CS 641 meeting -*- Outline -*-

* the semantic homomorphisms (4.8)

	We'd like to know that wp.c and wlp.c are homomorphisms.
	To do this we show that any language extentsion is a hom.

	Recall that MP is set of positively conjunctive predicate transformers

	Thm: if v \in A -> MP, then v(.) \in A(.) -> MP is a homomorphism.

	Q: What does it mean for w \in A(.) -> MP to be a hom?
		(all q,r \in A(.) :: w.(q;r) = w.q o w.r)
		(all C : {} \neq C \subseteq A(.) : w.([] c \in C :: c)
						    = (inf c \in C :: w.c))

	Q: Can you prove this?
		straightforward calculation.

	Corollary: (a) for every v \in (H -> MU),
			function v^1 is a hom in (A(.) -> MU).
		      So wlp is a hom in (A(.) -> MU).
		(b) for every v \in WT, function v^0 is a hom in A(.) -> MP.
		      So wp is a hom in (A(.) -> MP).