Today in class we defined what is called a Hoare triple, {A}c{B}, where A is a precondition, B is a postcondition and c is a command from IMP. Intuitively, the meaning of the Hoare triple is if A is true in sigma before c is evaluated, then B will be true in sigma’ after c is evaluated. We have that a formal definition using the concept of models or satisfies using the new semantic turnstyle. We started to give the assertion language used to write A and B a semantics towards the end of class. We were providing a semantics that was simply an extension of the semantics for a and b from IMP with the addition of integer variables. We don’t really know what those are quite yet, but we will shortly. We also defined the concept of an interpretation, denoted I, that is in effect a mapping from integer variables to values.

What’s going on here will be much clearer after Monday’s lecture, but Winskel’s description of this is excellent if you want to read it. I’m guessing that will happen after the project, which of course is perfectly fine.