FunctionalGraphOld.hs

module FunctionalGraphOld
       (
         Graph(..)
         , addNode
       ) where

data Node nodeLabelType = Node {
       nodeNum :: Int
       , nodeLabel :: nodeLabelType
       } deriving (Show, Eq)
         
-- Node tests 
n1 = Node 0 1.0
t1 = nodeNum n1 == 0
t2 = nodeLabel n1 == 1.0


-- We have parents and children nodes, since we are dealing with
-- digraphs and we want to create an inductive library

type Parents nodeLabelType edgeLabelType = [Parent nodeLabelType edgeLabelType]

data Parent nodeLabelType edgeLabelType = Parent {
  parentNode :: Node nodeLabelType
  , parentEdgeLabel :: edgeLabelType
    } deriving (Show, Eq)
               
p1 = Parent n1 4.0               
t3 = parentNode p1 == n1
t4 = parentEdgeLabel p1 == 4.0


type Children nodeLabelType edgeLabelType = [Child nodeLabelType edgeLabelType]
data Child nodeLabelType edgeLabelType = Child {
  childNode :: Node nodeLabelType
  , childEdgeLabel :: edgeLabelType
    } deriving (Show, Eq)
               
c1 = Child n1 5.0
t5 = childNode c1 == n1
t6 = childEdgeLabel c1 == 5.0



data Graph nodeLabelType edgeLabelType = 
  Empty
  | GraphAnd {
    graphContext :: Context nodeLabelType edgeLabelType
    , graphSubgraph :: Graph nodeLabelType edgeLabelType
      } deriving (Eq, Show)

data Context nodeLabelType edgeLabelType = Context {
  contextParents :: Parents nodeLabelType edgeLabelType
  , contextNode :: Node nodeLabelType
  , contextChildren :: Children nodeLabelType edgeLabelType
    } deriving (Eq, Show)
                                           
gEmpty = Empty :: Graph Double Double

-- represent the graph n1 with two self-loops

g1 = GraphAnd (Context [p1] n1 [c1]) gEmpty
  

-- we now have to define graph construction functions
-- addNode and addEdge which add a node and an edge respectively

-- the order of the arguments is important here because a graph
-- implicitly contains the type of its edges, and the addNode
-- operation needs to add in a context which means that we need to
-- know the type of the edges connected a node from its parents and to
-- its children, that type is associated with the graph edge label
-- types, hence the graph must be the first argument of the addNode
-- because the typing needs to be clear

addNode :: (Eq nodeLabelType) => (Eq edgeLabelType) =>
  Graph nodeLabelType edgeLabelType
  -> Node nodeLabelType
  -> Graph nodeLabelType edgeLabelType
addNode g n = GraphAnd (Context [] n []) g

g2 = GraphAnd (Context [] n1 []) gEmpty
t7 = addNode gEmpty n1 == g2

t = t1 && t2 && t3 && t4 && t5 && t6 && t7

-- data Graph a b

-- data Graph a b = Empty 
--                | GraphAnd (Context a b) graph
                 
-- data Context a b = Edges