{- |

Module : $Header$

Description : Composition rules in the development graphs calculus

Copyright : (c) Jorina F. Gerken, Till Mossakowski, Uni Bremen 2002-2006

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

Maintainer : ken@informatik.uni-bremen.de

Stability : provisional

Portability : non-portable(Logic)

Composition rules in the development graphs calculus.

Follows Sect. IV:4.4 of the CASL Reference Manual, while combining

several rules into one.

-}

module Proofs.Composition

( composition

, compositionCreatingEdges

, compositionFromList

, compositionCreatingEdgesFromList

) where

import Logic.Grothendieck

import Proofs.EdgeUtils

import Proofs.StatusUtils

import Syntax.AS_Library

import Static.DevGraph

-- import Static.DGToSpec

import qualified Common.Lib.Graph as Tree

import Data.Graph.Inductive.Graph

import Data.List

compositionCreatingEdgesFromList :: LIB_NAME -> [LEdge DGLinkLab] -> LibEnv

-> LibEnv

compositionCreatingEdgesFromList libname ls proofStatus =

let dgraph = lookupDGraph libname proofStatus

pathsToCompose = getAllPathsOfTypeFromGoalList dgraph isGlobalThm ls

(newDGraph, newHistoryElem)

= compositionCreatingEdgesAux dgraph pathsToCompose ([], [])

in mkResultProofStatus libname proofStatus newDGraph newHistoryElem

{- | creates new edges by composing all paths of global theorem edges

in the currenct development graph. These new edges are proven global

theorems with the morphism and the conservativity of the corresponding

path. If a new edge is the proven version of a previsously existing

edge, that edge is deleted. -}

compositionCreatingEdges :: LIB_NAME -> LibEnv -> LibEnv

compositionCreatingEdges libname proofStatus =

let dgraph = lookupDGraph libname proofStatus

allEdges = labEdgesDG dgraph

in compositionCreatingEdgesFromList libname allEdges proofStatus

{- auxiliary method for compositionCreatingEdges -}

compositionCreatingEdgesAux :: DGraph -> [[LEdge DGLinkLab]]

-> ([DGRule],[DGChange])

-> (DGraph,([DGRule],[DGChange]))

compositionCreatingEdgesAux dgraph [] historyElem = (dgraph,historyElem)

compositionCreatingEdgesAux dgraph (path:paths) (rules,changes) =

case calculateMorphismOfPath path of

Nothing -> compositionCreatingEdgesAux dgraph paths (rules,changes)

Just _ -> compositionCreatingEdgesAux newDGraph2 paths

(Composition path : rules,

changes ++ newChanges ++ newChanges2)

where

(src, _, _) = head path

(_, tgt, _) = last path

Just morph = calculateMorphismOfPath path

cons = case getConservativityOfPath path of

Mono -> if isTransportable morph then Mono else Cons

c -> c

consStatus = LeftOpen

newEdge = (src,

tgt,

DGLink {dgl_morphism = morph,

dgl_type = (GlobalThm (Proven (Composition path)

$ foldl addEdgeId emptyProofBasis

$ map getEdgeId path))

cons consStatus,

dgl_origin = DGLinkProof,

dgl_id = defaultEdgeId}

)

(newDGraph, newChanges) = deleteRedundantEdges dgraph newEdge

-- deleting does not work, because newEdge is not LeftOpen

(newDGraph2, newChanges2) =

updateWithOneChange (InsertEdge newEdge) newDGraph

{- | this method is used by compositionCreatingEdgesAux. It selects

all unproven global theorem edges in the given development graph that

have the same source, target, morphism and conservativity as the given

one. It then deletes them from the given graph and adds a

corresponding change -}

deleteRedundantEdges :: DGraph -> LEdge DGLinkLab -> (DGraph, [DGChange])

deleteRedundantEdges dgraph (src, tgt, labl) = let

redundantEdges =

[ (src, tgt, l) | l <- Tree.getLEdges src tgt $ dgBody dgraph

, isUnprovenGlobalThm $ dgl_type l

, dgl_morphism l == dgl_morphism labl

, haveSameCons l labl ]

haveSameCons :: DGLinkLab -> DGLinkLab -> Bool

haveSameCons lab1 lab2 = case (dgl_type lab1, dgl_type lab2) of

(GlobalThm LeftOpen cons1 status1,

GlobalThm LeftOpen cons2 status2) ->

cons1 == cons2 &&

isProvenThmLinkStatus status1 == isProvenThmLinkStatus status2

_ -> False

(newGraph, changes) =

mapAccumL deleteRedundantEdgesAux dgraph redundantEdges

in (newGraph, concat changes)

{- auxiliary method for deleteRedundantEdgesAux -}

deleteRedundantEdgesAux :: DGraph -> LEdge DGLinkLab -> (DGraph, [DGChange])

deleteRedundantEdgesAux dgraph edge =

updateWithOneChange (DeleteEdge edge) dgraph

-- | composition without creating new new edges

compositionFromList :: LIB_NAME -> [LEdge DGLinkLab] -> LibEnv -> LibEnv

compositionFromList libname glbThmEdge proofStatus = let

dgraph = lookupDGraph libname proofStatus

(newDGraph, newHistoryElems) = mapAccumL compositionAux dgraph

$ filter (liftE isGlobalThm) $ glbThmEdge

in mkResultProofStatus libname proofStatus newDGraph

(concatMap fst newHistoryElems, concatMap snd newHistoryElems)

{- | gets all unproven global theorem edges in the current development graph

and checks, if they are a composition of a global theorem path. If so,

the edge is proven, with the corresponding path as its proof basis.

If there is more than one path, the first of them is arbitrarily taken. -}

composition :: LIB_NAME -> LibEnv -> LibEnv

composition libname proofStatus =

let dgraph = lookupDGraph libname proofStatus

globalThmEdges = labEdgesDG dgraph

in compositionFromList libname globalThmEdges proofStatus

{- | auxiliary method for composition -}

compositionAux :: DGraph -> LEdge DGLinkLab -> (DGraph, ([DGRule], [DGChange]))

compositionAux dgraph edge =

case compositionForOneEdge dgraph edge of

Nothing -> (dgraph, emptyHistory)

Just (newEdge, proofbasis) -> let

(newDGraph, newChanges) =

updateWithChanges [DeleteEdge edge, InsertEdge newEdge] dgraph

in (newDGraph, ([Composition proofbasis], newChanges))

{- | checks for the given edges, if there is a path in the given

development graph that it is a composition of. If so, it is replaced

by a proven version with the path as its proof basis. The method

returns Nothing if there is no such path or else the new edge and the

path. -}

compositionForOneEdge :: DGraph -> LEdge DGLinkLab

-> Maybe (LEdge DGLinkLab,[LEdge DGLinkLab])

compositionForOneEdge dgraph edge@(src,tgt,labl) =

compositionForOneEdgeAux edge [path | path <- pathsOfMorphism,

noPath edge path]

where

globThmPaths = getAllPathsOfTypeBetween dgraph isGlobalThm src tgt

pathsOfMorphism = filterPathsByMorphism (dgl_morphism labl) globThmPaths

{- auxiliary method for compositionForOneEdge -}

compositionForOneEdgeAux :: LEdge DGLinkLab -> [[LEdge DGLinkLab]]

-> Maybe (LEdge DGLinkLab,[LEdge DGLinkLab])

compositionForOneEdgeAux _ [] = Nothing

compositionForOneEdgeAux edge@(src,tgt,labl) (path:paths)

| cons <= pathCons = if cons == Mono

then handleConservativityMono newEdge path

else Just (newEdge,path)

| otherwise = compositionForOneEdgeAux edge paths

where

cons = getConservativity edge

pathCons = getConservativityOfPath path

consStatus = getConservativityStatus edge

newEdge = (src,

tgt,

DGLink {dgl_morphism = dgl_morphism labl,

dgl_type = GlobalThm (Proven (Composition path)

$ foldl addEdgeId emptyProofBasis

$ map getEdgeId path) cons consStatus,

dgl_origin = DGLinkProof,

dgl_id = defaultEdgeId}

)

{- | checks if the morphism of the given path is transportable. This

is necessary for the composition of a path, if its conservativity is

Mono. This method is used by compositionForOneEdgeAux to check, if a

composition in case of conservativity Mono is possible. -}

handleConservativityMono :: LEdge DGLinkLab -> [LEdge DGLinkLab]

-> Maybe (LEdge DGLinkLab,[LEdge DGLinkLab])

handleConservativityMono newEdge path =

case calculateMorphismOfPath path of

Nothing -> Nothing

Just morph -> if isTransportable morph then Just (newEdge,path)

else Nothing

{- | returns the conservativity of the given edge -}

getConservativity :: LEdge DGLinkLab -> Conservativity

getConservativity (_,_,labl) =

case dgl_type labl of

LocalThm _ cons _ -> cons

GlobalThm _ cons _ -> cons

_ -> error "getConservativity"

{- | returns the conservativity of the given path -}

getConservativityOfPath :: [LEdge DGLinkLab] -> Conservativity

getConservativityOfPath path = minimum [getConservativity e | e <- path]

{- | returns the conservativity status of the given edge -}

getConservativityStatus :: LEdge DGLinkLab -> ThmLinkStatus

getConservativityStatus (_,_,labl) =

case dgl_type labl of

LocalThm _ _ consStatus -> consStatus

GlobalThm _ _ consStatus -> consStatus

_ -> error "getConservativityStatus"