CS 641 Lecture -*- Outline -*-

* Basic Predicate Transformers (Chapter 11.3)

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       PREDICATE TRANSFORMER SUGARS

<f>.q == f^{-1}.q      (functional update)
{g}.q == g \intersect q        (assertion)
[g].q == !g \union q          (assumption)

So...
 abort == {false}
 skip  == <id> == {true} == [true]
 magic == [false]
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        Q: With this notation, what is wp.<f>?  wp.skip?
           just <f>, skip

        Q: Why is abort called that?  What is the intuition behind "magic"?

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      ASSIGNMENT STATEMENTS

The most useful functional update

   <x := e>.q.s
 == { definition }
   q((x := e).s)
 == { substitution theorem }
   q[x := e].s

Thm 11.2:
Let x be an (list of) attribute(s),
let e be an (list of) expression(s),
and let q be a Boolean expression.  Then

  var x |- <x := e>.q == q[x := e]

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        Q: Can you simplify (<x := x*x>;<x := x*x>).(x > y) ?