{- |

Module : $Header$

Description : local proof rukes for development graphs

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

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

Maintainer : till@informatik.uni-bremen.de

Stability : provisional

Portability : non-portable(Logic)

local proof rukes for development graphs

Follows Sect. IV:4.4 of the CASL Reference Manual.

-}

{-

Order of rule application: try to use local links induced by %implies

for subsumption proofs (such that the %implied formulas need not be

re-proved)

-}

module Proofs.Local

( localInference

, locDecomp

, locDecompFromList

, localInferenceFromList

) where

import Proofs.EdgeUtils

import Proofs.StatusUtils

import Logic.Grothendieck

import Logic.Prover

import Static.GTheory

import Static.DevGraph

import Static.DGToSpec

import Syntax.AS_Library

import Common.Result

import Common.AS_Annotation

import qualified Data.Map as Map

import qualified Common.OrderedMap as OMap

import Data.Graph.Inductive.Graph

import Data.Maybe

-- --------------------

-- local decomposition

-- --------------------

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

locDecompFromList ln localThmEdges libEnv=

let dgraph = lookupDGraph ln libEnv

finalLocalThmEdges = filter (liftE isUnprovenLocalThm) localThmEdges

(nextDGraph, nextHistoryElem) =

locDecompAux libEnv ln dgraph ([],[]) finalLocalThmEdges

in mkResultProofStatus ln libEnv nextDGraph nextHistoryElem

locDecomp :: LIB_NAME -> LibEnv -> LibEnv

locDecomp ln libEnv =

let dgraph = lookupDGraph ln libEnv

localThmEdges = labEdgesDG dgraph

in locDecompFromList ln localThmEdges libEnv

{- auxiliary function for locDecomp (above)

actual implementation -}

locDecompAux :: LibEnv -> LIB_NAME -> DGraph -> ([DGRule],[DGChange])

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

locDecompAux _ _ dgraph historyElement [] = (dgraph, historyElement)

locDecompAux libEnv ln dgraph (rules,changes)

(ledge@(src, tgt, edgeLab) : list) =

if not (isIdentityEdge ledge libEnv dgraph) && nullProofBasis proofbasis

then

locDecompAux libEnv ln dgraph (rules, changes) list

else

locDecompAux libEnv ln newGraph (newRules,newChanges) list

where

morphism = dgl_morphism edgeLab

allPaths = getAllLocGlobPathsBetween dgraph src tgt

th = computeLocalTheory libEnv ln src

pathsWithoutEdgeItself = filter (noPath ledge) allPaths

filteredPaths = filterByTranslation th morphism pathsWithoutEdgeItself

proofbasis = selectProofBasis dgraph ledge filteredPaths

(auxGraph, auxChanges) =

updateWithOneChange (DeleteEdge ledge) dgraph changes

LocalThm _ conservativity conservStatus = dgl_type edgeLab

newEdge = (src,

tgt,

DGLink {dgl_morphism = morphism,

dgl_type =

(LocalThm (Proven (LocDecomp ledge) proofbasis)

conservativity conservStatus),

dgl_origin = DGLinkProof,

dgl_id = dgl_id edgeLab}

)

(newGraph, newChanges) =

insertDGLEdge newEdge auxGraph auxChanges

--updateWithChanges [DeleteEdge ledge, InsertEdge newEdge] dgraph changes

newRules = LocDecomp ledge : rules

{- | removes all paths from the given list of paths whose morphism does

not translate the given sentence list to the same resulting sentence

list as the given morphism. -}

filterByTranslation :: Maybe G_theory -> GMorphism -> [[LEdge DGLinkLab]]

-> [[LEdge DGLinkLab]]

filterByTranslation maybeTh morphism paths =

case maybeTh of

Just th -> filter (isSameTranslation th morphism) paths

Nothing -> []

{- | checks if the given morphism and the morphism of the given path

translate the given sentence list to the same resulting sentence list. -}

isSameTranslation :: G_theory -> GMorphism -> [LEdge DGLinkLab] -> Bool

isSameTranslation th morphism path =

case calculateMorphismOfPath path of

Just morphismOfPath ->

maybeResult (translateG_theory morphism th) ==

maybeResult (translateG_theory morphismOfPath th)

Nothing -> False

-- ----------------------------------------------

-- local inference

-- ----------------------------------------------

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

localInferenceFromList ln localThmEdges libEnv =

let dgraph = lookupDGraph ln libEnv

finalLocalThmEdges = filter (liftE isUnprovenLocalThm) localThmEdges

(nextDGraph, nextHistoryElem) =

localInferenceAux libEnv ln dgraph ([],[]) finalLocalThmEdges

in mkResultProofStatus ln libEnv nextDGraph nextHistoryElem

localInference :: LIB_NAME -> LibEnv -> LibEnv

localInference ln libEnv =

let dgraph = lookupDGraph ln libEnv

localThmEdges = filter (liftE isUnprovenLocalThm) (labEdgesDG dgraph)

in localInferenceFromList ln localThmEdges libEnv

-- auxiliary method for localInference

localInferenceAux :: LibEnv -> LIB_NAME -> DGraph -> ([DGRule], [DGChange])

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

localInferenceAux _ _ dgraph rc [] = (dgraph, rc)

localInferenceAux libEnv ln dgraph (rules, changes)

(ledge@(src,tgt,edgeLab) : list) =

case maybeThSrc of

Just thSrc ->

case (maybeResult (computeTheory libEnv ln tgt),

maybeResult (translateG_theory morphism thSrc)) of

(Just (G_theory lidTgt _ _ sensTgt _),

Just (G_theory lidSrc _ _ sensSrc _)) ->

case maybeResult (coerceThSens lidTgt lidSrc "" sensTgt) of

Nothing -> localInferenceAux libEnv ln dgraph (rules,changes) list

Just sentencesTgt ->

-- check if all source axioms are also axioms in the target

let goals = OMap.filter isAxiom sensSrc

`diffSens` sentencesTgt

goals' = markAsGoal goals

newTh = case (dgn_theory oldContents) of

G_theory lid sig ind sens ind' ->

case coerceThSens lidSrc lid "" goals' of

Nothing -> G_theory lid sig ind sens ind'

Just goals'' ->

G_theory lid sig ind

(sens `joinSens` goals'') startThId

in if OMap.null goals

then

let (newGraph, newChanges) =

updateWithChanges

[DeleteEdge ledge, InsertEdge newEdge]

dgraph changes

in localInferenceAux libEnv ln newGraph

(newRules,newChanges) list

else

let newContents = oldContents{dgn_theory = newTh}

(newGraph, newChanges) =

updateWithChanges

[ DeleteEdge ledge

, SetNodeLab oldContents

(tgt, newContents)

, InsertEdge newEdge]

dgraph changes

newLibEnv = Map.adjust (const newGraph) ln libEnv

in localInferenceAux newLibEnv ln newGraph

(newRules,newChanges) list

_ -> localInferenceAux libEnv ln dgraph (rules,changes) list

_ -> localInferenceAux libEnv ln dgraph (rules,changes) list

where

morphism = dgl_morphism edgeLab

maybeThSrc = computeLocalTheory libEnv ln src

LocalThm _ conservativity conservStatus = dgl_type edgeLab

-- notice that the original id from edgeLab is kept

newLab = DGLink

{ dgl_morphism = morphism

, dgl_type = LocalThm (Proven (LocInference ledge) emptyProofBasis)

conservativity conservStatus

, dgl_origin = DGLinkProof

, dgl_id = dgl_id edgeLab}

newEdge = (src, tgt, newLab)

newRules = LocInference ledge : rules

oldContents = labDG dgraph tgt