15-815 Automated Theorem Proving
Lecture 4: Proof Terms

The theorem provers we implement in this class will be certifying, that is, they will not just assert the truth of a proposition but deliver a proof for it. This means we need a compact notation for proofs that can serve as certificates. In this lecture we introduce such a notation in the form of proof terms, developed from the Curry-Howard isomorphism that relates constructive proofs to functional programs.

We then prove soundness of the sequent calculus by assigning proof terms to every deduction, which turns out to be rather straightforward.

We also discuss the counterpart to local completeness for natural deduction on the sequent calculus. We then apply this insight in order to write out the first decision procedure for propositional intuitionistic logic which is due to Dyckhoff [D92]. Its analysis was later refined by Dyckhoff and Negri [DN00].

[ Home | Schedule | Assignments | Handouts | Software | Resources ]

Frank Pfenning