In previous work ("From signatures to monads in UniMath"),we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant.
In the present work, we describe what was necessary to generalize that work to account for simply-typed languages. First, some definitions had to be generalized to account for the natural appearance of non-endofunctors in the simply-typed case. As it turns out, in many cases our mechanized results carried over to the generalized definitions without any code change. Second, an existing mechanized library on 𝜔-cocontinuous functors had to be extended by constructions and theorems necessary for constructing multi-sorted syntax. Third, the theoretical framework for the semantical signatures had to be generalized from a monoidal to a bicategorical setting, again to account for non-endofunctors arising in the typed case. This uses actions of endofunctors on functors with given source, and the corresponding notion of strong functors between actions, all formalized in UniMath using a recently developed library of bicategory theory. We explain what needed to be done to plug all of these ingredients together, modularly.
The main result of our work is a general construction that, when fed with a signature for a simply-typed language, returns an implementation of that language together with suitable boilerplate code, in particular, a certified monadic substitution operation.
|Title of host publication||CPP '22|
|Subtitle of host publication||Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs|
|Editors||Andrei Popescu, Steve Zdancewic|
|Publisher||Association for Computing Machinery (ACM)|
|Number of pages||17|
|Publication status||Published - 17 Jan 2022|
|Event||CPP '22: 11th ACM SIGPLAN International Conference on Certified Programs and Proofs - Philadelphia , United States|
Duration: 17 Jan 2022 → 18 Jan 2022
|Period||17/01/22 → 18/01/22|
- computer-checked proof
- typed abstract syntax
ASJC Scopus subject areas
- Computer Science Applications