15-399 Constructive Logic
Lecture 6: Subject Reduction

After reviewing proof terms and introducing their concrete syntax needed for the proof checker, we study properties of proof terms. We recall the substitution property of hypothetical judgments and extend it to encompass proof terms. The then prove subject reduction

If M : A and M ==> M' then M' : A.

The proof technique is proof by cases. We then generalize to allow reduction at an arbitrary subterm position. Then the proof requires structural induction, one of the main proof techniques in this domain.

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Frank Pfenning