CS 641 Lecture -*- Outline -*-

* Relational Updates (11.4)

  Q: Intuitively, what is does an angelic update, {R}, based on relation R do?
  Q: What does a demonic update, [R], based on relation R do?

     See also figure 11.1

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           RELATIONAL UPDATES

Definitions:
 {R}.q.s == (\exists g :: R.s.g /\ q.g)
 [R].q.s == (\forall g :: R.s.g ==> q.g)

Sugars
  wp.{R} == {R}
  wp.[R] == [R]

Special cases:
  choose == {True}     (arbitrary choice)
   chaos == [True]       (chaotic choice)
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        Q: How does that match intiution?

        Q: How would you describe these in terms of set notation?

        Q: What is {False}? [False]? 

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        RELATIONAL ASSIGNMENTS

Demonic:
   [x := x' | b]

Angelic:
   {x := x' | b}

Theorem 11.3.  Assume that x is a list of
program variables and b is Boolean
expression, and q is a Boolean expression
in which x' does not occur free.  Then

(a) var x |- {x := x' | b}.q
       == (\exists x' :: b /\ q[x := x'])

(b) var x |- [x := x' | b].q
       == (\forall x' :: b ==> q[x := x'])
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        Q: What is [x := x' | x' > x + y].(x > y)?
        Q: What is [x := x' | x' > x + y].q?
        Q: What is [x := x' | x * x <= x' /\ x' < (x+1)*(x+1)].(x == 2)?