15-851 Computation and Deduction
Lecture 6: Higher-Level Judgments
In this lecture we examine how to represent proofs of meta-theorems in
the logical framework. The basic difficulty is that mathematical proofs
are typically not themselves mathematical objects. In order to solve
this difficulty we introduce judgments relating derivations, so-called
higher-level judgments. We show how higher-level judgments can be used
to capture some of the intuitive contents of proofs and illustrate
the techniques with the proof of value soundness for Mini-ML.
Higher-level judgments require another (and final) generalization
of the type theory underlying the logical framework to also allow
dependent kinds.
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Frank Pfenning
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