{- |

Module : $Header$

Description : Central datastructures for development graphs

Copyright : (c) 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)

Central datastructures for development graphs

Follows Sect. IV:4.2 of the CASL Reference Manual.

We also provide functions for constructing and modifying development graphs.

However note that these changes need to be propagated to the GUI if they

also shall be visible in the displayed development graph.

See 'Proofs.EdgeUtils.updateWithChanges'

and 'Proofs.StatusUtils.mkResultProofStatus'.

-}

{-

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.

T. Mossakowski, S. Autexier, D. Hutter, P. Hoffman:

CASL Proof calculus. In: CASL reference manual, part IV.

Available from http://www.cofi.info

-}

module Static.DevGraph where

import Static.GTheory

import Logic.Logic

import Logic.ExtSign

import Logic.Comorphism

import Logic.Grothendieck

import Logic.Prover

import qualified Common.Lib.Rel as Rel

import qualified Common.Lib.Graph as Tree

import qualified Common.Lib.SizedList as SizedList

import qualified Common.OrderedMap as OMap

import Common.AS_Annotation

import Common.GlobalAnnotations

import Common.Id

import Common.LibName

import Control.Concurrent.MVar

import Control.Exception (assert)

import Data.Graph.Inductive.Basic

import Data.Graph.Inductive.Graph as Graph

import Data.Graph.Inductive.Query.DFS

import Data.List

import Data.Maybe

import qualified Data.Map as Map

import qualified Data.Set as Set

-- * types for structured specification analysis

-- ** basic types

-- | Node with signature in a DG

data NodeSig = NodeSig { getNode :: Node, getSig :: G_sign }

deriving (Show, Eq)

{- | NodeSig or possibly the empty sig in a logic

(but since we want to avoid lots of vacuous nodes with empty sig,

we do not assign a real node in the DG here) -}

data MaybeNode = JustNode NodeSig | EmptyNode AnyLogic deriving (Show, Eq)

{- | Conservativity annotations. For compactness, only the greatest applicable

value is used in a DG. PCons stands for prooftheoretic conservativity as

required for extending imports (no confusion) in Maude -}

data Conservativity = None | PCons | Cons | Mono | Def deriving (Show, Eq, Ord)

data BasicConsProof = BasicConsProof deriving (Show, Eq) -- needs more details

-- ** node label types

data XPathPart = ElemName String | ChildIndex Int deriving (Show, Eq, Ord)

-- | name of a node in a DG; auxiliary nodes may have extension string

-- and non-zero number (for these, names are usually hidden)

data NodeName = NodeName

{ getName :: SIMPLE_ID

, extString :: String

, extIndex :: Int

, xpath :: [XPathPart]

} deriving (Show, Eq, Ord)

isInternal :: NodeName -> Bool

isInternal n = extIndex n /= 0 || not (null $ extString n)

{- | Data type indicating the origin of nodes and edges in the input language

This is not used in the DG calculus, only may be used in the future

for reconstruction of input and management of change. -}

data DGOrigin =

DGEmpty

| DGBasic

| DGBasicSpec (Set.Set G_symbol)

| DGExtension

| DGTranslation

| DGUnion

| DGHiding

| DGRevealing

| DGRevealTranslation

| DGFreeOrCofree FreeOrCofree

| DGLocal

| DGClosed

| DGLogicQual

| DGData

| DGFormalParams

| DGImports

| DGInst SIMPLE_ID

| DGFitSpec

| DGFitView SIMPLE_ID

| DGProof

| DGNormalForm Node

| DGintegratedSCC

| DGFlattening

deriving (Show, Eq, Ord)

-- | node content or reference to another library's node

data DGNodeInfo = DGNode

{ node_origin :: DGOrigin -- origin in input language

, node_cons_status :: ConsStatus } -- like a link from the empty signature

| DGRef -- reference to node in a different DG

{ ref_libname :: LIB_NAME -- pointer to DG where ref'd node resides

, ref_node :: Node -- pointer to ref'd node

} deriving (Show, Eq)

-- | node inscriptions in development graphs.

-- Nothing entries indicate "not computed yet"

data DGNodeLab =

DGNodeLab

{ dgn_name :: NodeName -- name in the input language

, dgn_theory :: G_theory -- local theory

, labelHasHiding :: Bool -- has this node an ingoing hiding link

, dgn_nf :: Maybe Node -- normal form, for Theorem-Hide-Shift

, dgn_sigma :: Maybe GMorphism -- inclusion of signature into nf signature

, nodeInfo :: DGNodeInfo

, dgn_lock :: Maybe (MVar ())

} deriving (Show, Eq)

instance Show (MVar a) where

show _ = ""

isDGRef :: DGNodeLab -> Bool

isDGRef l = case nodeInfo l of

DGNode {} -> False

DGRef {} -> True

-- | test a theory sentence

isProvenSenStatus :: SenStatus a (AnyComorphism, BasicProof) -> Bool

isProvenSenStatus = any isProvenSenStatusAux . thmStatus

where isProvenSenStatusAux (_, BasicProof _ pst) = isProvedStat pst

isProvenSenStatusAux _ = False

hasSenKind :: (forall a . SenStatus a (AnyComorphism, BasicProof) -> Bool)

-> DGNodeLab -> Bool

hasSenKind f dgn = case dgn_theory dgn of

G_theory _lid _sigma _ sens _ -> not $ OMap.null $ OMap.filter f sens

-- | test if a given node label has local open goals

hasOpenGoals :: DGNodeLab -> Bool

hasOpenGoals = hasSenKind (\ s -> not (isAxiom s) && not (isProvenSenStatus s))

-- | check if the node has an internal name (wrong for DGRef!)

isInternalNode :: DGNodeLab -> Bool

isInternalNode l@DGNodeLab {dgn_name = n} = not (isDGRef l) && isInternal n

getNodeConsStatus :: DGNodeLab -> ConsStatus

getNodeConsStatus lbl = case nodeInfo lbl of

DGRef {} -> mkConsStatus None

DGNode { node_cons_status = c } -> c

getNodeCons :: DGNodeLab -> Conservativity

getNodeCons nl = case getNodeConsStatus nl of

ConsStatus cons _ _ -> cons

-- | returns the Conservativity if the given node has one, otherwise none

getNodeConservativity :: LNode DGNodeLab -> Conservativity

getNodeConservativity (_,nl) = getNodeCons nl

-- | test if a node conservativity is open,

-- return input for refs or nodes with normal forms

hasOpenNodeConsStatus :: Bool -> DGNodeLab -> Bool

hasOpenNodeConsStatus b lbl = if isJust $ dgn_nf lbl then b else

hasOpenConsStatus b $ getNodeConsStatus lbl

-- | test if a conservativity is open, return input for None

hasOpenConsStatus :: Bool -> ConsStatus -> Bool

hasOpenConsStatus b (ConsStatus cons _ thm) = case cons of

None -> b

_ -> not $ isProvenThmLinkStatus thm

data DGNodeType = DGNodeType

{ nonRefType :: NonRefType

, isLocallyEmpty :: Bool }

deriving (Eq, Ord, Show)

data NonRefType =

RefType

| NonRefType { isProvenCons :: Bool

, isInternalSpec :: Bool }

deriving (Eq, Ord, Show)

-- | creates a DGNodeType from a DGNodeLab

getRealDGNodeType :: DGNodeLab -> DGNodeType

getRealDGNodeType dgnlab = DGNodeType

{ nonRefType = if isDGRef dgnlab then RefType else

NonRefType { isProvenCons = not $ hasOpenNodeConsStatus False dgnlab

, isInternalSpec = isInternalNode dgnlab }

, isLocallyEmpty = not $ hasOpenGoals dgnlab

}

-- | Creates a list with all DGNodeType types

listDGNodeTypes :: [DGNodeType]

listDGNodeTypes =

[ DGNodeType { nonRefType = ref, isLocallyEmpty = isEmpty' }

| ref <- RefType :

[ NonRefType { isProvenCons = proven, isInternalSpec = spec }

| proven <- [True, False]

, spec <- [True, False]

]

, isEmpty' <- [True, False]

]

-- ** edge label types

{- an edge id used to be represented as a list of ints.

the reason of an edge can have multiple ids is, for example, there exists

an proven edge e1 with id 1 and an unproven edge e2 with id 2 between

two nodes. Now after applying some rules e2 is proven, but it's actually

the same as the proven edge e1, then the proven e2 should not be inserted

into the graph again, but e1 will take e2's id 2 because 2 is probably

saved in some other places. As a result, e1 would have 1 and 2 as its id.

This type can be extended to a more complicated struture, like a tree

suggested by Till.

-}

-- | unique number for edges

newtype EdgeId = EdgeId Int deriving (Show, Eq, Ord, Enum)

-- | the first edge in a graph

startEdgeId :: EdgeId

startEdgeId = EdgeId 0

showEdgeId :: EdgeId -> String

showEdgeId (EdgeId i) = show i

-- | a set of used edges

newtype ProofBasis = ProofBasis { proofBasis :: Set.Set EdgeId }

deriving (Show, Eq, Ord)

data DGLinkOrigin =

SeeTarget

| SeeSource

| DGImpliesLink

| DGLinkExtension

| DGLinkTranslation

| DGLinkClosedLenv

| DGLinkImports

| DGLinkInst SIMPLE_ID

| DGLinkView SIMPLE_ID

| DGLinkFitView SIMPLE_ID

| DGLinkFitViewImp SIMPLE_ID

| DGLinkProof

| DGLinkFlatteningUnion

| DGLinkFlatteningRename

deriving (Show, Eq)

{- | Rules in the development graph calculus,

Sect. IV:4.4 of the CASL Reference Manual explains them in depth

mutual recursive with 'DGLinkLab', 'DGLinkType', and 'ThmLinkStatus'

-}

data DGRule =

DGRule String

| DGRuleWithEdge String (LEdge DGLinkLab)

| DGRuleLocalInference [(String, String)] -- renamed theorems

| Composition [LEdge DGLinkLab]

| BasicInference AnyComorphism BasicProof -- coding and proof tree. obsolete?

| BasicConsInference Edge BasicConsProof

deriving (Show, Eq)

-- | proof status of a link

data ThmLinkStatus = LeftOpen | Proven DGRule ProofBasis deriving (Show, Eq)

isProvenThmLinkStatus :: ThmLinkStatus -> Bool

isProvenThmLinkStatus tls = case tls of

LeftOpen -> False

_ -> True

data Scope = Local | Global deriving (Show, Eq, Ord)

data LinkKind = DefLink | ThmLink ThmLinkStatus deriving (Show, Eq)

data FreeOrCofree = Free | Cofree deriving (Show, Eq, Ord)

data ConsStatus = ConsStatus Conservativity Conservativity ThmLinkStatus

deriving (Show, Eq)

isProvenConsStatusLink :: ConsStatus -> Bool

isProvenConsStatusLink = not . hasOpenConsStatus False

mkConsStatus :: Conservativity -> ConsStatus

mkConsStatus c = ConsStatus c None LeftOpen

-- | Link types of development graphs

-- Sect. IV:4.2 of the CASL Reference Manual explains them in depth

data DGLinkType =

ScopedLink Scope LinkKind ConsStatus

| HidingDefLink

| FreeOrCofreeDefLink FreeOrCofree MaybeNode -- the "parameter" node

| HidingFreeOrCofreeThm (Maybe FreeOrCofree) GMorphism ThmLinkStatus

-- DGLink S1 S2 m2 (DGLinkType m1 p) n

-- corresponds to a span of morphisms

-- S1 <--m1-- S --m2--> S2

deriving (Show, Eq)

-- | extract theorem link status from link type

thmLinkStatus :: DGLinkType -> Maybe ThmLinkStatus

thmLinkStatus t = case t of

ScopedLink _ (ThmLink s) _ -> Just s

HidingFreeOrCofreeThm _ _ s -> Just s

_ -> Nothing

-- | link inscriptions in development graphs

data DGLinkLab = DGLink

{ dgl_morphism :: GMorphism -- signature morphism of link

, dgl_type :: DGLinkType -- type: local, global, def, thm?

, dgl_origin :: DGLinkOrigin -- origin in input language

, dgl_id :: EdgeId -- id of the edge

} deriving (Show, Eq)

-- | describe the link type of the label

getDGLinkType :: DGLinkLab -> String

getDGLinkType = getDGEdgeTypeName . getRealDGLinkType

-- | converts a DGEdgeType to a String

getDGEdgeTypeName :: DGEdgeType -> String

getDGEdgeTypeName e =

(if isInc e then (++ "Inc") else id)

$ getDGEdgeTypeModIncName $ edgeTypeModInc e

getDGEdgeTypeModIncName :: DGEdgeTypeModInc -> String

getDGEdgeTypeModIncName et = case et of

ThmType thm isPrvn _ _ ->

let prvn = (if isPrvn then "P" else "Unp") ++ "roven" in

case thm of

HidingThm -> prvn ++ "HidingThm"

FreeOrCofreeThm -> prvn ++ "Thm"

GlobalOrLocalThm scope isHom ->

let het = if isHom then id else ("Het" ++) in

het (case scope of

Local -> "Local"

Global -> if isHom then "Global" else "") ++ prvn ++ "Thm"

FreeOrCofreeDef -> "Def"

_ -> show et

data DGEdgeType = DGEdgeType

{ edgeTypeModInc :: DGEdgeTypeModInc

, isInc :: Bool }

deriving (Eq, Ord, Show)

data DGEdgeTypeModInc =

GlobalDef

| HetDef

| HidingDef

| LocalDef

| FreeOrCofreeDef -- free or cofree

| ThmType { thmEdgeType :: ThmTypes

, isProvenEdge :: Bool

, isConservativ :: Bool

, isPending :: Bool }

deriving (Eq, Ord, Show)

data ThmTypes =

HidingThm

| FreeOrCofreeThm

| GlobalOrLocalThm { isLocalThmType :: Scope

, isHomThm :: Bool }

deriving (Eq, Ord, Show)

getHomEdgeType :: Bool -> DGLinkType -> DGEdgeTypeModInc

getHomEdgeType isHom lt = case lt of

ScopedLink scope lk cons -> case lk of

DefLink -> case scope of

Local -> LocalDef

Global -> if isHom then GlobalDef else HetDef

ThmLink st -> ThmType

{ thmEdgeType = GlobalOrLocalThm scope isHom

, isProvenEdge = isProvenThmLinkStatus st

, isConservativ = isProvenConsStatusLink cons

, isPending = False } -- needs to be checked

HidingDefLink -> HidingDef

FreeOrCofreeDefLink _ _ -> FreeOrCofreeDef

HidingFreeOrCofreeThm mh _ st -> ThmType

{ thmEdgeType = case mh of

Nothing -> HidingThm

_ -> FreeOrCofreeThm

, isProvenEdge = isProvenThmLinkStatus st

, isConservativ = True

, isPending = False }

-- | creates a DGEdgeType from a DGLinkLab

getRealDGLinkType :: DGLinkLab -> DGEdgeType

getRealDGLinkType lnk = let

gmor = dgl_morphism lnk

in DGEdgeType

{ edgeTypeModInc = getHomEdgeType (isHomogeneous gmor) $ dgl_type lnk

, isInc = case gmor of

GMorphism cid _ _ mor _ -> isInclusionComorphism cid && isInclusion mor

}

-- | Creates a list with all DGEdgeType types

listDGEdgeTypes :: [DGEdgeType]

listDGEdgeTypes =

[ DGEdgeType { edgeTypeModInc = modinc

, isInc = isInclusion' }

| modinc <-

[ GlobalDef

, HetDef

, HidingDef

, LocalDef

, FreeOrCofreeDef ] ++

[ ThmType { thmEdgeType = thmType

, isProvenEdge = proven

, isConservativ = cons

, isPending = pending }

| thmType <-

[ HidingThm

, FreeOrCofreeThm] ++

[ GlobalOrLocalThm { isLocalThmType = local

, isHomThm = hom }

| local <- [Local, Global]

, hom <- [True, False]

]

, proven <- [True, False]

, cons <- [True, False]

, pending <- [True, False]

]

, isInclusion' <- [True, False]

]

-- ** types for global environments

-- | import, formal parameters and united signature of formal params

data GenSig = GenSig MaybeNode [NodeSig] MaybeNode deriving Show

-- | genericity and body

data ExtGenSig = ExtGenSig GenSig NodeSig deriving Show

-- | source, morphism, parameterized target

data ExtViewSig = ExtViewSig NodeSig GMorphism ExtGenSig deriving Show

{- ** types for architectural and unit specification analysis

(as defined for basic static semantics in Chap. III:5.1) -}

data UnitSig = UnitSig [NodeSig] NodeSig deriving Show

data ImpUnitSigOrSig = ImpUnitSig MaybeNode UnitSig | Sig NodeSig deriving Show

type StUnitCtx = Map.Map SIMPLE_ID ImpUnitSigOrSig

emptyStUnitCtx :: StUnitCtx

emptyStUnitCtx = Map.empty

data ArchSig = ArchSig StUnitCtx UnitSig deriving Show

-- | an entry of the global environment

data GlobalEntry =

SpecEntry ExtGenSig

| ViewEntry ExtViewSig

| ArchEntry ArchSig

| UnitEntry UnitSig

| RefEntry

deriving Show

type GlobalEnv = Map.Map SIMPLE_ID GlobalEntry

-- ** change and history types

-- | the edit operations of the DGraph

data DGChange =

InsertNode (LNode DGNodeLab)

| DeleteNode (LNode DGNodeLab)

| InsertEdge (LEdge DGLinkLab)

| DeleteEdge (LEdge DGLinkLab)

-- it contains the old label and new label with node

| SetNodeLab DGNodeLab (LNode DGNodeLab)

deriving (Show, Eq)

data HistElem =

HistElem DGChange

| HistGroup DGRule ProofHistory

deriving (Show, Eq)

type ProofHistory = SizedList.SizedList HistElem

{- | the actual development graph with auxiliary information. A

'G_sign' should be stored in 'sigMap' under its 'gSignSelfIdx'. The

same applies to 'G_morphism' with 'morMap' and 'gMorphismSelfIdx'

resp. 'G_theory' with 'thMap' and 'gTheorySelfIdx'. -}

data DGraph = DGraph

{ globalAnnos :: GlobalAnnos -- ^ global annos of library

, globalEnv :: GlobalEnv -- ^ name entities (specs, views) of a library

, dgBody :: Tree.Gr DGNodeLab DGLinkLab -- ^ actual 'DGraph` tree

, getNewEdgeId :: EdgeId -- ^ edge counter

, refNodes :: Map.Map Node (LIB_NAME, Node) -- ^ unexpanded 'DGRef's

, allRefNodes :: Map.Map (LIB_NAME, Node) Node -- ^ all DGRef's

, sigMap :: Map.Map SigId G_sign -- ^ signature map

, thMap :: Map.Map ThId G_theory -- ^ morphism map

, morMap :: Map.Map MorId G_morphism -- ^ theory map

, proofHistory :: ProofHistory -- ^ applied proof steps

, redoHistory :: ProofHistory -- ^ undone proofs steps

, openlock :: Maybe (MVar ())

-- ^ control of graph display

} deriving Show

emptyDG :: DGraph

emptyDG = DGraph

{ globalAnnos = emptyGlobalAnnos

, globalEnv = Map.empty

, dgBody = Graph.empty

, getNewEdgeId = startEdgeId

, refNodes = Map.empty

, allRefNodes = Map.empty

, sigMap = Map.empty

, thMap = Map.empty

, morMap = Map.empty

, proofHistory = SizedList.empty

, redoHistory = SizedList.empty

, openlock = Nothing }

type LibEnv = Map.Map LIB_NAME DGraph

-- | an empty environment

emptyLibEnv :: LibEnv

emptyLibEnv = Map.empty

emptyDGwithMVar :: IO DGraph

emptyDGwithMVar = do

ol <- newEmptyMVar

return $ emptyDG { openlock = Just ol }

-- * utility functions

-- ** for node signatures

emptyG_sign :: AnyLogic -> G_sign

emptyG_sign (Logic lid) = G_sign lid (ext_empty_signature lid) startSigId

getMaybeSig :: MaybeNode -> G_sign

getMaybeSig (JustNode ns) = getSig ns

getMaybeSig (EmptyNode l) = emptyG_sign l

getLogic :: MaybeNode -> AnyLogic

getLogic (JustNode ns) = getNodeLogic ns

getLogic (EmptyNode l) = l

getNodeLogic :: NodeSig -> AnyLogic

getNodeLogic (NodeSig _ (G_sign lid _ _)) = Logic lid

-- ** for node names

emptyNodeName :: NodeName

emptyNodeName = NodeName (mkSimpleId "") "" 0 []

showExt :: NodeName -> String

showExt n = let i = extIndex n in extString n ++ if i == 0 then "" else show i

showName :: NodeName -> String

showName n = let ext = showExt n in

tokStr (getName n) ++ if null ext then ext else '_' : ext

makeName :: SIMPLE_ID -> NodeName

makeName n = NodeName n "" 0 [ElemName $ tokStr n]

incBy :: Int -> NodeName -> NodeName

incBy i n = n

{ extIndex = extIndex n + i

, xpath = case xpath n of

ChildIndex j : r -> ChildIndex (j + i) : r

l -> ChildIndex i : l }

inc :: NodeName -> NodeName

inc = incBy 1

extName :: String -> NodeName -> NodeName

extName s n = n

{ extString = showExt n ++ take 1 s

, extIndex = 0

, xpath = ElemName s : xpath n }

-- ** accessing node label

-- | get the origin of a non-reference node (partial)

dgn_origin :: DGNodeLab -> DGOrigin

dgn_origin = node_origin . nodeInfo

-- | get the referenced library (partial)

dgn_libname :: DGNodeLab -> LIB_NAME

dgn_libname = ref_libname . nodeInfo

-- | get the referenced node (partial)

dgn_node :: DGNodeLab -> Node

dgn_node = ref_node . nodeInfo

-- | get the signature of a node's theory (total)

dgn_sign :: DGNodeLab -> G_sign

dgn_sign dn = case dgn_theory dn of

G_theory lid sig ind _ _-> G_sign lid sig ind

-- | gets the name of a development graph node as a string (total)

getDGNodeName :: DGNodeLab -> String

getDGNodeName = showName . dgn_name

-- ** creating node content and label

-- | create default content

newNodeInfo :: DGOrigin -> DGNodeInfo

newNodeInfo orig = DGNode

{ node_origin = orig

, node_cons_status = mkConsStatus None }

-- | create a reference node part

newRefInfo :: LIB_NAME -> Node -> DGNodeInfo

newRefInfo ln n = DGRef

{ ref_libname = ln

, ref_node = n }

-- | create a new node label

newInfoNodeLab :: NodeName -> DGNodeInfo -> G_theory -> DGNodeLab

newInfoNodeLab name info gTh = DGNodeLab

{ dgn_name = name

, dgn_theory = gTh

, labelHasHiding = False

, dgn_nf = Nothing

, dgn_sigma = Nothing

, nodeInfo = info

, dgn_lock = Nothing }

-- | create a new node label using 'newNodeInfo' and 'newInfoNodeLab'

newNodeLab :: NodeName -> DGOrigin -> G_theory -> DGNodeLab

newNodeLab name = newInfoNodeLab name . newNodeInfo

-- ** handle the lock of a node

-- | wrapper to access the maybe lock

treatNodeLock :: (MVar () -> a) -> DGNodeLab -> a

treatNodeLock f = maybe (error "MVar not initialised") f . dgn_lock

{- | Acquire the local lock. If already locked it waits till it is unlocked

again.-}

lockLocal :: DGNodeLab -> IO ()

lockLocal = treatNodeLock $ flip putMVar ()

-- | Tries to acquire the local lock. Return False if already acquired.

tryLockLocal :: DGNodeLab -> IO Bool

tryLockLocal = treatNodeLock $ flip tryPutMVar ()

-- | Releases the local lock.

unlockLocal :: DGNodeLab -> IO ()

unlockLocal = treatNodeLock $ \ lock ->

tryTakeMVar lock >>= maybe (error "Local lock wasn't locked.") return

-- | checks if locking MVar is initialized

hasLock :: DGNodeLab -> Bool

hasLock = isJust . dgn_lock

-- ** handle edge numbers and proof bases

-- | create a default ID which has to be changed when inserting a certain edge.

defaultEdgeId :: EdgeId

defaultEdgeId = EdgeId (-1)

emptyProofBasis :: ProofBasis

emptyProofBasis = ProofBasis Set.empty

nullProofBasis :: ProofBasis -> Bool

nullProofBasis = Set.null . proofBasis

addEdgeId :: ProofBasis -> EdgeId -> ProofBasis

addEdgeId (ProofBasis s) e = ProofBasis $ Set.insert e s

-- | checks if the given edge is contained in the given proof basis..

roughElem :: LEdge DGLinkLab -> ProofBasis -> Bool

roughElem (_, _, label) = Set.member (dgl_id label) . proofBasis

-- ** edge label equalities

-- | equality without comparing the edge ids

eqDGLinkLabContent :: DGLinkLab -> DGLinkLab -> Bool

eqDGLinkLabContent l1 l2 = let

i1 = dgl_id l1

i2 = dgl_id l2

in if i1 <= defaultEdgeId || i2 <= defaultEdgeId then

dgl_morphism l1 == dgl_morphism l2

&& dgl_type l1 == dgl_type l2

&& dgl_origin l1 == dgl_origin l2

else let r = eqDGLinkLabContent l1 l2 { dgl_id = defaultEdgeId}

s = i1 == i2

in assert (r == s) s

-- | equality comparing ids only

eqDGLinkLabById :: DGLinkLab -> DGLinkLab -> Bool

eqDGLinkLabById l1 l2 = let

i1 = dgl_id l1

i2 = dgl_id l2

in if i1 > defaultEdgeId && i2 > defaultEdgeId then i1 == i2 else

error "eqDGLinkLabById"

-- ** setting index maps

setSigMapDG :: Map.Map SigId G_sign -> DGraph -> DGraph

setSigMapDG m dg = dg { sigMap = m }

setThMapDG :: Map.Map ThId G_theory -> DGraph -> DGraph

setThMapDG m dg = dg { thMap = m }

setMorMapDG :: Map.Map MorId G_morphism -> DGraph -> DGraph

setMorMapDG m dg = dg { morMap = m }

-- ** looking up in index maps

lookupSigMapDG :: SigId -> DGraph -> Maybe G_sign

lookupSigMapDG i = Map.lookup i . sigMap

lookupThMapDG :: ThId -> DGraph -> Maybe G_theory

lookupThMapDG i = Map.lookup i . thMap

lookupMorMapDG :: MorId -> DGraph -> Maybe G_morphism

lookupMorMapDG i = Map.lookup i . morMap

-- ** getting index maps and their maximal index

getMapAndMaxIndex :: Ord k => k -> (b -> Map.Map k a) -> b -> (Map.Map k a, k)

getMapAndMaxIndex c f gctx =

let m = f gctx in (m, if Map.null m then c else fst $ Map.findMax m)

sigMapI :: DGraph -> (Map.Map SigId G_sign, SigId)

sigMapI = getMapAndMaxIndex startSigId sigMap

thMapI :: DGraph -> (Map.Map ThId G_theory, ThId)

thMapI = getMapAndMaxIndex startThId thMap

morMapI :: DGraph -> (Map.Map MorId G_morphism, MorId)

morMapI = getMapAndMaxIndex startMorId morMap

-- ** lookup other graph parts

lookupGlobalEnvDG :: SIMPLE_ID -> DGraph -> Maybe GlobalEntry

lookupGlobalEnvDG sid = Map.lookup sid . globalEnv

-- | lookup a referenced node with a node id

lookupInRefNodesDG :: Node -> DGraph -> Maybe (LIB_NAME, Node)

lookupInRefNodesDG n = Map.lookup n . refNodes

-- | look up a refernced node with its parent infor.

lookupInAllRefNodesDG :: DGNodeInfo -> DGraph -> Maybe Node

lookupInAllRefNodesDG ref = case ref of

DGRef { ref_libname = libn, ref_node = refn } ->

Map.lookup (libn, refn) . allRefNodes

_ -> error "lookupInAllRefNodesDG"

-- ** treat reference nodes

-- | add a new referenced node into the refNodes map of the given DG

addToRefNodesDG :: Node -> DGNodeInfo -> DGraph -> DGraph

addToRefNodesDG n ref dg = case ref of

DGRef { ref_libname = libn, ref_node = refn } ->

dg { refNodes = Map.insert n (libn, refn) $ refNodes dg

, allRefNodes = Map.insert (libn, refn) n $ allRefNodes dg }

_ -> error "addToRefNodesDG"

-- | delete the given referenced node out of the refnodes map

deleteFromRefNodesDG :: Node -> DGraph -> DGraph

deleteFromRefNodesDG n dg = dg { refNodes = Map.delete n $ refNodes dg }

-- ** accessing the actual graph

-- | get the next available node id

getNewNodeDG :: DGraph -> Node

getNewNodeDG = Tree.getNewNode . dgBody

-- | get all the nodes

labNodesDG :: DGraph -> [LNode DGNodeLab]

labNodesDG = labNodes . dgBody

-- | get all the edges

labEdgesDG :: DGraph -> [LEdge DGLinkLab]

labEdgesDG = labEdges . dgBody

-- | checks if a DG is empty or not.

isEmptyDG :: DGraph -> Bool

isEmptyDG = isEmpty . dgBody

-- | checks if a given node belongs to a given DG

gelemDG :: Node -> DGraph -> Bool

gelemDG n = gelem n . dgBody

-- | get the number of nodes of a given DG

noNodesDG :: DGraph -> Int

noNodesDG = noNodes . dgBody

-- | get all nodes which links to the given node in a given DG

preDG :: DGraph -> Node -> [Node]

preDG = pre . dgBody

-- | get all the incoming ledges of the given node in a given DG

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

innDG = inn . dgBody

-- | get all the outgoing ledges of the given node in a given DG

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

outDG = out . dgBody

-- | get all the nodes of the given DG

nodesDG :: DGraph -> [Node]

nodesDG = nodes . dgBody

-- | get all the edges of the given DG

edgesDG :: DGraph -> [Edge]

edgesDG = edges . dgBody

-- | tries to get the label of the given node in a given DG

labDG :: DGraph -> Node -> DGNodeLab

labDG dg = fromMaybe (error "labDG") . lab (dgBody dg)

-- | get the name of a node from the number of node

getNameOfNode :: Node -> DGraph -> String

getNameOfNode index gc = getDGNodeName $ labDG gc index

-- | gets the given number of new node-ids in a given DG.

newNodesDG :: Int -> DGraph -> [Node]

newNodesDG n = newNodes n . dgBody

-- ** decompose the actual graph

-- | tear the given DGraph appart.

matchDG :: Node -> DGraph -> (MContext DGNodeLab DGLinkLab, DGraph)

matchDG n dg = let (mc, b) = match n $ dgBody dg in(mc, dg { dgBody = b })

-- | get the context of the given DG

contextDG :: DGraph -> Node -> Context DGNodeLab DGLinkLab

contextDG = context . dgBody

-- | safe context for graphs

safeContext :: (Show a, Show b, Graph gr) => String -> gr a b -> Node

-> Context a b

safeContext err g v =

fromMaybe (error $ err ++ ": Match Exception, Node: " ++ show v)

. fst $ match v g

-- | get the context and throw input string as error message

safeContextDG :: String -> DGraph -> Node -> Context DGNodeLab DGLinkLab

safeContextDG s = safeContext s . dgBody

-- ** manipulate graph

-- | sets the node with new label and returns the new graph and the old label

labelNodeDG :: LNode DGNodeLab -> DGraph -> (DGraph, DGNodeLab)

labelNodeDG p g =

let (b, l) = Tree.labelNode p $ dgBody g in (g { dgBody = b }, l)

-- | delete the node out of the given DG

delNodeDG :: Node -> DGraph -> DGraph

delNodeDG n dg = dg { dgBody = delNode n $ dgBody dg }

-- | delete the LNode out of the given DG

delLNodeDG :: LNode DGNodeLab -> DGraph -> DGraph

delLNodeDG n dg = dg { dgBody = Tree.delLNode (==) n $ dgBody dg }

-- | delete a list of nodes out of the given DG

delNodesDG :: [Node] -> DGraph -> DGraph

delNodesDG ns dg = dg { dgBody = delNodes ns $ dgBody dg }

-- | insert a new node into given DGraph

insNodeDG :: LNode DGNodeLab -> DGraph -> DGraph

insNodeDG n dg = dg { dgBody = insNode n $ dgBody dg }

-- | inserts a lnode into a given DG

insLNodeDG :: LNode DGNodeLab -> DGraph -> DGraph

insLNodeDG n@(v, _) g =

if gelemDG v g then error $ "insLNodeDG " ++ show v else insNodeDG n g

-- | insert a new node with the given node content into a given DGraph

insNodesDG :: [LNode DGNodeLab] -> DGraph -> DGraph

insNodesDG ns dg = dg { dgBody = insNodes ns $ dgBody dg }

-- | delete an edge out of a given DG

delEdgeDG :: Edge -> DGraph -> DGraph

delEdgeDG e dg = dg { dgBody = delEdge e $ dgBody dg }

-- | delete a list of edges

delEdgesDG :: [Edge] -> DGraph -> DGraph

delEdgesDG es dg = dg { dgBody = delEdges es $ dgBody dg }

-- | delete a labeled edge out of the given DG

delLEdgeDG :: LEdge DGLinkLab -> DGraph -> DGraph

delLEdgeDG e g = g

{ dgBody = Tree.delLEdge (\ l1 l2 -> compare (dgl_id l1) $ dgl_id l2) e

$ dgBody g }

-- | insert a labeled edge into a given DG, return possibly new id of edge

insLEdgeDG :: LEdge DGLinkLab -> DGraph -> (LEdge DGLinkLab, DGraph)

insLEdgeDG (s, t, l) g =

let eId = dgl_id l

nId = getNewEdgeId g

newId = dgl_id l == defaultEdgeId

e = (s, t, if newId then l { dgl_id = nId } else l)

in (e, g

{ getNewEdgeId = if newId then succ nId else max nId $ succ eId

, dgBody = fst $ Tree.insLEdge True (\ l1 l2 ->

if eqDGLinkLabContent l1 { dgl_id = defaultEdgeId } l2

then EQ else compare (dgl_id l1) $ dgl_id l2) e $ dgBody g })

{- | tries to insert a labeled edge into a given DG, but if this edge

already exists, then does nothing. -}

insLEdgeNubDG :: LEdge DGLinkLab -> DGraph -> DGraph

insLEdgeNubDG (v, w, l) g =

let oldEdgeId = getNewEdgeId g

(ng, change) = Tree.insLEdge False (\ l1 l2 ->

if eqDGLinkLabContent l1 { dgl_id = defaultEdgeId } l2

then EQ else compare (dgl_id l1) $ dgl_id l2)

(v, w, l { dgl_id = oldEdgeId }) $ dgBody g

in

g { getNewEdgeId = if change then succ oldEdgeId else oldEdgeId

, dgBody = ng }

{- | insert an edge into the given DGraph, which updates

the graph body and the edge counter as well. -}

insEdgeDG :: LEdge DGLinkLab -> DGraph -> DGraph

insEdgeDG l oldDG =

oldDG { dgBody = insEdge l $ dgBody oldDG

, getNewEdgeId = succ $ getNewEdgeId oldDG }

-- | insert a list of labeled edge into a given DG

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

insEdgesDG = flip $ foldr insEdgeDG

-- | merge a list of lnodes and ledges into a given DG

mkGraphDG :: [LNode DGNodeLab] -> [LEdge DGLinkLab] -> DGraph -> DGraph

mkGraphDG ns ls = insEdgesDG ls . insNodesDG ns

-- ** handle proof history

-- | add a history item to current history.

addToProofHistoryDG :: HistElem -> DGraph -> DGraph

addToProofHistoryDG x dg =

dg { proofHistory = SizedList.cons x $ proofHistory dg }

-- | get the old history and the new offset

splitHistory :: DGraph -> DGraph -> (ProofHistory, ProofHistory)

splitHistory oldGraph newGraph = let

oldHist = proofHistory oldGraph

newHist = proofHistory newGraph

diff = SizedList.take (SizedList.size newHist - SizedList.size oldHist)

newHist

in (oldHist, diff)

-- | reverse the history list

reverseHistory :: SizedList.SizedList HistElem -> SizedList.SizedList HistElem

reverseHistory = SizedList.reverse . SizedList.map

(\ e -> case e of

HistElem _ -> e

HistGroup r l -> HistGroup r $ reverseHistory l)

-- | group pushd changes, leave history of old graph unchanged

groupHistory :: DGraph -> DGRule -> DGraph -> DGraph

groupHistory oldGraph rule newGraph = let

(oldHist, diff) = splitHistory oldGraph newGraph

in if SizedList.null diff then newGraph else

newGraph { proofHistory = SizedList.cons (HistGroup rule diff) oldHist }

-- | get most recent step

getLastHistElem :: DGraph -> HistElem

getLastHistElem dg = let hist = proofHistory dg in

if SizedList.null hist then error "Static.DevGraph.getHistElem"

else SizedList.head hist

-- | get most recent change

getLastChange :: DGraph -> DGChange

getLastChange dg = case getLastHistElem dg of

HistElem c -> c

HistGroup _ _ -> error "Static.DevGraph.getLastChange"

-- ** top-level functions

-- | initializes the MVar for locking if nessesary

initLocking :: DGraph -> LNode DGNodeLab -> IO (DGraph, DGNodeLab)

initLocking dg (node, dgn) = do

lock <- newEmptyMVar

let dgn' = dgn { dgn_lock = Just lock }

return (fst $ labelNodeDG (node, dgn') dg, dgn')

-- | returns the DGraph that belongs to the given library name

lookupDGraph :: LIB_NAME -> LibEnv -> DGraph

lookupDGraph ln = Map.findWithDefault (error $ "lookupDGraph " ++ show ln) ln

{- | compute the theory of a given node.

If this node is a DGRef, the referenced node is looked up first. -}

computeLocalTheory :: Monad m => LibEnv -> LIB_NAME -> Node -> m G_theory

computeLocalTheory libEnv ln =

computeLocalNodeTheory libEnv $ lookupDGraph ln libEnv

computeLocalNodeTheory :: Monad m => LibEnv -> DGraph -> Node -> m G_theory

computeLocalNodeTheory libEnv dg = computeLocalLabelTheory libEnv . labDG dg

computeLocalLabelTheory :: Monad m => LibEnv -> DGNodeLab -> m G_theory

computeLocalLabelTheory libEnv nodeLab =

if isDGRef nodeLab

then

computeLocalTheory libEnv (dgn_libname nodeLab) $ dgn_node nodeLab

else return $ dgn_theory nodeLab

-- ** test link types

liftE :: (DGLinkType -> Bool) -> LEdge DGLinkLab -> Bool

liftE f (_, _, edgeLab) = f $ dgl_type edgeLab

-- | or two predicates

liftOr :: (a -> Bool) -> (a -> Bool) -> a -> Bool

liftOr f g x = f x || g x

isGlobalDef :: DGLinkType -> Bool

isGlobalDef lt = case lt of

ScopedLink Global DefLink _ -> True

_ -> False

isLocalDef :: DGLinkType -> Bool

isLocalDef lt = case lt of

ScopedLink Local DefLink _ -> True

_ -> False

isHidingDef :: DGLinkType -> Bool

isHidingDef lt = case lt of

HidingDefLink -> True

_ -> False

isDefEdge :: DGLinkType -> Bool

isDefEdge edge = case edge of

ScopedLink _ DefLink _ -> True

HidingDefLink -> True

FreeOrCofreeDefLink _ _ -> True

_ -> False

isLocalEdge :: DGLinkType -> Bool

isLocalEdge edge = case edge of

ScopedLink Local _ _ -> True

_ -> False

isHidingEdge :: DGLinkType -> Bool

isHidingEdge edge = case edge of

HidingDefLink -> True

HidingFreeOrCofreeThm Nothing _ _ -> True

_ -> False

-- ** create link types

hidingThm :: GMorphism -> DGLinkType

hidingThm m = HidingFreeOrCofreeThm Nothing m LeftOpen

globalThm :: DGLinkType

globalThm = localOrGlobalThm Global None

localThm :: DGLinkType

localThm = localOrGlobalThm Local None

globalConsThm :: Conservativity -> DGLinkType

globalConsThm = localOrGlobalThm Global

localConsThm :: Conservativity -> DGLinkType

localConsThm = localOrGlobalThm Local

localOrGlobalThm :: Scope -> Conservativity -> DGLinkType

localOrGlobalThm sc = ScopedLink sc (ThmLink LeftOpen) . mkConsStatus

localOrGlobalDef :: Scope -> Conservativity -> DGLinkType

localOrGlobalDef sc = ScopedLink sc DefLink . mkConsStatus

globalConsDef :: Conservativity -> DGLinkType

globalConsDef = localOrGlobalDef Global

globalDef :: DGLinkType

globalDef = localOrGlobalDef Global None

localDef :: DGLinkType

localDef = localOrGlobalDef Local None

-- ** link conservativity

getLinkConsStatus :: DGLinkType -> ConsStatus

getLinkConsStatus lt = case lt of

ScopedLink _ _ c -> c

_ -> mkConsStatus None

getCons :: DGLinkType -> Conservativity

getCons lt = case getLinkConsStatus lt of

ConsStatus cons _ _ -> cons

-- | returns the Conservativity if the given edge has one, otherwise none

getConservativity :: LEdge DGLinkLab -> Conservativity

getConservativity (_, _, edgeLab) = getCons $ dgl_type edgeLab

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

getConservativityOfPath :: [LEdge DGLinkLab] -> Conservativity

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

-- * bottom up traversal

-- | Creates a LIB_NAME relation wrt dependencies via reference nodes

getLibDepRel :: LibEnv -> Rel.Rel LIB_NAME

getLibDepRel = Rel.transClosure

. Rel.fromSet . Map.foldWithKey (\ ln dg s ->

foldr (\ x -> if isDGRef x then Set.insert (ln, dgn_libname x) else id) s

$ map snd $ labNodesDG dg) Set.empty

topsortedLibsWithImports :: Rel.Rel LIB_NAME -> [LIB_NAME]

topsortedLibsWithImports = concatMap Set.toList . Rel.topSort

getTopsortedLibs :: LibEnv -> [LIB_NAME]

getTopsortedLibs le = let

rel = getLibDepRel le

ls = reverse $ topsortedLibsWithImports rel

restLs = Set.toList $ Set.difference (Map.keysSet le) $ Rel.nodes rel

in ls ++ restLs

{- | Get imported libs in topological order, i.e. lib(s) without imports first.

The input lib-name will be last -}

dependentLibs :: LIB_NAME -> LibEnv -> [LIB_NAME]

dependentLibs ln le =

let rel = getLibDepRel le

ts = topsortedLibsWithImports rel

is = Set.toList (Rel.succs rel ln)

in reverse $ ln : intersect ts is

topsortedNodes :: DGraph -> [LNode DGNodeLab]

topsortedNodes dgraph = let dg = dgBody dgraph in

reverse $ postorderF $ dffWith (\ (_, n, nl, _) -> (n, nl)) (nodes dg)

$ efilter (\ (s, t, el) -> s /= t && isDefEdge (dgl_type el)) dg

-- * nodes with incoming hiding definition links

nodeHasHiding :: DGraph -> Node -> Bool

nodeHasHiding dg = labelHasHiding . labDG dg

{- | mark all nodes if they have incoming hiding edges.

Assume reference nodes to other libraries being properly marked already.

-}

markHiding :: LibEnv -> DGraph -> DGraph

markHiding le dgraph =

foldl (\ dg (n, lbl) -> let

ingoingEdges = innDG dg n

defEdges = filter (liftE isDefEdge) ingoingEdges

hidingDefEdges = filter (liftE isHidingDef ) defEdges

next = map (\ (s, _, _) -> s) defEdges

in fst $ labelNodeDG (n, lbl { labelHasHiding =

if isDGRef lbl

then nodeHasHiding (lookupDGraph (dgn_libname lbl) le)

$ dgn_node lbl

else not (null hidingDefEdges) || any (nodeHasHiding dg) next }) dg)

dgraph $ topsortedNodes dgraph

markAllHiding :: LibEnv -> LibEnv

markAllHiding libEnv =

foldl (\ le ln -> Map.adjust (markHiding le) ln le) libEnv

$ getTopsortedLibs libEnv