{- |

Module : $Header$

Description : Morphism of Common Logic

Copyright : (c) Uni Bremen DFKI 2010

License : similar to LGPL, see HetCATS/LICENSE.txt

Maintainer : kluc@informatik.uni-bremen.de

Stability : experimental

Portability : non-portable (via Logic.Logic)

Morphism of Common Logic

-}

module CommonLogic.Morphism

( Morphism (..)

, pretty -- pretty printing

, idMor -- identity morphism

, isLegalMorphism -- check if morhpism is ok

, composeMor -- composition

, inclusionMap -- inclusion map

, mkMorphism -- create Morphism

, mapSentence -- map of sentences

, mapSentenceH -- map of sentences, without Result type

, applyMap -- application function for maps

, applyMorphism -- application function for morphism

, morphismUnion

) where

import qualified Data.Map as Map

import qualified Data.Set as Set

import qualified Common.Result as Result

import Common.Id as Id

import Common.Result

import Common.Doc

import Common.DocUtils

import CommonLogic.AS_CommonLogic as AS_BASIC

import CommonLogic.Sign as Sign

-- maps of sets

data Morphism = Morphism

{ source :: Sign

, target :: Sign

, propMap :: Map.Map Id Id

} deriving (Eq, Ord, Show)

instance Pretty Morphism where

pretty = printMorphism

-- | Constructs an id-morphism

idMor :: Sign -> Morphism

idMor a = inclusionMap a a

-- | Determines whether a morphism is valid

isLegalMorphism :: Morphism -> Bool

isLegalMorphism pmor =

let psource = items $ source pmor

ptarget = items $ target pmor

pdom = Map.keysSet $ propMap pmor

pcodom = Set.map (applyMorphism pmor) psource

in Set.isSubsetOf pcodom ptarget && Set.isSubsetOf pdom psource

-- | Application funtion for morphisms

applyMorphism :: Morphism -> Id -> Id

applyMorphism mor idt = Map.findWithDefault idt idt $ propMap mor

-- | Application function for propMaps

applyMap :: Map.Map Id Id -> Id -> Id

applyMap pmap idt = Map.findWithDefault idt idt pmap

-- | Composition of morphisms in propositional Logic

composeMor :: Morphism -> Morphism -> Result Morphism

composeMor f g =

let fSource = source f

gTarget = target g

fMap = propMap f

gMap = propMap g

in return Morphism

{ source = fSource

, target = gTarget

, propMap = if Map.null gMap then fMap else

Set.fold ( \ i -> let j = applyMap gMap (applyMap fMap i) in

if i == j then id else Map.insert i j)

Map.empty $ items fSource }

-- | Pretty printing for Morphisms

printMorphism :: Morphism -> Doc

printMorphism m = pretty (source m) <> text "-->" <> pretty (target m)

<> vcat (map ( \ (x, y) -> lparen <> pretty x <> text ","

<> pretty y <> rparen) $ Map.assocs $ propMap m)

-- | Inclusion map of a subsig into a supersig

inclusionMap :: Sign.Sign -> Sign.Sign -> Morphism

inclusionMap s1 s2 = Morphism

{ source = s1

, target = s2

, propMap = Map.empty }

-- | creates a Morphism

mkMorphism :: Sign.Sign -> Sign.Sign -> Map.Map Id Id -> Morphism

mkMorphism s t p =

Morphism { source = s

, target = t

, propMap = p }

-- | sentence translation along signature morphism

-- here just the renaming of formulae

mapSentence :: Morphism -> AS_BASIC.SENTENCE -> Result.Result AS_BASIC.SENTENCE

mapSentence mor = return . mapSentenceH mor

mapSentenceH :: Morphism -> AS_BASIC.SENTENCE -> AS_BASIC.SENTENCE

mapSentenceH mor frm = case frm of

AS_BASIC.Quant_sent qs rn -> case qs of

AS_BASIC.Universal xs sen -> AS_BASIC.Quant_sent

(AS_BASIC.Universal xs (mapSentenceH mor sen)) rn -- fix

AS_BASIC.Existential xs sen -> AS_BASIC.Quant_sent

(AS_BASIC.Existential xs (mapSentenceH mor sen)) rn -- fix

AS_BASIC.Bool_sent bs rn -> case bs of

AS_BASIC.Conjunction sens -> AS_BASIC.Bool_sent

(AS_BASIC.Conjunction (map (mapSentenceH mor) sens)) rn

AS_BASIC.Disjunction sens -> AS_BASIC.Bool_sent

(AS_BASIC.Disjunction (map (mapSentenceH mor) sens)) rn

AS_BASIC.Negation sen -> AS_BASIC.Bool_sent

(AS_BASIC.Negation (mapSentenceH mor sen)) rn

AS_BASIC.Implication s1 s2 -> AS_BASIC.Bool_sent

(AS_BASIC.Implication (mapSentenceH mor s1) (mapSentenceH mor s2)) rn

AS_BASIC.Biconditional s1 s2 -> AS_BASIC.Bool_sent

(AS_BASIC.Biconditional (mapSentenceH mor s1) (mapSentenceH mor s2))

rn

AS_BASIC.Atom_sent atom rn -> AS_BASIC.Atom_sent atom rn -- fix

AS_BASIC.Comment_sent cm sen rn -> AS_BASIC.Comment_sent cm sen rn -- unused

AS_BASIC.Irregular_sent sen rn -> AS_BASIC.Irregular_sent sen rn -- unused

{-

AS_BASIC.Predication predH -> AS_BASIC.Predication

$ id2SimpleId $ applyMorphism mor $ Id.simpleIdToId predH

-}

morphismUnion :: Morphism -> Morphism -> Result.Result Morphism

morphismUnion mor1 mor2 =

let pmap1 = propMap mor1

pmap2 = propMap mor2

p1 = source mor1

p2 = source mor2

up1 = Set.difference (items p1) $ Map.keysSet pmap1

up2 = Set.difference (items p2) $ Map.keysSet pmap2

(pds, pmap) = foldr ( \ (i, j) (ds, m) -> case Map.lookup i m of

Nothing -> (ds, Map.insert i j m)

Just k -> if j == k then (ds, m) else

(Diag Error

("incompatible mapping of prop " ++ showId i " to "

++ showId j " and " ++ showId k "")

nullRange : ds, m)) ([], pmap1)

(Map.toList pmap2 ++ map (\ a -> (a, a))

(Set.toList $ Set.union up1 up2))

in if null pds then return Morphism

{ source = unite p1 p2

, target = unite (target mor1) $ target mor2

, propMap = pmap } else Result pds Nothing