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arXiv · 2306.15375

Frex: dependently-typed algebraic simplification

Guillaume Allais·Edwin Brady·Nathan Corbyn·Ohad Kammar·Jeremy Yallop
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Abstract

We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library's dependently typed interface guarantees that both built-in and user-defined simplification modules are terminating, sound, and complete with respect to a well-specified class of equations. We have implemented the design in the Idris 2 and Agda dependently typed programming languages and shown that it supports modular extension to new theories, proof extraction and certification, goal extraction via reflection, and interactive development.

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Guillaume Allais, Edwin Brady, Nathan Corbyn, Ohad Kammar, Jeremy Yallop. 2023-06-27. Frex: dependently-typed algebraic simplification. https://doi.org/10.1145/3747506

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