Generating Bijections between HOAS and the Natural Numbers

Abstract

A provably correct bijection between higher-order abstract syntax (HOAS) and the natural numbers enables one to define a “not equals” relationship between ter ms and also to have an adequate encoding of sets of terms, and maps from one term family to another. Sets and maps are useful in many situations and are preferably provided in a library of some sort. I have released a map and set library for use with Twelf which can be used with any type for which a bijection to the natural numbers exists. Since creating such bijections is tedious and error-prone, I have created a “bijection generator” that generates such bijections automatically together wit h proofs of correctness, all in the context of Twelf.