CS 641 Lecture -*- Outline -*-

* Duality (11.5)

  This characterizes the way the other team views a predicate
  transformer.  For example, the dual of an assertion is an
  assumption.

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     DUAL OF A PREDICATE TRANSFORMER

Definition
  S^{o}.q == !S.(!q)   (dual pred. trans.)

Theorem 11.4.  The following dualities
hold between predicate transformers:

   <f>^{o} == <f>

   {p}^{o} == [p]

   {R}^{o} == [R]

   (S1;S2)^{o} == S1^{o};S2^{o}

   (\join i \in i :: S.i)^{o}
     == (\meet i \in i :: S.i^{o})
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        Q: What is the dual of the dual of a predicate transformer?

        Q: What is [p]^{o}?  [R]^{o}?  magic^{o}?  abort^{o}?  skip^{o}?