- mapLiteral cSig lit

oPropH <- mapDataProp cSig dpe 1 2

let oProp = case posneg of

Positive -> oPropH

Negative -> Negation oPropH nullRange

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

(mkImpl (conjunct

[mkStEq (toQualVar

(mkVarDecl (mkNName 1) thing)) inS,

mkStEq (toQualVar

(mkVarDecl (mkNName 2) thing)) inT]

) oProp)]

, cSig)

_ -> fail "DataPropertyFact EntityType fail"

_ -> fail "DataPropertyFact Entity fail"

_ -> fail "DataPropertyFacts fail"

ObjectCharacteristics ace ->

let map2nd = map snd ace

in

case ex of

ObjectEntity ope ->

case map2nd of

[Functional] ->

do

so1 <- mapObjProp cSig ope 1 2

so2 <- mapObjProp cSig ope 1 3

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing,

mkVarDecl (mkNName 3) thing]

(mkImpl

(conjunct [so1, so2])

(mkStEq

(toQualVar (mkVarDecl (mkNName 2) thing))

(toQualVar (mkVarDecl (mkNName 3) thing))

)

)], cSig)

[InverseFunctional] ->

do

so1 <- mapObjProp cSig ope 1 3

so2 <- mapObjProp cSig ope 2 3

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing,

mkVarDecl (mkNName 3) thing]

(mkImpl

(conjunct [so1, so2])

(mkStEq

(toQualVar (mkVarDecl (mkNName 1) thing))

(toQualVar (mkVarDecl (mkNName 2) thing))

)

)], cSig)

[Reflexive] ->

do

so <- mapObjProp cSig ope 1 1

return ([mkForall

[mkVarDecl (mkNName 1) thing]

(mkImpl (Membership (toQualVar

(mkVarDecl (mkNName 1) thing))

thing nullRange)

so)

], cSig)

[Irreflexive] ->

do

so <- mapObjProp cSig ope 1 1

return ([mkForall

[mkVarDecl (mkNName 1) thing]

(mkImpl (Membership (toQualVar

(mkVarDecl (mkNName 1) thing))

thing nullRange)

(mkNeg so))

], cSig)

[Symmetric] ->

do

so1 <- mapObjProp cSig ope 1 2

so2 <- mapObjProp cSig ope 2 1

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

(mkImpl so1 so2)

], cSig)

[Asymmetric] ->

do

so1 <- mapObjProp cSig ope 1 2

so2 <- mapObjProp cSig ope 2 1

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

(mkImpl so1 (mkNeg so2))

], cSig)

[Antisymmetric] ->

do

so1 <- mapObjProp cSig ope 1 2

so2 <- mapObjProp cSig ope 2 1

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing]

(mkImpl

(conjunct [so1, so2])

(mkStEq

(toQualVar (mkVarDecl (mkNName 1) thing))

(toQualVar (mkVarDecl (mkNName 2) thing))

)

)], cSig)

[Transitive] ->

do

so1 <- mapObjProp cSig ope 1 2

so2 <- mapObjProp cSig ope 2 3

so3 <- mapObjProp cSig ope 1 3

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) thing,

mkVarDecl (mkNName 3) thing]

(mkImpl (conjunct [so1, so2]) so3)

], cSig)

_ -> fail "ObjectCharacteristics Character fail"

_ -> fail "ObjectCharacteristics Entity fail"

-- | Mapping of AnnFrameBit

mapAnnFrameBit :: CASLSign

-> Extended

-> AnnFrameBit

-> Result ([CASLFORMULA], CASLSign)

mapAnnFrameBit cSig ex afb =

case afb of

AnnotationFrameBit -> return ([], cSig)

DataFunctional ->

case ex of

SimpleEntity (Entity ty iri) ->

case ty of

DataProperty ->

do

so1 <- mapDataProp cSig iri 1 2

so2 <- mapDataProp cSig iri 1 3

return ([mkForall

[mkVarDecl (mkNName 1) thing,

mkVarDecl (mkNName 2) dataS,

mkVarDecl (mkNName 3) dataS]

(mkImpl

(conjunct [so1, so2])

(mkStEq

(toQualVar (mkVarDecl (mkNName 2) thing))

(toQualVar (mkVarDecl (mkNName 3) thing))

)

)], cSig)

_ -> fail "DataFunctional EntityType fail"

_ -> fail "DataFunctional Extend fail"

DatatypeBit dr ->

case ex of

SimpleEntity (Entity ty iri) ->

case ty of

Datatype ->

do

odes <- mapDataRange cSig dr 2

let dtb = uriToId iri

return ([mkForall

[mkVarDecl (mkNName 1) thing]

(mkEqv

odes

(Membership

(toQualVar (mkVarDecl (mkNName 2) thing))

dtb

nullRange

)

)

], cSig)

_ -> fail "DatatypeBit EntityType fail"

_ -> fail "DatatypeBit Extend fail"

ClassDisjointUnion clsl ->

case ex of

SimpleEntity (Entity ty iri) ->

case ty of

Class ->

do

decrs <- mapDescriptionList cSig 1 clsl

decrsS <- mapDescriptionListP cSig 1 $ comPairs clsl clsl

let decrsP = map (\ (x, y) -> conjunct [x, y]) decrsS

mcls <- mapClassURI cSig iri (mkNName 1)

return ([mkForall

[mkVarDecl (mkNName 1) thing]

(mkEqv mcls

(conjunct

[disjunct decrs,

mkNeg (conjunct decrsP)]

)

)

], cSig)

_ -> fail "ClassDisjointUnion EntityType fail"

_ -> fail "ClassDisjointUnion Extend fail"

ClassHasKey _obpe _dpe -> return ([], cSig)

ObjectSubPropertyChain oplst ->

do

os <- mapM (\ cd -> mapSubObjPropChain cSig afb cd 3) oplst

return (os, cSig)

-- | Mapping of ObjectSubPropertyChain

mapSubObjPropChain :: CASLSign

-> AnnFrameBit

-> ObjectPropertyExpression

-> Int

-> Result CASLFORMULA

mapSubObjPropChain cSig prop oP num1 =

let num2 = num1 + 1

in

case prop of

ObjectSubPropertyChain props ->

do

let zprops = zip (tail props) [(num2 + 1) ..]

(_, vars) = unzip zprops

oProps <- mapM (\ (z, x, y) -> mapObjProp cSig z x y) $

zip3 props ((num1 : vars) ++ [num2]) $

tail ((num1 : vars) ++ [num2])

ooP <- mapObjProp cSig oP num1 num2

return $ mkForall

[mkVarDecl (mkNName 1) thing

, mkVarDecl (mkNName 2) thing]

(mkForall (map (\ x -> mkVarDecl

(mkNName x) thing) vars)

(mkImpl (conjunct oProps) ooP))

_ -> fail "mapping of ObjectSubPropertyChain failed"

{- | Mapping along ObjectPropsList for creation of pairs for commutative

operations. -}

mapComObjectPropsList :: CASLSign -- ^ CASLSignature

-> Maybe ObjectPropertyExpression

-> [ObjectPropertyExpression]

-> Int -- ^ First variable

-> Int -- ^ Last variable

-> Result [(CASLFORMULA, CASLFORMULA)]

mapComObjectPropsList cSig mol props num1 num2 = do

fs <- mapM (\ x -> mapObjProp cSig x num1 num2) props

case mol of

Nothing -> return $ comPairs fs fs

Just ol -> do

f <- mapObjProp cSig ol num1 num2

return $ comPairsaux f fs

-- | mapping of individual list

mapComIndivList :: CASLSign -- ^ CASLSignature

-> SameOrDifferent

-> Maybe Individual

-> [Individual]

-> Result [CASLFORMULA]

mapComIndivList cSig sod mol inds = do

fs <- mapM (mapIndivURI cSig) inds

tps <- case mol of

Nothing -> return $ comPairs fs fs

Just ol -> do

f <- mapIndivURI cSig ol

return $ comPairsaux f fs

return $ map (\ (x, y) -> case sod of

Same -> mkStEq x y

Different -> mkNeg (mkStEq x y)) tps

-- | mapping of data constants

mapLiteral :: CASLSign

-> Literal

-> Result (TERM ())

mapLiteral _ c =

do

let cl = case c of

Literal l _ -> l

return $ mkAppl

(mkQualOp (stringToId cl)

(Op_type Total [] dataS nullRange)

)

[]

-- | Mapping of subobj properties

mapSubObjProp :: CASLSign

-> ObjectPropertyExpression

-> ObjectPropertyExpression

-> Int

-> Result CASLFORMULA

mapSubObjProp cSig oPL oP num1 = do

let num2 = num1 + 1

l <- mapObjProp cSig oPL num1 num2

r <- mapObjProp cSig oP num1 num2

return $ mkForallRange [mkVarDecl (mkNName num1) thing,

mkVarDecl (mkNName num2) thing]

(mkImpl r l )

nullRange

{- | Mapping along DataPropsList for creation of pairs for commutative

operations. -}

mapComDataPropsList :: CASLSign

-> [DataPropertyExpression]

-> Int -- ^ First variable

-> Int -- ^ Last variable

-> Result [(CASLFORMULA, CASLFORMULA)]

mapComDataPropsList cSig props num1 num2 =

mapM (\ (x, z) -> do

l <- mapDataProp cSig x num1 num2

r <- mapDataProp cSig z num1 num2

return (l, r)

) $ comPairs props props

-- | Mapping of data properties

mapDataProp :: CASLSign

-> DataPropertyExpression

-> Int

-> Int

-> Result CASLFORMULA

mapDataProp _ dP nO nD =

do

let

l = mkNName nO

r = mkNName nD

ur <- uriToIdM dP

return $ mkPredication

(mkQualPred ur (toPRED_TYPE dataPropPred))

[Qual_var l thing nullRange, Qual_var r dataS nullRange]

-- | Mapping of obj props

mapObjProp :: CASLSign

-> ObjectPropertyExpression

-> Int

-> Int

-> Result CASLFORMULA

mapObjProp cSig ob num1 num2 =

case ob of

ObjectProp u ->

do

let l = mkNName num1

r = mkNName num2

ur <- uriToIdM u

return $ mkPredication

(mkQualPred ur (toPRED_TYPE objectPropPred))

[Qual_var l thing nullRange, Qual_var r thing nullRange]

ObjectInverseOf u ->

mapObjProp cSig u num2 num1

-- | Mapping of obj props with Individuals

mapObjPropI :: CASLSign

-> ObjectPropertyExpression

-> VarOrIndi

-> VarOrIndi

-> Result CASLFORMULA

mapObjPropI cSig ob lP rP =

case ob of

ObjectProp u ->

do

lT <- case lP of

OVar num1 -> return $ Qual_var (mkNName num1)

thing nullRange

OIndi indivID -> mapIndivURI cSig indivID

rT <- case rP of

OVar num1 -> return $ Qual_var (mkNName num1)

thing nullRange

OIndi indivID -> mapIndivURI cSig indivID

ur <- uriToIdM u

return $ mkPredication

(mkQualPred ur (toPRED_TYPE objectPropPred))

[lT, rT]

ObjectInverseOf u -> mapObjPropI cSig u rP lP

-- | Mapping of Class URIs

mapClassURI :: CASLSign

-> Class

-> Token

-> Result CASLFORMULA

mapClassURI _ uril uid =

do

ur <- uriToIdM uril

return $ mkPredication

(mkQualPred ur (toPRED_TYPE conceptPred))

[Qual_var uid thing nullRange]

-- | Mapping of Individual URIs

mapIndivURI :: CASLSign

-> Individual

-> Result (TERM ())

mapIndivURI _ uriI =

do

ur <- uriToIdM uriI

return $ mkAppl

(mkQualOp ur (Op_type Total [] thing nullRange))

[]

uriToIdM :: IRI -> Result Id

uriToIdM = return . uriToId

-- | Extracts Id from URI

uriToId :: IRI -> Id

uriToId urI =

let l = localPart urI

ur = if isThing urI then mkQName l else urI

repl a = if isAlphaNum a

then

a

else

'_'

nP = map repl $ namePrefix ur

lP = map repl l

in stringToId $ nP ++ "" ++ lP

-- | Mapping of a list of descriptions

mapDescriptionList :: CASLSign

-> Int

-> [ClassExpression]

-> Result [CASLFORMULA]

mapDescriptionList cSig n lst =

mapM (uncurry $ mapDescription cSig)

$ zip lst $ replicate (length lst) n

-- | Mapping of a list of pairs of descriptions

mapDescriptionListP :: CASLSign

-> Int

-> [(ClassExpression, ClassExpression)]

-> Result [(CASLFORMULA, CASLFORMULA)]

mapDescriptionListP cSig n lst =

do

let (l, r) = unzip lst

llst <- mapDescriptionList cSig n l

rlst <- mapDescriptionList cSig n r

let olst = zip llst rlst

return olst

-- | Get all distinct pairs for commutative operations

comPairs :: [t] -> [t1] -> [(t, t1)]

comPairs [] [] = []

comPairs _ [] = []

comPairs [] _ = []

comPairs (a : as) (_ : bs) = comPairsaux a bs ++ comPairs as bs

comPairsaux :: t -> [t1] -> [(t, t1)]

comPairsaux a = map (\ b -> (a, b))

-- | mapping of Data Range

mapDataRange :: CASLSign

-> DataRange

-> Int

-> Result CASLFORMULA

mapDataRange cSig dr inId =

do

let uid = mkNName inId

case dr of

DataType d _ ->

do

ur <- uriToIdM d

return $ Membership

(Qual_var uid thing nullRange)

ur

nullRange

DataComplementOf drc ->

do

dc <- mapDataRange cSig drc inId

return $ mkNeg dc

DataOneOf _ -> error "nyi"

DataJunction _ _ -> error "nyi"

-- | mapping of OWL2 Descriptions

mapDescription :: CASLSign

-> ClassExpression

-> Int

-> Result CASLFORMULA

mapDescription cSig desc var = case desc of

Expression u -> mapClassURI cSig u (mkNName var)

ObjectJunction ty ds ->

do

des0 <- mapM (flip (mapDescription cSig) var) ds

return $ case ty of

UnionOf -> disjunct des0

IntersectionOf -> conjunct des0

ObjectComplementOf d ->

do

des0 <- mapDescription cSig d var

return $ mkNeg des0

ObjectOneOf is ->

do

ind0 <- mapM (mapIndivURI cSig) is

let var0 = toQualVar (mkVarDecl (mkNName var) thing)

let forms = map (mkStEq var0) ind0

return $ disjunct forms

ObjectValuesFrom ty o d ->

do

oprop0 <- mapObjProp cSig o var (var + 1)

desc0 <- mapDescription cSig d (var + 1)

case ty of

SomeValuesFrom ->

return $ mkExist

[mkVarDecl (mkNName (var + 1)) thing]

(conjunct [oprop0, desc0])

AllValuesFrom ->

return $ mkForall

[mkVarDecl (mkNName (var + 1)) thing]

(mkImpl oprop0 desc0)

ObjectHasSelf o -> mapObjProp cSig o var var

ObjectHasValue o i -> mapObjPropI cSig o (OVar var) (OIndi i)

ObjectCardinality c ->

case c of

Cardinality ct n oprop d

->

do

let vlst = [(var + 1) .. (n + var)]

vlstM = [(var + 1) .. (n + var + 1)]

dOut <- (\ x -> case x of

Nothing -> return []

Just y ->

mapM (mapDescription cSig y) vlst

) d

let dlst = map (\ (x, y) ->

mkNeg

(

mkStEq

(toQualVar (mkVarDecl

(mkNName x) thing))

(toQualVar (mkVarDecl

(mkNName y) thing))

)

) $ comPairs vlst vlst

dlstM = map (\ (x, y) ->

mkStEq

(toQualVar (mkVarDecl

(mkNName x) thing))

(toQualVar (mkVarDecl

(mkNName y) thing))

) $ comPairs vlstM vlstM

qVars = map (\ x ->

mkVarDecl (mkNName x) thing

) vlst

qVarsM = map (\ x ->

mkVarDecl (mkNName x) thing

) vlstM

oProps <- mapM (mapObjProp cSig oprop var) vlst

oPropsM <- mapM (mapObjProp cSig oprop var) vlstM

let minLst = mkExist

qVars

(conjunct (dlst ++ dOut ++ oProps))

let maxLst = mkForall

qVarsM

(

mkImpl

(conjunct (oPropsM ++ dOut))

(disjunct dlstM)

)

case ct of

MinCardinality -> return minLst

MaxCardinality -> return maxLst

ExactCardinality -> return $ conjunct [minLst, maxLst]

DataValuesFrom ty dpe dr ->

do

oprop0 <- mapDataProp cSig dpe var (var + 1)

desc0 <- mapDataRange cSig dr (var + 1)

case ty of

SomeValuesFrom ->

return $ mkExist

[mkVarDecl (mkNName (var + 1)) thing]

(conjunct [oprop0, desc0])

AllValuesFrom ->

return $ mkForall

[mkVarDecl (mkNName (var + 1)) thing]

(mkImpl oprop0 desc0)

DataHasValue _ _ -> fail "DataHasValue handling nyi"

DataCardinality _ -> fail "DataCardinality handling nyi"