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-- updated Mon Jul  3 12:32:35 PDT 2017

-----------------------------------------------------------------------------
-- A representation of "compositional" graphs
-----------------------------------------------------------------------------

module Graph(Graph(..),Node(..),Edge(..),NodeId,
             joinGraphs,addNode,addEdge,isFinalizedGraph,showGraph) where

-- A graph is a list of nodes and edges:
data Graph = Graph [Node] [Edge]

-- A node identifier is basically a natural number.
-- However, this data type is abstract so that the user cannot
-- explicitly construct node identifiers.
data NodeId = NodeId Int

-- A node is identified by a node identifier but more node infos
-- could be added:
data Node = Node NodeId

-- An edge consists of a source and a target node which are
-- identified by their node identifiers:
data Edge = Edge NodeId NodeId

-- Combine two graphs.
joinGraphs (Graph ns1 es1) (Graph ns2 es2) = Graph (ns1++ns2) (es1++es2)

-- Add a node two a graph.
addNode n (Graph ns es) = Graph (Node n : ns) es

-- Add a new edge between two nodes of a graph.
addEdge n1 n2 (Graph ns es) = Graph ns (Edge n1 n2 : es)

-- A graph is finalized for further processing if all nodes
-- have uniquely assigned node identifiers:
isFinalizedGraph :: Graph -> Bool
isFinalizedGraph (Graph nodes _) = numberNodes 1 nodes
  where
     numberNodes _ [] = True
     numberNodes n (Node ni : ns)
         | ni == NodeId n  -- assign unique identifier
         = numberNodes (n+1) ns

-- As an example, we convert this representation into the daVinci
-- representation by grouping edges to their source node
-- and displaying the graph:
showGraph :: Graph -> IO ()
showGraph graph@(Graph nodes edges)
   | isFinalizedGraph graph
   = do putStrLn "Graph"
        putStrLn ("  Nodes " ++ shownodes)
        putStrLn ("  Edges " ++ showedges)	
  where shownodes = show [id | Node (NodeId id) <- nodes]
        showedges = show [(id1,id2) | Edge (NodeId id1) (NodeId id2) <-edges]


-- end of Graph library