-----------------------------------------------------------------------------
-- Some simple tests of the graph library.
-----------------------------------------------------------------------------

import Graph

-------------------------------------------------------------------------
-- ...and now some simple tests:

-- a simple graph:
graph1 = Graph [Node n1, Node n2, Node n3]
               [Edge n1 n2, Edge n3 n2, Edge n1 n3, Edge n3 n3]
   where n1,n2,n3 free

-- show this graph:
main1 = showGraph graph1

-- a simple graph with an exported node:
graph2 = (Graph [Node n1, Node n2, Node n3]
                [Edge n1 n2, Edge n3 n2, Edge n1 n3, Edge n3 n3], n1)
   where n1,n2,n3 free

-- connect two graphs with their exported nodes:
connectRootedGraphs (g1,r1) (g2,r2) = addEdge r1 r2 (joinGraphs g1 g2)

main2 = showGraph (connectRootedGraphs graph2 graph2)


-- a binary tree:
btree n = if n==0 then (n1, Graph [Node n1] [])
                  else joinRootedGraphs (btree (n-1)) (btree (n-1))
 where n1 free

main3 n = showGraph (snd (btree n))


-- a triangle structure:
triag n = if n==0
          then (n1,n2,n3, Graph [Node n1,Node n2,Node n3]
                                [Edge n1 n2, Edge n2 n3, Edge n1 n3])
                  else joinTriags (triag (n-1)) (triag (n-1)) (triag (n-1))
 where n1,n2,n3 free

main4 n = let (_,_,_,g) = triag n in showGraph g


k_4 = Graph [Node n1, Node n2, Node n3, Node n4]
            [Edge n1 n2, Edge n1 n3, Edge n1 n4,
             Edge n2 n3, Edge n2 n4, Edge n3 n4]
   where n1,n2,n3,n4 free

k_5 = Graph [Node n1, Node n2, Node n3, Node n4, Node n5]
            [Edge n1 n2, Edge n1 n3, Edge n1 n4, Edge n1 n5,
             Edge n2 n3, Edge n2 n4, Edge n2 n5,
             Edge n3 n4, Edge n3 n5, Edge n4 n5]
   where n1,n2,n3,n4,n5 free

-- some auxiliary functions for graph construction:
joinRootedGraphs (r1,g1) (r2,g2) =
  (r, addEdge r r1 (addEdge r r2 (addNode r (joinGraphs g1 g2))))
 where r free

joinTriags (r1a,r1b,r1c,g1) (r2a,r2b,r2c,g2) (r3a,r3b,r3c,g3) =
  (r1a,r2b,r3c,addEdge r1b r2a
                (addEdge r1c r3a
                  (addEdge r2c r3b
                    (joinGraphs g1 (joinGraphs g2 g3)))))