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.

• Reading: ??-??.pdf
• Code: verif.elf, code directory
• Key concepts:
  • Verifications and uses
  • Sequent calculus in LF
  • Extracting verifications from sequent deduction
• Previous lecture: Certifying Theorem Proving
• Next lecture: ??

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Frank Pfenning