COMP 426 Automated Reasoning
Lecture 22: Higher-order abstract syntax

So far we have shown how hereditary harrop formulas can be used to encode the propositional fragment of the natural deduction calculus. In this lecture, we discuss a final extension to allow the simple and elegant representation of the natural deduction rules for universal quantifers and existential quantifiers.

For this purpose, we will extend our term language to allow for lambda-functions. The crucial idea will be to represent bound variables in our object language (first-order logic) as bound variables in the meta-language. This powerful idea goes back to Church, and is the basis for higher-order abstract syntax. We will show several examples which employ higher-order abstract syntax, and we will give a brief demo of Twelf.

• Reading: in preparation
• Code: in preparation
• Previous lecture: Week 11

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bp@cs.mcgill.ca
Brigitte Pientka