--

-- Graph.hs -- Inductive Graphs (c) 2000 by Martin Erwig

--

-- The implementation is based on extensible finite maps.

-- For fixed size graphs, see StaticGraph.hs

--

-- Example Graphs: GraphData.hs

--

module Common.Lib.Graph (

-- types

Node,LNode,UNode, -- plain, labeled, and unit-labeled node

Edge,LEdge,UEdge, -- plain, labeled, and unit-labeled edge

Graph,UGraph, -- plain and unit-labeled graph

Adj,Context,MContext,Decomp,GDecomp, -- inductive graph view

Path,LPath,UPath, -- plain, labeled, and unit-labeled path

-- main functions

empty,embed,(&),match,matchP,matchAny,

emptyU,embedU,matchU,matchAnyU,

-- derived operations

isEmpty,matchSome,matchThe,context,contextP,

delNode,delNodes,delEdge,delEdges,

suc,pre,neighbors,out,inn,indeg,outdeg,deg,

suc',pre',neighbors',out',inn',indeg',outdeg',deg',node',lab',labNode',

noNodes,nodeRange,nodes,labNodes,edges,labEdges,

-- graph folds

-- ufold,gfold, --> see Basic.hs

-- graph transformations

-- undir, gmap, --> see Basic.hs

-- utilities to for (un)labeling

labUEdges,labUNodes,labUAdj,

unlabEdges,unlabNodes,unlabAdj,

-- utilities to build graphs

newNodes,insNode,insNodes,insEdge,insEdges,

mkGraph,mkUGraph,buildGr

) where

import Common.Lib.SimpleMap

import Data.Maybe (fromJust)

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

-- TYPES

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

-- basic types

--

type Node = Int

type LNode a = (Node,a)

type UNode = LNode ()

type Edge = (Node,Node)

type LEdge b = (Node,Node,b)

type UEdge = LEdge ()

data Graph a b = Graph (GraphRep a b)

type UGraph = Graph () ()

-- type NGraph a = Graph a ()

-- type EGraph b = Graph () b

type Path = [Node]

type LPath a = [LNode a]

type UPath = [UNode]

-- types supporting inductive graph view

--

type Adj b = [(b,Node)]

type Context a b = (Adj b,Node,a,Adj b) -- Context a b "=" Context' a b "+" Node

type MContext a b = Maybe (Context a b)

type Decomp a b = (MContext a b,Graph a b)

type GDecomp a b = (Context a b,Graph a b)

type UContext = ([Node],Node,[Node])

type UDecomp = (Maybe UContext,UGraph)

-- local

--

type Context' a b = (Adj b,a,Adj b)

type GraphRep a b = FiniteMap Node (Context' a b)

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

-- UTILITIES

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

-- pretty printing

--

showsGraph :: (Show a,Show b) => GraphRep a b -> ShowS

showsGraph Empty = id

showsGraph (Node l (v,(_,lab,suc)) r) = showsGraph l . ('\n':) .

shows v . (':':) . shows lab . ("->"++) . shows suc . showsGraph r

instance (Show a,Show b) => Show (Graph a b) where

showsPrec _ (Graph g) = showsGraph g

-- other

--

addSucc v l (pre,lab,suc) = (pre,lab,(l,v):suc)

addPred v l (pre,lab,suc) = ((l,v):pre,lab,suc)

clearSucc v l (pre,lab,suc) = (pre,lab,filter ((/=v).snd) suc)

clearPred v l (pre,lab,suc) = (filter ((/=v).snd) pre,lab,suc)

updAdj :: GraphRep a b -> Adj b -> (b -> Context' a b -> Context' a b) -> GraphRep a b

updAdj g [] f = g

updAdj g ((l,v):vs) f | elemFM g v = updAdj (updFM g v (f l)) vs f

| otherwise = error ("Edge Exception, Node: "++show v)

-- pairL x ys = map ((,) x) ys

-- pairR x ys = map (flip (,) x) ys

fst4 (x,_,_,_) = x

snd4 (_,x,_,_) = x

thd4 (_,_,x,_) = x

fth4 (_,_,_,x) = x

-- some (un)labeling functions

--

labUEdges = map (\(v,w)->(v,w,()))

labUNodes = map (\v->(v,()))

labUAdj = map (\v->((),v))

unlabEdges = map (\(v,w,_)->(v,w))

unlabNodes = map fst

unlabAdj = map snd

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

-- MAIN FUNCTIONS

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

-- constructing graphs

--

empty :: Graph a b

empty = Graph emptyFM

isEmpty :: Graph a b -> Bool

isEmpty (Graph g) = case g of {Empty -> True; _ -> False}

embed :: Context a b -> Graph a b -> Graph a b

embed (pre,v,l,suc) (Graph g) | elemFM g v = error ("Node Exception, Node: "++show v)

| otherwise = Graph g3

where g1 = addToFM g v (pre,l,suc)

g2 = updAdj g1 pre (addSucc v)

g3 = updAdj g2 suc (addPred v)

infixr &

c & g = embed c g

-- decomposing graphs

--

match :: Node -> Graph a b -> Decomp a b

match v (Graph g) =

case splitFM g v of

Nothing -> (Nothing,Graph g)

Just (g,(_,(pre,lab,suc))) -> (Just (pre',v,lab,suc),Graph g2)

where suc' = filter ((/=v).snd) suc

pre' = filter ((/=v).snd) pre

g1 = updAdj g suc' (clearPred v)

g2 = updAdj g1 pre' (clearSucc v)

-- the same for unlabeled graphs

--

emptyU :: UGraph

emptyU = empty

embedU :: UContext -> UGraph -> UGraph

embedU (p,v,s) = embed (labUAdj p,v,(),labUAdj s)

matchU :: Node -> UGraph -> UDecomp

matchU v g = case match v g of

(Nothing,g') -> (Nothing,g')

(Just (p,v,_,s),g') -> (Just (unlabAdj p,v,unlabAdj s),g')

matchAnyU :: UGraph -> (UContext,UGraph)

matchAnyU g = ((unlabAdj p,v,unlabAdj s),g') where ((p,v,_,s),g') = matchAny g

{-

-- Note that with

membed :: Decomp a b -> Graph a b

membed (Nothing,g) = g

membed (Just c, g) = embed c g

-- and

gid :: Node -> Graph a b -> Graph a b

gid v = membed . match v

-- we have that gid is an identity on graphs for any node v.

-}

-- derived/specialized decompositions

--

-- match matches a specified node (regards loops as successors)

-- matchP matches a specified node (regards loops as predecessors)

-- matchAny matches an arbitrary node

-- matchSome matches any node with a specified property

-- matchThe matches a node if it is uniquely characterized by the given property

--

matchP :: Node -> Graph a b -> Decomp a b

matchP v (Graph g) =

case splitFM g v of

Nothing -> (Nothing,Graph g)

Just (g,(_,(pre,lab,suc))) -> (Just (pre,v,lab,suc'),Graph g2)

where suc' = filter ((/=v).snd) suc

pre' = filter ((/=v).snd) pre

g1 = updAdj g suc' (clearPred v)

g2 = updAdj g1 pre' (clearSucc v)

matchAny :: Graph a b -> GDecomp a b

matchAny (Graph Empty) = error "Match Exception, Empty Graph"

matchAny g@(Graph (Node _ (v,_) _)) = (c,g') where (Just c,g') = match v g

matchSome :: (Graph a b -> Node -> Bool) -> Graph a b -> GDecomp a b

matchSome _ (Graph Empty) = error "Match Exception, Empty Graph"

matchSome p g = case filter (p g) (nodes g) of

[] -> error "Match Exception, no such node found"

(v:vs) -> (c,g') where (Just c,g') = match v g

matchThe :: (Graph a b -> Node -> Bool) -> Graph a b -> GDecomp a b

matchThe _ (Graph Empty) = error "Match Exception, Empty Graph"

matchThe p g = case filter (p g) (nodes g) of

[] -> error "Match Exception, no such node found"

[v] -> (c,g') where (Just c,g') = match v g

_ -> error "Match Exception, more than one node found"

-- decompositions ignoring remaining graph

--

context :: Node -> Graph a b -> Context a b

context v (Graph g) =

case lookupFM g v of

Nothing -> error ("Match Exception, Node: "++show v)

Just (pre,lab,suc) -> (filter ((/=v).snd) pre,v,lab,suc)

contextP :: Node -> Graph a b -> Context a b

contextP v (Graph g) =

case lookupFM g v of

Nothing -> error ("Match Exception, Node: "++show v)

Just (pre,lab,suc) -> (pre,v,lab,filter ((/=v).snd) suc)

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

-- TYPE CLASSES

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

-- newtype XNode a = X (LNode a)

-- type LNodes a = [LNode a]

--

-- class Label a l b where

-- label :: a -> l -> b

-- unlabel :: l -> a

--

-- instance Lab Node (LNode b) b where

-- label v l = (v,l)

-- unlabel (v,_) = v

--

-- instance Lab [Node] LNodes where

-- label vs l = zip vs (repeat l)

-- unlabel = map fst

--

-- instance Lab Edge LEdge where

-- label (v,w) l = (v,w,l)

-- unlabel (v,w,_) = (v,w)

--

-- instance Lab Node LNode where

-- label v l = (v,l)

-- unlabel (v,_) = v

-- class Insert a b c where

-- ins :: c -> Graph a b -> Graph a b

--

-- instance Insert () b Node where ins g v = insNode g (v,())

-- instance Insert a b (LNode a) where ins = insNode

-- instance Insert a b [LNode a] where ins = insNodes

-- instance Insert a b (LEdge b) where ins = insEdge

-- instance Insert a b [LEdge b] where ins = insEdges

-- decompositions ignoring contexts

--

delNode :: Node -> Graph a b -> Graph a b

delNode v = delNodes [v]

delNodes :: [Node] -> Graph a b -> Graph a b

delNodes [] g = g

delNodes (v:vs) g = delNodes vs (snd (match v g))

delEdge :: Edge -> Graph a b -> Graph a b

delEdge (v,w) g = case match v g of

(Nothing,_) -> g

(Just (p,v,l,s),g) -> embed (p,v,l,filter ((/=w).snd) s) g

delLEdge :: Eq b => LEdge b -> Graph a b -> Graph a b

delLEdge (v,w,lab) g = case match v g of

(Nothing,_) -> g

(Just (p,v,l,s),g) -> embed (p,v,l,filter ((/=(lab,w))) s) g

delEdges :: [Edge] -> Graph a b -> Graph a b

delEdges es g = foldr delEdge g es

-- projecting on context elements

--

context1 v g = fst4 (contextP v g)

context2 v g = snd4 (context v g)

context3 v g = thd4 (context v g)

context4 v g = fth4 (context v g)

-- informations derived from specific contexts

--

suc :: Graph a b -> Node -> [Node]

suc g v = map snd (context4 v g)

pre :: Graph a b -> Node -> [Node]

pre g v = map snd (context1 v g)

neighbors :: Graph a b -> Node -> [Node]

neighbors g v = (\(p,_,_,s) -> map snd (p++s)) (context v g)

out :: Graph a b -> Node -> [LEdge b]

out g v = map (\(l,w)->(v,w,l)) (context4 v g)

inn :: Graph a b -> Node -> [LEdge b]

inn g v = map (\(l,w)->(w,v,l)) (context1 v g)

outdeg :: Graph a b -> Node -> Int

outdeg g v = length (context4 v g)

indeg :: Graph a b -> Node -> Int

indeg g v = length (context1 v g)

deg :: Graph a b -> Node -> Int

deg g v = (\(p,_,_,s) -> length p+length s) (context v g)

-- above operations for already given contexts

--

suc' :: Context a b -> [Node]

suc' (_,_,_,s) = map snd s

pre' :: Context a b -> [Node]

pre' (p,_,_,_) = map snd p

neighbors' :: Context a b -> [Node]

neighbors' (p,_,_,s) = map snd p++map snd s

out' :: Context a b -> [LEdge b]

out' (_,v,_,s) = map (\(l,w)->(v,w,l)) s

inn' :: Context a b -> [LEdge b]

inn' (p,v,_,_) = map (\(l,w)->(w,v,l)) p

outdeg' :: Context a b -> Int

outdeg' (_,_,_,s) = length s

indeg' :: Context a b -> Int

indeg' (p,_,_,_) = length p

deg' :: Context a b -> Int

deg' (p,_,_,s) = length p+length s

node' :: Context a b -> Node

node' (_,v,_,_) = v

lab' :: Context a b -> a

lab' (_,_,l,_) = l

labNode' :: Context a b -> LNode a

labNode' (_,v,l,_) = (v,l)

-- gobal projections/selections

--

noNodes :: Graph a b -> Int

noNodes (Graph g) = sizeFM g

nodeRange :: Graph a b -> (Node,Node)

nodeRange (Graph Empty) = (0,-1)

nodeRange (Graph g) = (ix (minFM g),ix (maxFM g)) where ix = fst.fromJust

nodes :: Graph a b -> [Node]

nodes (Graph g) = (map fst (fmToList g))

labNodes :: Graph a b -> [LNode a]

labNodes (Graph g) = map (\(v,(_,l,_))->(v,l)) (fmToList g)

edges :: Graph a b -> [Edge]

edges (Graph g) = concatMap (\(v,(_,_,s))->map (\(_,w)->(v,w)) s) (fmToList g)

labEdges :: Graph a b -> [LEdge b]

labEdges (Graph g) = concatMap (\(v,(_,_,s))->map (\(l,w)->(v,w,l)) s) (fmToList g)

-- some utilities to build graphs

--

newNodes :: Int -> Graph a b -> [Node]

newNodes i g = [n..n+i] where n = 1+foldr max 0 (nodes g)

insNode :: LNode a -> Graph a b -> Graph a b

insNode (v,l) = embed ([],v,l,[])

insNodes :: [LNode a] -> Graph a b -> Graph a b

insNodes vs g = foldr insNode g vs

insEdge :: LEdge b -> Graph a b -> Graph a b

insEdge (v,w,l) g = embed (pre,v,lab,(l,w):suc) g'

where (Just (pre,_,lab,suc),g') = match v g

insEdges :: [LEdge b] -> Graph a b -> Graph a b

insEdges es g = foldr insEdge g es

mkGraph :: [LNode a] -> [LEdge b] -> Graph a b

mkGraph vs es = (insEdges es . insNodes vs) empty

mkUGraph :: [Node] -> [Edge] -> UGraph

mkUGraph vs es = mkGraph (labUNodes vs) (labUEdges es)

buildGr :: [Context a b] -> Graph a b

buildGr = foldr embed empty