15-851 Computation and Deduction
Lecture 4: Higher-Order Abstract Syntax

In this course, we will implement the expressions, the judgments, and the proofs of meta-theorems in a logical framework called LF. In this lecture we take the first step, showing how to represent expressions as objects in LF. A critical decision is how to represent variables. In the technique of higher-order abstract syntax, variables of the object language (Mini-ML) are represented by variables in the meta-language (LF). This has far-reaching consequences. In particular, renaming of a bound variable in the object language is modelled immediately by renaming of the corresponding bound variable in the meta-language, thereby greatly simplifying our next two steps: representation of judgments and representation of meta-theoretic proofs.

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Frank Pfenning