GraphSetSucc

 module GraphSetSucc

A graph is represented by a pair (vertices, successor)

• vertices : this constant is the set of graph vertices
• successor : this function gives for each vertex the set of vertices directly joinable from it

  use export set.Fset

  type vertex

  constant vertices: set vertex

  function successors vertex : set vertex

  axiom successors_vertices:
    forall x. mem x vertices -> subset (successors x) vertices

  predicate edge (x y: vertex) = mem x vertices /\ mem y (successors x)

  clone export graph.Path with type vertex = vertex, predicate edge = edge

end

GraphListSucc

 module GraphListSucc

A graph is represented by a pair (vertices, successor)

• vertices : this constant is the set of graph vertices
• successor : this function gives for each vertex the list of vertices directly joinable from it

  use import list.List
  use import list.Mem as L
  use import list.Elements as E
  use export set.Fset

  type vertex

  constant vertices: set vertex

  function successors vertex : list vertex

  axiom successors_vertices:
    forall x. mem x vertices -> subset (elements (successors x)) vertices

  predicate edge (x y: vertex) = mem x vertices /\ L.mem y (successors x)

  clone export graph.Path with type vertex = vertex, predicate edge = edge

end

GraphListArraySucc

 module GraphListArraySucc

A graph is represented by a pair (vertices, successor)

• vertices : this constant is the set of integers representing the graph vertices
• successor : this function gives for each vertex the list of vertices directly joinable from it

  use import int.Int
  use import list.List
  use import list.Mem as L
  use import list.Elements as E
  use export set.Fset

  type vertex = int

  constant vertices: set vertex
  axiom vertices_number:
    forall x. mem x vertices <->  0 <= x < cardinal vertices

  function successors vertex : list vertex

  axiom successors_vertices:
    forall x. mem x vertices -> subset (elements (successors x)) vertices

  predicate edge (x y: vertex) = mem x vertices /\ L.mem y (successors x)

  clone export graph.Path with type vertex = vertex, predicate edge = edge

end