15-317 Constructive Logic
Lecture 5: Subject Reduction

In this lecture we follow through on the promise to study the structure of proofs with syntactic means, exploiting the notion of proof term. We rewrite local reductions as operations on proof terms and then verify that they preserve types, and similarly for local expansion. This is the first significant example of a metalogical property that we establish rigorously for the logical systems we construct.

• Reading: 05-subred.pdf
• Previous lecture: Proofs as Programs
• Next lecture: Quantification
• Key concepts:
  • Proof term reductions
  • Inversion
  • Local notation for hypotheses
  • Weakening
  • Substitution principle on proof terms

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Frank Pfenning