class
	GRAPH [V -> attached ANY]

General
	cluster: mathmodels
	description: 
		"Mathematical model for a Directed Graph = (vertices, edges)
		where vertices is a set of vertices in generic parameter V, 
		and edges is a relation in vertices:
		vertices: SET [V]
		edges: REL [V, V]
		Has immutable queries and commands 
		to add and remove vertices and edges. 
		Also derived queries for outgoing and incoming edges:
		outgoing (v: V): REL[V, V]
		incoming (v: V): REL[V, V]
		adjacent (v: V): SEQ [V]
		adjacent is a sequence of vertices that may be
		ordered in descendants such as COMPARABLE_GRAPH[G].
		Derived queries such as: 
		reachable (src: V): SEQ[V]
		shortest_path(v1, v2: V): detachable SEQ[V]
		is_a_shortest_path (v1, v2: V; seq: SEQ[V]): BOOLEAN
		cycle (v: V): detachable SEQ[V]
		is_acyclic: BOOLEAN
		topologically_sorted: SEQ[V]
		is_topologically_sorted (seq: SEQ[V]): BOOLEAN
		where reachable uses breadth-first search starting with vertex src,
		to return the set of all nodes reachable from src.
		shortest_path returns the shortest path between v1 and v2 if it exists."
	create: make_empty, make_from_tuple_array

Ancestors
	DEBUG_OUTPUT*
	ITERABLE* [G]

Queries
	adjacent (v: V): SEQ [V]
	array_compare (a, b: ARRAY [TUPLE [V, V]]): BOOLEAN
	as_array: ARRAY [TUPLE [V, V]]
	cycle (v: V): detachable SEQ [V]
	debug_output: STRING_8
	edge_count: INTEGER_32
	edge_extended alias "|\/|" (e: PAIR [V, V]): [like Current] GRAPH [V]
	edge_removed alias "|\" (e: PAIR [V, V]): [like Current] GRAPH [V]
	edges: REL [V, V]
	has_edge (p: PAIR [V, V]): BOOLEAN
	has_vertex (v: V): BOOLEAN
	in_degree_count (v: V): INTEGER_32
	incoming (v: V): REL [V, V]
	Infinity: INTEGER_64
	is_a_shortest_path (v1, v2: V; seq: SEQ [V]): BOOLEAN
	is_acyclic: BOOLEAN
	is_empty: BOOLEAN
	is_equal (other: [like Current] GRAPH [V]): BOOLEAN
	is_reachable (v1, v2: V): BOOLEAN
	is_subgraph alias "|<:" (other: [like Current] GRAPH [V]): BOOLEAN
	is_topologically_sorted (seq: [like topologically_sorted] SEQ [V]): BOOLEAN
	is_valid_path (seq: SEQ [V]): BOOLEAN
	new_cursor: ITERATION_CURSOR [V]
	out: STRING_8
	out_degree_count (v: V): INTEGER_32
	outgoing (v: V): REL [V, V]
	paths (v1, v2: V): SET [SEQ [V]]
	reachable (src: V): SEQ [V]
	shortest_path (v1, v2: V): detachable SEQ [V]
	shortest_path_via_dijkstra (v1, v2: V): detachable SEQ [V]
	topologically_sorted: SEQ [V]
	vertex_count: INTEGER_32
	vertex_extended alias "+" (v: V): [like Current] GRAPH [V]
	vertex_removed alias "-" (v: V): [like Current] GRAPH [V]
	vertices: SET [V]
	vertices_edge_count: INTEGER_32
	vertices_incoming_edge_count: INTEGER_32
	vertices_outgoing_edge_count: INTEGER_32
	Zero: INTEGER_64

Commands
	edge_extend (e: PAIR [V, V])
	edge_remove (e: PAIR [V, V])
	vertex_extend (v: V)
	vertex_remove (v: V)

Constraints
	empty consistency
	valid edge ends
	valid edge ends
	consistency incoming outgoing
	consistency incoming outgoing2
	count property symmetry 1
	count property symmetry 2
	self loops are incomng and outgoing

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