Ayari, Abdelwaheb

A Reinterpretation of the Deductive Tableaux System in Higher-Order Logic

Our research investigates frameworks supporting the formalization of
programming calculi and their application to deduction-based progr am
synthesis. Here we report on a case study: within a conservative
extension of higher-order logic implemented in the Isabelle system, we
derived rules for program development which can simulate those of the
deductive tableau proposed by Manna and Waldinger. We have used the
resulting theory to synthesize a library of verified programs, focusing
in particular on sorting algorithms. Our experience suggests
that the methodology we propose is well suited both to implement and
use programming calculi, extend them, partially automate them, and
even formally reason about their correctness.