CS 641 meeting -*- Outline -*-

* repetition (2.8)
	treat while loop as sugar for a recursion
	example of extending core language semantics to bigger language

------------------------
  THE REPETITION

A loop

	L = while b do c od

is translated into:

	proc L()
	  (?~b [] ?b; c; L)
------------------------
	If we had higher order procedures we'd only need one loop proc,
	but as it is, we need one for each loop

	Thm: Let p be a predicate and vf \in X -> Integers a state function
	such that:
	(all m \in Integers :: {p /\ b /\ vf <= m} c {p /\ vf < m /\ m >= 0})
	Then
		{p} L {p /\ ~b}

	Remark, see Hesselink for a variant rule more like Cohen's.
		The given rule works for nontotal commands,
		and has a simple annotation.

	Pf: (use the recursion theorem).

	Q: so what would the annotation rule look like?

	Thm 30 is partial correctness and necessity for loops.

	Thm: The repitition L is total if and only if (!b;c) is total.
	(Proof is a calculation showing that wp.L.false equiv false
		by mutual implication.)