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].