Starting axiomatic semantics by defining the meaning of a Hoare triple. Read More...

As promised, I’ve written up the IMP operational and denotational semantics verification for the sequence operation. Attached are the PDF and LaTeX source. The LaTeX file uses the semantic package (semantic.sty) that can be found on any of the LaTeX module sites.

I will add the proof case for while that we’re doing in class sometime soon.

Why did we look at the fixed point of phi? Read More...

Trust me. Structural induction is your best friend. Read More...

Sorry folks - the flu and proofs really don’t mix at all. I should have shut down class about 10 minutes before I did.

Take a look at the proof that C[[while b do c]] == C[[if b then c;while b do c else skip]] in the text. It’s about 2 steps long and is trivial. Very sorry about that.

The key insight today is that by establishing Gamma(phi)=phi and that the fixed point exists, we can just use phi straight up as we have defined it. This should make sense because phi is Gamma(phi) and we can just substitute. However, if we don’t establish that the fixed point exists we can’t make that equivalence assertion.

Again, sorry about the lecture today. I should be back to normal on Wednesday.