15-317 Constructive Logic
Lecture 19: Verifications and Sequent Calculus
The proof annotations for the contraction-free sequent calculus
tend to become rather large and unwieldy. In part this is because
the deductions have detours. Verifications, on the other hand,
are composed entirely of subformulas. Can we extract verifications
instead of just arbitrary proofs?
We investigate this question by giving a representation of
verifications in LF and then return to the old analogy between
verifications and sequent calculus deductions. This requires
a notation for sequent calculus in LF, which takes advantage of
its intrinsic expressive power in rather unexpected ways.