+
+ redef fun clone do return sub(self)
+
+ # Return an induced sub-poset
+ #
+ # The elements of the result are those given in argument.
+ #
+ # ~~~
+ # var pos = new POSet[String]
+ # pos.add_chain(["A", "B", "C", "D", "E"])
+ # pos.add_chain(["A", "X", "C", "Y", "E"])
+ #
+ # var pos2 = pos.sub(["A", "B", "D", "Y", "E"])
+ # assert pos2.has_exactly(["A", "B", "D", "Y", "E"])
+ # ~~~
+ #
+ # The full relationship is preserved between the provided elements.
+ #
+ # ~~~
+ # for e1 in pos2 do for e2 in pos2 do
+ # assert pos2.has_edge(e1, e2) == pos.has_edge(e1, e2)
+ # end
+ # ~~~
+ #
+ # Not that by definition, the direct relationship is the transitive
+ # reduction of the full reduction. Thus, the direct relationship of the
+ # sub-poset may not be included in the direct relationship of self because an
+ # indirect edge becomes a direct one if all the intermediates elements
+ # are absent in the sub-poset.
+ #
+ # ~~~
+ # assert pos.has_direct_edge("B", "D") == false
+ # assert pos2.has_direct_edge("B", "D") == true
+ #
+ # assert pos2["B"].direct_greaters.has_exactly(["D", "Y"])
+ # ~~~
+ #
+ # If the `elements` contains all then the result is a clone of self.
+ #
+ # ~~~
+ # var pos3 = pos.sub(pos)
+ # assert pos3 == pos
+ # assert pos3 == pos.clone
+ # ~~~
+ fun sub(elements: Collection[E]): POSet[E]
+ do
+ var res = new POSet[E]
+ for e in self do
+ if not elements.has(e) then continue
+ res.add_node(e)
+ end
+ for e in res do
+ for f in self[e].greaters do
+ if not elements.has(f) then continue
+ res.add_edge(e, f)
+ end
+ end
+ return res
+ end
+
+ # Two posets are equal if they contain the same elements and edges.
+ #
+ # ~~~
+ # var pos1 = new POSet[String]
+ # pos1.add_chain(["A", "B", "C", "D", "E"])
+ # pos1.add_chain(["A", "X", "C", "Y", "E"])
+ #
+ # var pos2 = new POSet[Object]
+ # pos2.add_edge("Y", "E")
+ # pos2.add_chain(["A", "X", "C", "D", "E"])
+ # pos2.add_chain(["A", "B", "C", "Y"])
+ #
+ # assert pos1 == pos2
+ #
+ # pos1.add_edge("D", "Y")
+ # assert pos1 != pos2
+ #
+ # pos2.add_edge("D", "Y")
+ # assert pos1 == pos2
+ #
+ # pos1.add_node("Z")
+ # assert pos1 != pos2
+ # ~~~
+ redef fun ==(other) do
+ if not other isa POSet[nullable Object] then return false
+ if not self.elements.keys.has_exactly(other.elements.keys) then return false
+ for e, ee in elements do
+ if ee.direct_greaters != other[e].direct_greaters then return false
+ end
+ assert hash == other.hash
+ return true
+ end
+
+ redef fun hash
+ do
+ var res = 0
+ for e, ee in elements do
+ if e == null then continue
+ res += e.hash
+ res += ee.direct_greaters.length
+ end
+ return res
+ end