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- Ahrens, Benedikt, et al.
(författare)
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Implementing a category-theoretic framework for typed abstract syntax
- 2022
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Ingår i: CPP '22. - New York : Association for Computing Machinery (ACM). - 9781450391825 ; , s. 307-323
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Konferensbidrag (refereegranskat)abstract
- 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 ?-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.
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