{-# OPTIONS -cpp #-}

{-|

Module : $Header$

Copyright : (c) Jorina F. Gerken, Till Mossakowski, Uni Bremen 2002-2004

Licence : similar to LGPL, see HetCATS/LICENCE.txt or LIZENZ.txt

Maintainer : jfgerken@tzi.de

Stability : provisional

Portability : non-portable(Logic)

Proofs in development graphs.

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

-}

{-

References:

T. Mossakowski, S. Autexier and D. Hutter:

Extending Development Graphs With Hiding.

H. Hussmann (ed.): Fundamental Approaches to Software Engineering 2001,

Lecture Notes in Computer Science 2029, p. 269-283,

Springer-Verlag 2001.

todo in general:

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)

Integrate stuff from Saarbr�cken

Add proof status information

what should be in proof status:

- proofs of thm links according to rules

- cons, def and mono annos, and their proofs

todo for Jorina:

todo:

- bei GlobDecomp hinzuf�gen:

zus�tzlich alle Pfade K<--theta-- M --sigma-->N in den aktuellen

Knoten N, die mit einem HidingDef anfangen, und danach nur GlobalDef

theta ist der Signaturmorphismus des HidingDef's (geht "falsch rum")

sigma ist die Komposition der Signaturmorphismen auf dem restl. Pfad

f�r jeden solchen Pfad: einen HidingThm theta einf�gen. sigma ist

der normale Morphismus (wie bei jedem anderen Link)

siehe auch Seite 302 des CASL Reference Manual

-}

module Proofs.Proofs where

--import Debug.Trace

import Data.Dynamic

import Data.List(nub)

import Logic.Logic

import Logic.Prover

import Logic.Grothendieck

import Logic.Comorphism

import Static.DevGraph

import Static.DGToSpec

import Common.Result

import Common.Lib.Graph

import qualified Common.Lib.Map as Map

import Common.Id

import Common.AS_Annotation

import Syntax.AS_Library

import Syntax.Print_AS_Library

#ifdef UNI_PACKAGE

import GUI.HTkUtils

#else

import Data.Char(isDigit, digitToInt)

listBox :: String -> [String] -> IO (Maybe Int)

listBox prompt choices = do

putStrLn prompt

mapM_ putStrLn $ zipWith (\ n c -> shows n ": " ++ c) [0::Int ..] choices

putStrLn "Please enter a number on the next line"

s <- getLine

if all isDigit s then

let n = foldl ( \ r a -> r * 10 + digitToInt a) 0 s in

if n >= length choices then

putStrLn "number to large, try again"

>> listBox prompt choices

else putStrLn ("you have chosen entry \"" ++ choices!!n)

>> return (Just n)

else putStrLn ("illegal input \"" ++ s ++ "\" try again")

>> listBox prompt choices

#endif

{-

proof status = (DG0,[(R1,DG1),...,(Rn,DGn)])

DG0 is the development graph resulting from the static analysis

Ri is a list of rules that transforms DGi-1 to DGi

With the list of intermediate proof states, one can easily implement

an undo operation

-}

type ProofStatus = (GlobalContext,LibEnv,[([DGRule],[DGChange])],DGraph)

data DGRule =

TheoremHideShift

| HideTheoremShift (LEdge DGLinkLab)

| Borrowing

| ConsShift

| DefShift

| MonoShift

| ConsComp

| DefComp

| MonoComp

| DefToMono

| MonoToCons

| FreeIsMono

| MonoIsFree

| Composition

| GlobDecomp (LEdge DGLinkLab) -- edge in the conclusion

| LocDecomp (LEdge DGLinkLab)

| LocSubsumption (LEdge DGLinkLab)

| GlobSubsumption (LEdge DGLinkLab)

| LocalInference

| BasicInferendge BasicProof

| BasicConsInference Edge BasicConsProof

deriving (Eq, Show)

data DGChange = InsertNode (LNode DGNodeLab)

| DeleteNode (LNode DGNodeLab)

| InsertEdge (LEdge DGLinkLab)

| DeleteEdge (LEdge DGLinkLab)

deriving (Eq,Show)

data BasicProof =

forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

BasicProof lid (Proof_status proof_tree)

| Guessed

| Conjectured

| Handwritten

instance Eq BasicProof where

Guessed == Guessed = True

Conjectured == Conjectured = True

Handwritten == Handwritten = True

BasicProof lid1 p1 == BasicProof lid2 p2 =

coerce lid1 lid2 p1 == Just p2

instance Show BasicProof where

show (BasicProof lid1 p1) = show p1

show Guessed = "Guessed"

show Conjectured = "Conjectured"

show Handwritten = "Handwritten"

data BasicConsProof = BasicConsProof -- more detail to be added ...

deriving (Eq, Show)

{- todo: implement apply for GlobDecomp and Subsumption

the list of DGChage must be constructed in parallel to the

new DGraph -}

applyRule :: DGRule -> DGraph -> Maybe ([DGChange],DGraph)

applyRule = error "Proofs.hs:applyRule"

automatic :: ProofStatus -> IO ProofStatus

automatic = automaticRecursive 0

{- applies the rules recursively until no further changes can be made -}

automaticRecursive :: Int -> ProofStatus -> IO ProofStatus

automaticRecursive cnt proofStatus = do

(globalContext, libEnv, history, dgraph) <- automaticAux proofStatus

let (newHistoryPart, oldHistory) = splitAt (5+cnt) history

if (null (concat (map snd (take 5 newHistoryPart)))) && (cnt == 1) then

return proofStatus

else do

let (rules, changes) = concatHistoryElems (reverse newHistoryPart)

newHistoryElem = (rules, removeContraryChanges changes)

newHistory = newHistoryElem:oldHistory

automaticRecursive 1 (globalContext, libEnv, newHistory, dgraph)

removeContraryChanges :: [DGChange] -> [DGChange]

removeContraryChanges [] = []

removeContraryChanges (change:changes) =

if elem contraryChange changes

then removeContraryChanges (removeChange contraryChange changes)

else change:(removeContraryChanges changes)

where

contraryChange = getContraryChange change

getContraryChange :: DGChange -> DGChange

getContraryChange change =

case change of

InsertEdge edge -> DeleteEdge edge

DeleteEdge edge -> InsertEdge edge

InsertNode node -> DeleteNode node

DeleteNode node -> InsertNode node

removeChange :: DGChange -> [DGChange] -> [DGChange]

removeChange change changes =

(takeWhile (change /=) changes)

++(tail (dropWhile (change /=) changes))

automaticAux :: ProofStatus -> IO ProofStatus

automaticAux = (hideTheoremShift True).locDecomp.locSubsume.globDecomp.globSubsume

concatHistoryElems :: [([DGRule],[DGChange])] -> ([DGRule],[DGChange])

concatHistoryElems [] = ([],[])

concatHistoryElems ((rules,changes):elems) =

(rules++(fst (concatHistoryElems elems)),changes++(snd (concatHistoryElems elems)))

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

-- global decomposition

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

{- apply rule GlobDecomp to all global theorem links in the current DG

current DG = DGm

add to proof status the pair ([GlobDecomp e1,...,GlobDecomp en],DGm+1)

where e1...en are the global theorem links in DGm

DGm+1 results from DGm by application of GlobDecomp e1,...,GlobDecomp en -}

{- applies global decomposition to all unproven global theorem edges

if possible -}

globDecomp :: ProofStatus -> ProofStatus

globDecomp proofStatus@(globalContext,libEnv,history,dgraph) =

(globalContext, libEnv, ((finalHistoryElem):history), finalDGraph)

where

globalThmEdges = filter isUnprovenGlobalThm (labEdges dgraph)

(newDGraph, newHistoryElem) = globDecompAux dgraph globalThmEdges ([],[])

(finalDGraph, finalHistoryElem)

= removeSuperfluousInsertions newDGraph newHistoryElem

{- removes all superfluous insertions from the list of changes as well as

from the development graph (i.e. insertions of edges that are

equivalent to edges or paths resulting from the other insertions) -}

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

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

removeSuperfluousInsertions dgraph (rules,changes)

= (newDGraph,(rules,newChanges))

where

localThms = [edge | (InsertEdge edge)

<- filter isLocalThmInsertion changes]

(newDGraph, localThmsToInsert)

= removeSuperfluousEdges dgraph localThms

newChanges = (filter (not.isLocalThmInsertion) changes)

++ [InsertEdge edge | edge <- localThmsToInsert]

{- auxiliary function for globDecomp (above)

actual implementation -}

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

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

globDecompAux dgraph [] historyElem = (dgraph, historyElem)

globDecompAux dgraph (edge:edges) historyElem =

globDecompAux newDGraph edges newHistoryElem

where

(newDGraph, newChanges) = globDecompForOneEdge dgraph edge

newHistoryElem = (((GlobDecomp edge):(fst historyElem)),

(newChanges++(snd historyElem)))

-- applies global decomposition to a single edge

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

globDecompForOneEdge dgraph edge =

globDecompForOneEdgeAux dgraph edge [] paths

where

pathsToSource

= getAllLocOrHideGlobDefPathsTo dgraph (getSourceNode edge) []

paths = [(node, path++(edge:[]))| (node,path) <- pathsToSource]

{- auxiliary funktion for globDecompForOneEdge (above)

actual implementation -}

globDecompForOneEdgeAux :: DGraph -> LEdge DGLinkLab -> [DGChange] ->

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

{- if the list of paths is empty from the beginning, nothing is done

otherwise the unprovenThm edge is replaced by a proven one -}

globDecompForOneEdgeAux dgraph edge@(source,target,edgeLab) changes [] =

if null changes then (dgraph, changes)

else

if isDuplicate provenEdge dgraph changes

then (delLEdge edge dgraph,

((DeleteEdge edge):changes))

else ((insEdge provenEdge (delLEdge edge dgraph)),

((DeleteEdge edge):((InsertEdge provenEdge):changes)))

where

(GlobalThm _ conservativity conservStatus) = (dgl_type edgeLab)

proofBasis = getLabelsOfInsertedEdges changes

provenEdge = (source,

target,

DGLink {dgl_morphism = dgl_morphism edgeLab,

dgl_type =

(GlobalThm (Proven proofBasis)

conservativity conservStatus),

dgl_origin = DGProof}

)

-- for each path an unproven localThm edge is inserted

globDecompForOneEdgeAux dgraph edge@(source,target,edgeLab) changes

((node,path):list) =

if isRedundant newEdge dgraph changes list

then globDecompForOneEdgeAux dgraph edge changes list

else globDecompForOneEdgeAux newGraph edge newChanges list

where

isHiding = not (null path) && isHidingDef (head path)

morphismPath = if isHiding then tail path else path

morphism = case calculateMorphismOfPath morphismPath of

Just morph -> morph

Nothing ->

error "globDecomp: could not determine morphism of new edge"

newEdge = if isHiding then hidingEdge else localEdge

hidingEdge =

(node,

target,

DGLink {dgl_morphism = morphism,

dgl_type = (HidingThm (dgl_morphism (getLabelOfEdge (head path))) (Static.DevGraph.Open)),

dgl_origin = DGProof})

localEdge = (node,

target,

DGLink {dgl_morphism = morphism,

dgl_type = (LocalThm (Static.DevGraph.Open)

None (Static.DevGraph.Open)),

dgl_origin = DGProof}

)

newGraph = insEdge newEdge dgraph

newChanges = ((InsertEdge newEdge):changes)

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

-- global subsumption

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

-- applies global subsumption to all unproven global theorem edges if possible

globSubsume :: ProofStatus -> ProofStatus

globSubsume proofStatus@(globalContext,libEnv,history,dGraph) =

(globalContext, libEnv, nextHistoryElem:history, nextDGraph)

where

globalThmEdges = filter isUnprovenGlobalThm (labEdges dGraph)

-- the 'nub' is just a workaround, because some of the edges in the graph

-- do not differ from each other in this represetation - which causes

-- problems on deletion

result = globSubsumeAux libEnv dGraph ([],[]) (nub globalThmEdges)

nextDGraph = fst result

nextHistoryElem = snd result

{- auxiliary function for globSubsume (above)

the actual implementation -}

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

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

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

globSubsumeAux libEnv dgraph (rules,changes) ((ledge@(src,tgt,edgeLab)):list) =

if not (null proofBasis) || isIdentityEdge ledge libEnv dgraph

then

if isDuplicate newEdge dgraph changes then

globSubsumeAux libEnv (delLEdge ledge dgraph)

(newRules,(DeleteEdge ledge):changes) list

else

globSubsumeAux libEnv (insEdge newEdge (delLEdge ledge dgraph))

(newRules,(DeleteEdge ledge):((InsertEdge newEdge):changes)) list

else

globSubsumeAux libEnv dgraph (rules,changes) list

where

morphism = dgl_morphism edgeLab

allPaths = getAllGlobPathsOfMorphismBetween dgraph morphism src tgt

filteredPaths = [path| path <- allPaths, notElem ledge path]

proofBasis = selectProofBasis edgeLab filteredPaths

(GlobalThm _ conservativity conservStatus) = dgl_type edgeLab

newEdge = (src,

tgt,

DGLink {dgl_morphism = morphism,

dgl_type = (GlobalThm (Proven proofBasis)

conservativity conservStatus),

dgl_origin = DGProof}

)

newRules = (GlobSubsumption ledge):rules

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

-- local decomposition

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

{- a merge of the rules local subsumption, local decomposition I and

local decomposition II -}

-- applies this merge of rules to all unproven localThm edges if possible

locDecomp :: ProofStatus -> ProofStatus

locDecomp proofStatus@(globalContext,libEnv,history,dGraph) =

(globalContext, libEnv, nextHistoryElem:history, nextDGraph)

where

localThmEdges = filter isUnprovenLocalThm (labEdges dGraph)

result = locDecompAux libEnv dGraph ([],[]) localThmEdges

nextDGraph = fst result

nextHistoryElem = snd result

{- auxiliary function for locDecomp (above)

actual implementation -}

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

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

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

locDecompAux libEnv dgraph (rules,changes) ((ledge@(src,tgt,edgeLab)):list) =

if (null proofBasis && not (isIdentityEdge ledge libEnv dgraph))

then

locDecompAux libEnv dgraph (rules,changes) list

else

if isDuplicate newEdge dgraph changes

then locDecompAux libEnv auxGraph

(newRules,(DeleteEdge ledge):changes) list

else locDecompAux libEnv newGraph (newRules,newChanges) list

where

morphism = dgl_morphism edgeLab

allPaths = getAllLocGlobPathsBetween dgraph src tgt

th = computeLocalTheory libEnv dgraph src

pathsWithoutEdgeItself = [path|path <- allPaths, notElem ledge path]

filteredPaths = filterByTranslation th morphism pathsWithoutEdgeItself

proofBasis = selectProofBasis edgeLab filteredPaths

auxGraph = delLEdge ledge dgraph

(LocalThm _ conservativity conservStatus) = (dgl_type edgeLab)

newEdge = (src,

tgt,

DGLink {dgl_morphism = morphism,

dgl_type =

(LocalThm (Proven proofBasis)

conservativity conservStatus),

dgl_origin = DGProof}

)

newGraph = insEdge newEdge auxGraph

newRules = (LocDecomp ledge):rules

newChanges = (DeleteEdge ledge):((InsertEdge newEdge):changes)

{- returns the sentence list of the given node -}

getSignature :: LibEnv -> DGraph -> Node -> Maybe G_sign

getSignature libEnv dgraph node =

if isDGRef nodeLab

then case Map.lookup (dgn_libname nodeLab) libEnv of

Just (_,_,refDgraph) ->

getSignature libEnv refDgraph (dgn_node nodeLab)

Nothing -> Nothing

else Just (dgn_sign nodeLab)

where nodeLab = lab' (context node dgraph)

{- 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 -> [path| path <- paths, isSameTranslation th morphism path]

Nothing -> []

-- isSameTranslation th morphism (calculateMorphismOfPath path)]

{- 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 ->

translateG_theory morphism th == translateG_theory morphismOfPath th

Nothing -> False

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

-- local subsumption

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

-- applies local subsumption to all unproven local theorem edges

locSubsume :: ProofStatus -> ProofStatus

locSubsume proofStatus@(globalContext,libEnv,history,dGraph) =

(globalContext, libEnv, nextHistoryElem:history, nextDGraph)

where

localThmEdges = filter isUnprovenLocalThm (labEdges dGraph)

result = locSubsumeAux libEnv dGraph ([],[]) localThmEdges

nextDGraph = fst result

nextHistoryElem = snd result

-- auxiliary method for locSubsume

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

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

locSubsumeAux libEnv dgraph historyElement [] = (dgraph, historyElement)

locSubsumeAux libEnv dgraph (rules,changes) ((ledge@(src,tgt,edgeLab)):list) =

case (getDGNode libEnv dgraph tgt, maybeThSrc) of

(Just (target,_), Just thSrc) ->

case (maybeResult (computeTheory libEnv dgraph target), maybeResult (translateG_theory morphism thSrc)) of

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

case maybeResult (coerceTheory lidSrc theoryTgt) of

Nothing -> locSubsumeAux libEnv dgraph (rules,changes) list

Just (_,sentencesTgt) ->

if (all (`elem` sentencesTgt) sensSrc)

then locSubsumeAux libEnv newGraph (newRules,newChanges) list

else locSubsumeAux libEnv dgraph (rules,changes) list

otherwise -> locSubsumeAux libEnv dgraph (rules,changes) list

otherwise -> -- showDiags defaultHetcatsOpts (errSrc++errTgt)

locSubsumeAux libEnv dgraph (rules,changes) list

where

morphism = dgl_morphism edgeLab

maybeThSrc = computeLocalTheory libEnv dgraph src

auxGraph = delLEdge ledge dgraph

(LocalThm _ conservativity conservStatus) = (dgl_type edgeLab)

newEdge = (src,

tgt,

DGLink {dgl_morphism = morphism,

dgl_type =

(LocalThm (Proven [])

conservativity conservStatus),

dgl_origin = DGProof}

)

newGraph = insEdge newEdge auxGraph

newRules = (LocSubsumption ledge):rules

newChanges = (DeleteEdge ledge):((InsertEdge newEdge):changes)

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

-- hide theorem shift

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

hideTheoremShift :: Bool -> ProofStatus -> IO ProofStatus

hideTheoremShift isAutomatic proofStatus@(globalContext,libEnv,history,dGraph)=

do result <- hideTheoremShiftAux dGraph ([],[]) hidingThmEdges isAutomatic

let nextDGraph = fst result

nextHistoryElem = snd result

return (globalContext, libEnv, nextHistoryElem:history, nextDGraph)

where

hidingThmEdges = filter isUnprovenHidingThm (labEdges dGraph)

{- auxiliary method for hideTheoremShift -}

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

-> [LEdge DGLinkLab] -> Bool

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

hideTheoremShiftAux dgraph historyElement [] _ =

return (dgraph, historyElement)

hideTheoremShiftAux dgraph (rules,changes) (ledge:list) isAutomatic =

do proofBasis <- findProofBasisForHideTheoremShift dgraph ledge isAutomatic

if (null proofBasis)

then hideTheoremShiftAux dgraph (rules,changes) list isAutomatic

else do

let newEdge = makeProvenHidingThmEdge proofBasis ledge

auxDGraph = insEdge newEdge (delLEdge ledge dgraph)

auxChanges = (DeleteEdge ledge):((InsertEdge newEdge):changes)

(newDGraph,newChanges) =

insertNewEdges auxDGraph auxChanges proofBasis

newRules = (HideTheoremShift ledge):rules

hideTheoremShiftAux newDGraph (newRules,newChanges) list isAutomatic

{- inserts the given edges into the development graph and adds a corresponding entry to the changes -}

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

insertNewEdges dgraph changes [] = (dgraph,changes)

insertNewEdges dgraph changes (edge:edges) =

if isDuplicate edge dgraph changes then insertNewEdges dgraph changes edges

else insertNewEdges (insEdge edge dgraph) ((InsertEdge edge):changes) edges

{- creates a new proven HidingThm edge from the given HidingThm edge using the edge list as the proofBasis -}

makeProvenHidingThmEdge :: [LEdge DGLinkLab] -> LEdge DGLinkLab -> LEdge DGLinkLab

makeProvenHidingThmEdge proofBasisEdges (src,tgt,edgeLab) =

(src,

tgt,

DGLink {dgl_morphism = morphism,

dgl_type = (HidingThm hidingMorphism

(Proven (map getLabelOfEdge proofBasisEdges))),

dgl_origin = DGProof}

)

where

morphism = dgl_morphism edgeLab

(HidingThm hidingMorphism _) = (dgl_type edgeLab)

{- selects a proof basis for 'hide theorem shift' if there is one-}

findProofBasisForHideTheoremShift :: DGraph -> LEdge DGLinkLab -> Bool

-> IO [LEdge DGLinkLab]

findProofBasisForHideTheoremShift dgraph (ledge@(src,tgt,edgelab)) isAutomatic=

if (null pathPairsFilteredByConservativity) then return []

else

do pb <- hideTheoremShift_selectProofBasis dgraph

pathPairsFilteredByConservativity isAutomatic

case pb of

Nothing -> return []

Just proofBasis -> do let fstPath = fst proofBasis

sndPath = snd proofBasis

return [createEdgeForPath fstPath,

createEdgeForPath sndPath]

where

pathsFromSrc = getAllPathsOfTypeFrom dgraph src (ledge /=)

pathsFromTgt = getAllPathsOfTypeFrom dgraph tgt (ledge /=)

possiblePathPairs = selectPathPairs pathsFromSrc pathsFromTgt

(HidingThm hidingMorphism _) = (dgl_type edgelab)

morphism = dgl_morphism edgelab

pathPairsFilteredByMorphism

= filterPairsByResultingMorphisms possiblePathPairs

hidingMorphism morphism

pathPairsFilteredByConservativity

= filterPairsByConservativityOfSecondPath pathPairsFilteredByMorphism

{- removes all pairs from the given list whose second path does not have a

conservativity greater than or equal to Cons -}

filterPairsByConservativityOfSecondPath ::

[([LEdge DGLinkLab],[LEdge DGLinkLab])]

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

filterPairsByConservativityOfSecondPath [] = []

filterPairsByConservativityOfSecondPath (([],_):list) =

filterPairsByConservativityOfSecondPath list

filterPairsByConservativityOfSecondPath ((_,[]):list) =

filterPairsByConservativityOfSecondPath list

filterPairsByConservativityOfSecondPath (pair:list) =

if (and [cons >= Cons | cons <- map getConservativity (snd pair)])

then pair:(filterPairsByConservativityOfSecondPath list)

else filterPairsByConservativityOfSecondPath list

{- selects a proofBasis (i.e. a path tuple) from the list of possible ones:

If there is exaclty one proofBasis in the list, this is returned.

If there are more than one and the method is called in automatic mode Nothing is returned. In non-automatic mode the user is asked to select a proofBasis via listBox. -}

hideTheoremShift_selectProofBasis ::

DGraph -> [([LEdge DGLinkLab], [LEdge DGLinkLab])] -> Bool

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

hideTheoremShift_selectProofBasis _ (basis:[]) _ = return (Just basis)

hideTheoremShift_selectProofBasis dgraph basisList isAutomatic =

case isAutomatic of

True -> return Nothing

False -> do sel <- listBox

"Choose a path tuple as the proof basis"

(map (prettyPrintPathTuple dgraph) basisList)

i <- case sel of

Just j -> return j

_ -> error ("Proofs.Proofs: " ++

"selection of proof basis failed")

return (Just (basisList!!i))

{- returns a string representation of the given paths:

for each path a tuple of the names of its nodes is shown, the two are combined by an 'and' -}

prettyPrintPathTuple :: DGraph -> ([LEdge DGLinkLab],[LEdge DGLinkLab])

-> String

prettyPrintPathTuple dgraph (p1,p2) =

(prettyPrintPath dgraph p1) ++ " and " ++ (prettyPrintPath dgraph p2)

{- returns the names of the nodes of the path, separated by commas-}

prettyPrintNodesOfPath :: DGraph -> [LEdge DGLinkLab] -> String

prettyPrintNodesOfPath _ [] = ""

prettyPrintNodesOfPath dgraph (edge:path) =

(prettyPrintSourceNode dgraph edge) ++ ", "

++ (prettyPrintNodesOfPath dgraph path)

++ end

where

end = case path of

[] -> prettyPrintTargetNode dgraph edge

_ -> ""

{- returns a string reprentation of the path: showing a tuple of its nodes-}

prettyPrintPath :: DGraph -> [LEdge DGLinkLab] -> String

prettyPrintPath dgraph [] = "<empty path>"

prettyPrintPath dgraph path =

"(" ++ (prettyPrintNodesOfPath dgraph path) ++ ")"

{- returns the name of the source node of the given edge-}

prettyPrintSourceNode :: DGraph -> LEdge DGLinkLab -> String

prettyPrintSourceNode dgraph (src,_,_) =

getDGNodeName $ lab' (context src dgraph)

{- returns the name of the target node of the given edge-}

prettyPrintTargetNode :: DGraph -> LEdge DGLinkLab -> String

prettyPrintTargetNode dgraph (_,tgt,_) =

getDGNodeName $ lab' (context tgt dgraph)

{- creates a unproven global thm edge for the given path, i.e. with the same source and target nodes and the same morphism as the path -}

createEdgeForPath :: [LEdge DGLinkLab] -> LEdge DGLinkLab

createEdgeForPath path =

case (calculateMorphismOfPath path) of

Just morphism -> (getSourceNode (head path),

getTargetNode (last path),

DGLink {dgl_morphism = morphism,

dgl_type = (GlobalThm Static.DevGraph.Open None

Static.DevGraph.Open),

dgl_origin = DGProof}

)

Nothing -> error ("Could not determine morphism of path " ++ (show path))

{- returns a list of path pairs, as shorthand the pairs are not returned as path-path tuples but as path-<list of path> tuples. Every path in the list is a pair of the single path.

The path pairs are selected by having the same target node. -}

selectPathPairs :: [[LEdge DGLinkLab]] -> [[LEdge DGLinkLab]]

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

selectPathPairs [] _ = []

selectPathPairs _ [] = []

selectPathPairs paths1 paths2 =

[(p1, [p2| p2 <- paths2, haveSameTgt (last p1) (last p2) ] )| p1 <- paths1]

where

haveSameTgt :: LEdge DGLinkLab -> LEdge DGLinkLab -> Bool

haveSameTgt (_,tgt1,_) (_,tgt2,_) = tgt1 == tgt2

{- returns a list of path pairs by keeping those pairs, whose first path composed with the first given morphism and whose second path composed with the second given morphism result in the same morphism, and droping all other pairs.-}

filterPairsByResultingMorphisms :: [([LEdge DGLinkLab],[[LEdge DGLinkLab]])]

-> GMorphism -> GMorphism

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

filterPairsByResultingMorphisms [] _ _ = []

filterPairsByResultingMorphisms (pair:pairs) morph1 morph2 =

[((fst pair),path)| path <- suitingPaths]

++ (filterPairsByResultingMorphisms pairs morph1 morph2)

where

compMorph1

= compMaybeMorphisms (Just morph1) (calculateMorphismOfPath (fst pair))

suitingPaths :: [[LEdge DGLinkLab]]

suitingPaths = if (compMorph1 /= Nothing) then

[path |path <- (snd pair),

(compMaybeMorphisms (Just morph2)

(calculateMorphismOfPath path))

== compMorph1]

else []

{- if the given maybe morphisms are both not Nothing,

this method composes their GMorphisms -

returns Nothing otherwise -}

compMaybeMorphisms :: Maybe GMorphism -> Maybe GMorphism -> Maybe GMorphism

compMaybeMorphisms morph1 morph2 =

case (morph1, morph2) of

(Just m1, Just m2) -> resultToMaybe $ compHomInclusion m1 m2

otherwise -> Nothing

{- returns the Conservativity if the given edge has one,

otherwise an error is raised -}

getConservativity :: LEdge DGLinkLab -> Conservativity

getConservativity edge@(_,_,edgeLab) =

case dgl_type edgeLab of

(LocalThm _ cons _) -> cons

(GlobalThm _ cons _) -> cons

otherwise -> None

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

-- theorem hide shift

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

theoremHideShift :: ProofStatus -> IO ProofStatus

theoremHideShift proofStatus@(globalContext,libEnv,history,dgraph) = do

let nodePathsList =

[(node,

getAllPathsBeginningWithHidingDefTo

dgraph

node

([]::[LEdge DGLinkLab]))|

node <- nodes dgraph]

let (newDgraph,newChanges) = theoremHideShiftAux dgraph nodePathsList

putStrLn "d o n e"

return (globalContext,

libEnv,

([TheoremHideShift],newChanges):history,

newDgraph)

theoremHideShiftAux :: DGraph -> [(Node,[(Node,[LEdge DGLinkLab])])]

-> (DGraph,[DGChange])

theoremHideShiftAux dgraph [] = (dgraph,[])

theoremHideShiftAux dgraph ((node, []):list) =

replaceNode dgraph oldNode newNode

where

nodeContext = (context node dgraph)

oldNode = labNode' nodeContext

oldNodeLab = lab' nodeContext

newNode = (node, DGNode {dgn_name = dgn_name oldNodeLab,

dgn_sign = dgn_sign oldNodeLab,

dgn_sens = dgn_sens oldNodeLab,

dgn_nf = Just node,

dgn_sigma = Nothing, --Just ID,

dgn_origin = dgn_origin oldNodeLab})

theoremHideShiftAux dgraph ((node,pathsToNode):list) =

error ("theoremHideShiftAux: not yet implemented")

replaceNode :: DGraph -> LNode DGNodeLab -> LNode DGNodeLab

-> (DGraph,[DGChange])

replaceNode dgraph oldNode@(on,_) newNode@(nn,_) =

(newDGraph,

[DeleteEdge edge|edge <- (oldInEdges ++ oldOutEdges)]

++ [DeleteNode oldNode, InsertNode newNode]

++ [InsertEdge edge| edge <- (newEdges)])

where

oldInEdges = inn dgraph on

oldOutEdges = out dgraph on

oldInEdges' = removeDuplicatesFromFstList oldInEdges oldOutEdges

newInEdges = [(src,nn,edgelab)|(src,_,edgelab) <- oldInEdges']

newOutEdges = [(nn,tgt,edgelab)|(_,tgt,edgelab) <- oldOutEdges]

newEdges = newInEdges ++ newOutEdges

auxGraph = delNode on (removeEdges (oldInEdges'++oldOutEdges) dgraph)

newDGraph = insEdges newEdges (insNode newNode dgraph)

removeDuplicatesFromFstList :: Eq a => [a] -> [a] -> [a]

removeDuplicatesFromFstList fstList sndList =

[e | e <- fstList, notElem e sndList]

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

removeEdges [] dgraph = dgraph

removeEdges (edge:list) dgraph = removeEdges list (delLEdge edge dgraph)

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

-- methods that calculate paths of certain types

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

{- returns a list of all proven global paths of the given morphism between

the given source and target node-}

getAllGlobPathsOfMorphismBetween :: DGraph -> GMorphism -> Node -> Node

-> [[LEdge DGLinkLab]]

getAllGlobPathsOfMorphismBetween dgraph morphism src tgt =

filterPathsByMorphism morphism allPaths

where

allPaths = getAllGlobPathsBetween dgraph src tgt

{- returns all paths from the given list whose morphism is equal to the

given one-}

filterPathsByMorphism :: GMorphism -> [[LEdge DGLinkLab]]

-> [[LEdge DGLinkLab]]

filterPathsByMorphism morphism paths =

[path| path <- paths, (calculateMorphismOfPath path) == (Just morphism)]

{- returns a list of all paths to the given node

that consist of globalDef edge only

or

that consist of a localDef or hidingDef edge

followed by any number of globalDef edges -}

getAllLocOrHideGlobDefPathsTo :: DGraph -> Node -> [LEdge DGLinkLab]

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

getAllLocOrHideGlobDefPathsTo =

getAllGlobDefPathsBeginningWithTypesTo

([isLocalDef, isHidingDef]::[LEdge DGLinkLab -> Bool])

{- returns a list of all paths to the given node

that consist of globalDef edges only

or

that consist of a localDef edge followed by any number of globalDef edges -}

getAllLocGlobDefPathsTo :: DGraph -> Node -> [LEdge DGLinkLab]

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

getAllLocGlobDefPathsTo = getAllGlobDefPathsBeginningWithTypesTo

([isLocalDef]::[LEdge DGLinkLab -> Bool])

getAllPathsBeginningWithHidingDefTo :: DGraph -> Node -> [LEdge DGLinkLab]

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

getAllPathsBeginningWithHidingDefTo dgraph node path =

resultPath ++

(concat ( [getAllPathsBeginningWithHidingDefTo

dgraph (getSourceNode edge) (edge:path) |

edge <- nextEdges]))

where

inEdges = inn dgraph node

nextEdges = [edge| edge <- inEdges, not (elem edge path)]

resultPath =

if ((not (null path)) && (isHidingDef (head path)))

then [(node,path)] else []

{- returns all paths consisting of global edges only

or

of one local edge followed by any number of global edges-}

getAllLocGlobPathsBetween :: DGraph -> Node -> Node -> [[LEdge DGLinkLab]]

getAllLocGlobPathsBetween dgraph src tgt =

locGlobPaths ++ globPaths

where

outEdges = out dgraph src

locEdges = [(edge,target)|edge@(_,target,_) <-

(filterByTypes [isLocalEdge] outEdges)]

locGlobPaths = (concat [map ([edge]++)

(getAllPathsOfTypesBetween dgraph [isGlobalEdge] node tgt [])|

(edge,node) <- locEdges])

globPaths = getAllPathsOfTypesBetween dgraph [isGlobalEdge] src tgt []

{- returns all paths of globalDef edges or globalThm edges

between the given source and target node -}

getAllGlobPathsBetween :: DGraph -> Node -> Node -> [[LEdge DGLinkLab]]

getAllGlobPathsBetween dgraph src tgt =

getAllPathsOfTypesBetween dgraph [isGlobalDef,isGlobalThm] src tgt []

{- gets all paths consisting of local/global thm/def edges

of the given morphism -}

getAllThmDefPathsOfMorphismBetween :: DGraph -> GMorphism -> Node -> Node

-> [[LEdge DGLinkLab]]

getAllThmDefPathsOfMorphismBetween dgraph morphism src tgt =

filterPathsByMorphism morphism allPaths

where

allPaths = getAllPathsOfTypesBetween dgraph types src tgt []

types =

[isGlobalThm,

isProvenLocalThm,

isProvenLocalThm,

isUnprovenLocalThm,

isGlobalDef,

isLocalDef]

{- returns all paths of globalDef edges between the given source and

target node -}

getAllGlobDefPathsBetween :: DGraph -> Node -> Node -> [[LEdge DGLinkLab]]

getAllGlobDefPathsBetween dgraph src tgt =

getAllPathsOfTypeBetween dgraph isGlobalDef src tgt

{- returns all paths consiting of edges of the given type between the

given node -}

getAllPathsOfTypeBetween :: DGraph -> (LEdge DGLinkLab -> Bool) -> Node

-> Node -> [[LEdge DGLinkLab]]

getAllPathsOfTypeBetween dgraph isType src tgt =

getAllPathsOfTypesBetween dgraph (isType:[]) src tgt []

{- returns all paths consisting of edges of the given types between

the given nodes -}

getAllPathsOfTypesBetween :: DGraph -> [LEdge DGLinkLab -> Bool] -> Node

-> Node -> [LEdge DGLinkLab]

-> [[LEdge DGLinkLab]]

getAllPathsOfTypesBetween dgraph types src tgt path =

[edge:path| edge <- edgesFromSrc]

++ (concat

[getAllPathsOfTypesBetween dgraph types src nextTgt (edge:path)|

(edge,nextTgt) <- nextStep] )

where

inGoingEdges = inn dgraph tgt

edgesOfTypes =

[edge| edge <- filterByTypes types inGoingEdges, notElem edge path]

edgesFromSrc =

[edge| edge@(source,_,_) <- edgesOfTypes, source == src]

nextStep =

[(edge, source)| edge@(source,_,_) <- edgesOfTypes, source /= src]

{-

getAllPathsFrom :: DGraph -> Node -> [[LEdge DGLinkLab]]

getAllPathsFrom = getAllPathsFromAux []

getAllPathsFromAux :: [LEdge DGLinkLab] -> DGraph -> Node

-> [[LEdge DGLinkLab]]

getAllPathsFromAux path dgraph src =

[path ++ [edge]| edge <- edgesFromSrc, notElem edge path]

++(concat

[getAllPathsFromAux (path ++ [edge]) dgraph nextSrc|

(edge,nextSrc) <- nextStep])

where

edgesFromSrc = out dgraph src

nextStep = [(edge,tgt)| edge@(_,tgt,_) <- edgesFromSrc,

tgt /= src && notElem edge path] -}

getAllPathsOfTypeFrom :: DGraph -> Node -> (LEdge DGLinkLab -> Bool) -> [[LEdge DGLinkLab]]

getAllPathsOfTypeFrom = getAllPathsOfTypeFromAux []

getAllPathsOfTypeFromAux :: [LEdge DGLinkLab] -> DGraph -> Node

-> (LEdge DGLinkLab -> Bool) -> [[LEdge DGLinkLab]]

getAllPathsOfTypeFromAux path dgraph src isType =

[path ++ [edge]| edge <- edgesFromSrc, notElem edge path && isType edge]

++(concat

[getAllPathsOfTypeFromAux (path ++ [edge]) dgraph nextSrc isType|

(edge,nextSrc) <- nextStep])

where

edgesFromSrc = out dgraph src

nextStep = [(edge,tgt)| edge@(_,tgt,_) <- edgesFromSrc,

tgt /= src && notElem edge path && isType edge]

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

-- methods to check the type of an edge

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

isProven :: LEdge DGLinkLab -> Bool

isProven edge = isGlobalDef edge || isLocalDef edge

|| isProvenGlobalThm edge || isProvenLocalThm edge

|| isProvenHidingThm edge

isGlobalEdge :: LEdge DGLinkLab -> Bool

isGlobalEdge edge = isGlobalDef edge || isGlobalThm edge

isLocalEdge :: LEdge DGLinkLab -> Bool

isLocalEdge edge = isLocalDef edge || isLocalThm edge

isGlobalThm :: LEdge DGLinkLab -> Bool

isGlobalThm edge = isProvenGlobalThm edge || isUnprovenGlobalThm edge

isLocalThm :: LEdge DGLinkLab -> Bool

isLocalThm edge = isProvenLocalThm edge || isUnprovenLocalThm edge

isProvenGlobalThm :: LEdge DGLinkLab -> Bool

isProvenGlobalThm (_,_,edgeLab) =

case dgl_type edgeLab of

(GlobalThm (Proven _) _ _) -> True

_ -> False

isUnprovenGlobalThm :: LEdge DGLinkLab -> Bool

isUnprovenGlobalThm (_,_,edgeLab) =

case dgl_type edgeLab of

(GlobalThm Static.DevGraph.Open _ _) -> True

_ -> False

isProvenLocalThm :: LEdge DGLinkLab -> Bool

isProvenLocalThm (_,_,edgeLab) =

case dgl_type edgeLab of

(LocalThm (Proven _) _ _) -> True

_ -> False

isUnprovenLocalThm :: LEdge DGLinkLab -> Bool

isUnprovenLocalThm (_,_,edgeLab) =

case dgl_type edgeLab of

(LocalThm (Static.DevGraph.Open) _ _) -> True

_ -> False

isHidingEdge :: LEdge DGLinkLab -> Bool

isHidingEdge edge = isHidingDef edge || isHidingThm edge

isHidingDef :: LEdge DGLinkLab -> Bool

isHidingDef (_,_,edgeLab) =

case dgl_type edgeLab of

HidingDef -> True

_ -> False

isHidingThm :: LEdge DGLinkLab -> Bool

isHidingThm edge = isProvenHidingThm edge || isUnprovenHidingThm edge

isProvenHidingThm :: LEdge DGLinkLab -> Bool

isProvenHidingThm (_,_,edgeLab) =

case dgl_type edgeLab of

(HidingThm _ (Proven _)) -> True

_ -> False

isUnprovenHidingThm :: LEdge DGLinkLab -> Bool

isUnprovenHidingThm (_,_,edgeLab) =

case dgl_type edgeLab of

(HidingThm _ Static.DevGraph.Open) -> True

_ -> False

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

-- other methods on edges

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

{- returns true, if an identical edge is already in the graph or marked to be inserted,

false otherwise-}

isDuplicate :: LEdge DGLinkLab -> DGraph -> [DGChange] -> Bool

isDuplicate newEdge dgraph changes =

elem (InsertEdge newEdge) changes || elem newEdge (labEdges dgraph)

{- returns true, if the given edge is duplicate or

if there already exists a parallel path,

which starts with a localThmEdge to one of the startnodes in 'otherNewEdge'

and has the same morphism as the given edge,

false otherwise -}

isRedundant :: LEdge DGLinkLab -> DGraph -> [DGChange]

->[(Node, [LEdge DGLinkLab])] -> Bool

isRedundant newEdge@(src,_,label) dgraph changes otherNewEdges =

isDuplicate newEdge dgraph changes

|| elem (Just (dgl_morphism label)) morphismsOfParallelPaths

where

localThmEdgesToOtherSources =

[outEdge|outEdge@(_,tgt,_) <- out dgraph src,

elem tgt (map fst otherNewEdges)

&& isLocalThm outEdge]

parallelPaths

= concat (map (combineSucceedingEdges otherNewEdges)

localThmEdgesToOtherSources)

morphismsOfParallelPaths = map calculateMorphismOfPath parallelPaths

{- combines the given edge with each of those given paths that start

with the target node of the edge-}

combineSucceedingEdges :: [(Node,[LEdge DGLinkLab])] -> LEdge DGLinkLab

-> [[LEdge DGLinkLab]]

combineSucceedingEdges [] _ = []

combineSucceedingEdges ((src,path):paths) edge@(_,tgt,_) =

if tgt == src

then ((edge:path)):(combineSucceedingEdges paths edge)

else combineSucceedingEdges paths edge

isIdentityEdge :: LEdge DGLinkLab -> LibEnv -> DGraph -> Bool

isIdentityEdge (src,tgt,edgeLab) libEnv dgraph =

if isDGRef nodeLab then

case Map.lookup (dgn_libname nodeLab) libEnv of

Just globContext@(_,_,refDgraph) -> isIdentityEdge (dgn_node nodeLab,tgt,edgeLab) libEnv refDgraph

Nothing -> False

else if src == tgt && (dgl_morphism edgeLab) == (ide Grothendieck (dgn_sign nodeLab)) then True else False

where nodeLab = lab' (context src dgraph)

{- returns the DGLinkLab of the given LEdge -}

getLabelOfEdge :: (LEdge b) -> b

getLabelOfEdge (_,_,label) = label

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

-- methods to determine the labels of the inserted edges in the given dgchange

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

{- filters the list of changes for insertions of edges and returns the label

of one of these; or Nothing if no insertion was found -}

getLabelsOfInsertedEdges :: [DGChange] -> [DGLinkLab]

getLabelsOfInsertedEdges changes =

[label | (_,_,label) <- getInsertedEdges changes]

{- returns all insertions of edges from the given list of changes -}

getInsertedEdges :: [DGChange] -> [LEdge DGLinkLab]

getInsertedEdges [] = []

getInsertedEdges (change:list) =

case change of

(InsertEdge edge) -> edge:(getInsertedEdges list)

otherwise -> getInsertedEdges list

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

-- methods to check and select proof basis

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

{- determines all proven paths in the given list and tries to selet a

proof basis from these (s. selectProofBasisAux);

if this fails the same is done for the rest of the given paths, i.e.

for the unproven ones -}

selectProofBasis :: DGLinkLab -> [[LEdge DGLinkLab]] -> [DGLinkLab]

selectProofBasis label paths =

if null provenProofBasis then selectProofBasisAux label unprovenPaths

else provenProofBasis

where

provenPaths = filterProvenPaths paths

provenProofBasis = selectProofBasisAux label provenPaths

unprovenPaths = [path | path <- paths, notElem path provenPaths]

{- selects the first path that does not form a proof cycle with the given

label (if such a path exits) and returns the labels of its edges -}

selectProofBasisAux :: DGLinkLab -> [[LEdge DGLinkLab]] -> [DGLinkLab]

selectProofBasisAux _ [] = []

selectProofBasisAux label (path:list) =

if notProofCycle label path then nub (calculateProofBasis path)

else selectProofBasisAux label list

{- calculates the proofBasis of the given path,

i.e. the list of all DGLinkLabs the proofs of the edges contained in the path

are based on, plus the DGLinkLabs of the edges themselves;

duplicates are not removed here, but in the calling method

selectProofBasisAux -}

calculateProofBasis :: [LEdge DGLinkLab] -> [DGLinkLab]

calculateProofBasis [] = []

calculateProofBasis ((_,_,lab):edges) =

lab:((getProofBasis lab)++(calculateProofBasis edges))

{- returns the proofBasis contained in the given DGLinkLab -}

getProofBasis :: DGLinkLab -> [DGLinkLab]

getProofBasis lab =

case dgl_type lab of

(GlobalThm (Proven proofBasis) _ _) -> proofBasis

(LocalThm (Proven proofBasis) _ _) -> proofBasis

_ -> []

{- returns all proven paths from the given list -}

filterProvenPaths :: [[LEdge DGLinkLab]] -> [[LEdge DGLinkLab]]

filterProvenPaths [] = []

filterProvenPaths (path:list) =

if (and [isProven edge| edge <- path]) then path:(filterProvenPaths list)

else filterProvenPaths list

{- opposite of isProofCycle -}

notProofCycle :: DGLinkLab -> [LEdge DGLinkLab] -> Bool

notProofCycle label = not.(isProofCycle label)

{- checks if the given label is contained in the ProofBasis of one of the

edges of the given path -}

isProofCycle :: DGLinkLab -> [LEdge DGLinkLab] -> Bool

isProofCycle _ [] = False

isProofCycle label (edge:path) =

if (elemOfProofBasis label edge) then True else (isProofCycle label path)

{- checks if the given label is contained in the ProofBasis of the given

edge -}

elemOfProofBasis :: DGLinkLab -> (LEdge DGLinkLab) -> Bool

elemOfProofBasis label (_,_,dglink) =

case dgl_type dglink of

(GlobalThm (Proven proofBasis) _ _) -> elem label proofBasis

(LocalThm (Proven proofBasis) _ _) -> elem label proofBasis

_ -> False

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

-- methods for the extension of globDecomp (avoid insertion ofredundant edges)

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

{- returns all paths consisting of local theorem links whose src and tgt nodes

are contained in the given list of nodes -}

localThmPathsBetweenNodes :: DGraph -> [Node] -> [[LEdge DGLinkLab]]

localThmPathsBetweenNodes _ [] = []

localThmPathsBetweenNodes dgraph nodes@(x:xs) =

localThmPathsBetweenNodesAux dgraph nodes nodes

{- auxiliary method for localThmPathsBetweenNodes -}

localThmPathsBetweenNodesAux :: DGraph -> [Node] -> [Node] -> [[LEdge DGLinkLab]]

localThmPathsBetweenNodesAux _ [] _ = []

localThmPathsBetweenNodesAux dgraph (node:srcNodes) tgtNodes =

(concat (map (getAllPathsOfTypeBetween dgraph isUnprovenLocalThm node) tgtNodes))

++ (localThmPathsBetweenNodesAux dgraph srcNodes tgtNodes)

{- combines each of the given paths with matching edges from the given list

(i.e. every edge that has as its source node the tgt node of the path)-}

combinePathsWithEdges :: [[LEdge DGLinkLab]] -> [LEdge DGLinkLab]

-> [[LEdge DGLinkLab]]

combinePathsWithEdges paths edges =

concat (map (combinePathsWithEdge paths) edges)

{- combines the given path with each matching edge from the given list

(i.e. every edge that has as its source node the tgt node of the path)-}

combinePathsWithEdge :: [[LEdge DGLinkLab]] -> LEdge DGLinkLab

-> [[LEdge DGLinkLab]]

combinePathsWithEdge [] _ = []

combinePathsWithEdge (path:paths) edge@(src,_,_) =

case path of

[] -> combinePathsWithEdge paths edge

(x:xs) -> if (getTargetNode (last path)) == src

then (path++[edge]):(combinePathsWithEdge paths edge)

else combinePathsWithEdge paths edge

{- todo: choose a better name for this method...

returns for each of the given paths a pair consisting of the last edge

contained in the path and - as a triple - the src, tgt and morphism of the

complete path

if there is an empty path in the given list or the morphsim cannot be

calculated, it is simply ignored -}

calculateResultingEdges :: [[LEdge DGLinkLab]] -> [(LEdge DGLinkLab,(Node,Node,GMorphism))]

calculateResultingEdges [] = []

calculateResultingEdges (path:paths) =

case path of

[] -> calculateResultingEdges paths

(x:xs) ->

case calculateMorphismOfPath path of

Nothing -> calculateResultingEdges paths

Just morphism -> (last path, (src,tgt,morphism)):(calculateResultingEdges paths)

where src = getSourceNode (head path)

tgt = getTargetNode (last path)

{- removes from the given list every edge for which there is already an

equivalent edge or path (i.e. an edge or path with the same src, tgt and

morphsim) -}

removeSuperfluousEdges :: DGraph -> [LEdge DGLinkLab]

-> (DGraph,[LEdge DGLinkLab])

removeSuperfluousEdges dgraph [] = (dgraph,[])

removeSuperfluousEdges dgraph edges

= removeSuperfluousEdgesAux dgraph edges

(calculateResultingEdges combinedPaths) []

where

localThmPaths

= localThmPathsBetweenNodes dgraph (map (getSourceNode) edges)

combinedPaths = combinePathsWithEdges localThmPaths edges

{- auxiliary method for removeSuperfluousEdges -}

removeSuperfluousEdgesAux :: DGraph -> [LEdge DGLinkLab]

-> [(LEdge DGLinkLab,(Node,Node,GMorphism))]

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

removeSuperfluousEdgesAux dgraph [] _ edgesToInsert= (dgraph,edgesToInsert)

removeSuperfluousEdgesAux dgraph ((src,tgt,lab):edges)

resultingEdges edgesToInsert =

if not (null equivalentEdges)

then removeSuperfluousEdgesAux

newDGraph edges newResultingEdges edgesToInsert

else removeSuperfluousEdgesAux

dgraph edges resultingEdges ((src,tgt,lab):edgesToInsert)

where

equivalentEdges

= [e | e <- resultingEdges,(snd e) == (src,tgt,dgl_morphism lab)]

newResultingEdges = [e | e <- resultingEdges,(fst e) /= (src,tgt,lab)]

newDGraph = delLEdge (src,tgt,lab) dgraph

{- returns true, if the given change is an insertion of an local theorem edge,

false otherwise -}

isLocalThmInsertion :: DGChange -> Bool

isLocalThmInsertion change

= case change of

InsertEdge edge -> isLocalThm edge

otherwise -> False

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

-- further methods

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

-- | Calculate the morphism of a path with given start node

calculateMorphismOfPathWithStart :: DGraph -> LibEnv

-> (Node,[LEdge DGLinkLab])

-> Maybe GMorphism

calculateMorphismOfPathWithStart dg libEnv (n,[]) = do

ctx <- fst $ match n dg

case getDGNode libEnv dg (fst (labNode' ctx)) of

Just dgNode_ctx -> return $ ide Grothendieck (dgn_sign (snd (dgNode_ctx))) -- ??? to simplistic

Nothing -> Nothing

calculateMorphismOfPathWithStart _ _ (_,p) = calculateMorphismOfPath p

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

-- basic inference

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

getGoals :: LibEnv -> DGraph -> LEdge DGLinkLab -> Result G_l_sentence_list

getGoals libEnv dg (n,_,edge) = do

th <- maybeToMonad ("Could node find node "++show n)

$ computeLocalTheory libEnv dg n

let mor = dgl_morphism edge

fmap sensOf $ translateG_theory mor th

getProvers :: Bool -> LogicGraph -> G_sublogics -> [(G_prover,AnyComorphism)]

getProvers consCheck lg gsub =

if consCheck then

[(G_cons_checker (targetLogic cid) p,Comorphism cid) |

Comorphism cid <- cms,

p <- cons_checkers (targetLogic cid)]

else

[(G_prover (targetLogic cid) p,Comorphism cid) |

Comorphism cid <- cms,

p <- provers (targetLogic cid)]

where cms = findComorphismPaths lg gsub

selectProver :: [(G_prover,AnyComorphism)] -> IOResult (G_prover,AnyComorphism)

selectProver [p] = return p

selectProver [] = resToIORes $ fatal_error "No pover available" nullPos

selectProver provers = do

sel <- ioToIORes $ listBox

"Choose a translation to a prover-supported logic"

(map (show.snd) provers)

i <- case sel of

Just j -> return j

_ -> resToIORes $ fatal_error "Proofs.Proofs: selection" nullPos

return (provers!!i)

-- applies basic inference to a given node

basicInferenceNode :: Bool -> LogicGraph -> (LIB_NAME,Node) -> ProofStatus

-> IO (Result ProofStatus)

basicInferenceNode checkCons lg (ln,node)

proofStatus@(globalContext,libEnv,history,dGraph) =

ioresToIO (do

-- compute the theory of the node, and its name

G_theory lid1 sign axs <-

resToIORes $ computeTheory libEnv dGraph node

ctx <- resToIORes

$ maybeToMonad ("Could node find node "++show node)

$ fst $ match node dGraph

let nlab = lab' ctx

nodeName = case nlab of

DGNode _ _ _ _ _ _-> dgn_name nlab

DGRef _ _ _ -> dgn_renamed nlab

thName = showPretty (getLIB_ID ln) "_"

++ {-maybe (show node)-} showName nodeName

-- compute the list of proof goals

let inEdges = inn dGraph node

localEdges = filter isUnprovenLocalThm inEdges

goalslist <- if checkCons then return []

else resToIORes $ mapM (getGoals libEnv dGraph) localEdges

G_l_sentence_list lid3 goals <-

if null goalslist then return $ G_l_sentence_list lid1 []

else resToIORes (maybeToMonad

"Logic mismatch for proof goals"

(flatG_l_sentence_list goalslist))

goals1 <- coerce lid1 lid3 goals

-- select a suitable translation and prover

let provers = getProvers checkCons lg $ sublogicOfTh $

(G_theory lid1 sign (axs++goals1))

(prover,Comorphism cid) <- selectProver provers

-- Borrowing: translate theory

let lidS = sourceLogic cid

lidT = targetLogic cid

sign' <- coerce lidS lid1 sign

axs' <- coerce lidS lid1 axs

(sign'',sens'') <- resToIORes $ map_theory cid (sign',axs')

case prover of

G_prover lid4 p -> do

-- Borrowing: translate goal

goals' <- coerce lidS lid3 goals

goals'' <- resToIORes $ mapM (mapNamedM $ map_sentence cid sign') goals'

-- call the prover

p' <- coerce lidT lid4 p

ps <- ioToIORes $ prove p' thName (sign'',sens'') goals''

-- update the development graph

let (nextDGraph, nextHistoryElem) = proveLocalEdges dGraph localEdges

return (globalContext, libEnv, nextHistoryElem:history, nextDGraph)

G_cons_checker lid4 p -> do

incl <- resToIORes $ inclusion lidT (empty_signature lidT) sign''

let mor = TheoryMorphism { t_source = empty_theory lidT,

t_target = (sign'',sens''),

t_morphism = incl }

p' <- coerce lidT lid4 p

ps <- ioToIORes $ cons_check p' thName mor

let nextHistoryElem = ([LocalInference],[])

-- ??? to be implemented

return (globalContext, libEnv, nextHistoryElem:history, dGraph)

)

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

proveLocalEdges dGraph edges = (nextDGraph,([LocalInference],changes))

where (nextDGraph,(_,changes)) = proveLocalEdgesAux ([],[]) dGraph edges

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

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

proveLocalEdgesAux historyElem dGraph [] = (dGraph, historyElem)

proveLocalEdgesAux (rules,changes) dGraph ((edge@(src, tgt, edgelab)):edges) =

if True then proveLocalEdgesAux (rules,(DeleteEdge edge):((InsertEdge provenEdge):changes)) (insEdge provenEdge(delLEdge edge dGraph)) edges

else proveLocalEdgesAux (rules,changes) dGraph edges

where

morphism = dgl_morphism edgelab

(LocalThm _ conservativity conservStatus) = (dgl_type edgelab)

proofBasis = [] -- to be implemented

provenEdge = (src,

tgt,

DGLink {dgl_morphism = morphism,

dgl_type =

(LocalThm (Proven proofBasis)

conservativity conservStatus),

dgl_origin = DGProof}

)