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Computer Science > Programming Languages

arXiv:2306.15375 (cs)
[Submitted on 27 Jun 2023]

Title:Frex: dependently-typed algebraic simplification

Authors:Guillaume Allais, Edwin Brady, Nathan Corbyn, Ohad Kammar, Jeremy Yallop
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Abstract:We present an extensible, mathematically-structured algebraic simplification library design. We structure the library using universal algebraic concepts: a free algebra -- fral -- and a free extension -- frex -- of an algebra by a set of variables. The library's dependently-typed API guarantees simplification modules, even user-defined ones, are terminating, sound, and complete with respect to a well-specified class of equations. Completeness offers intangible benefits in practice -- our main contribution is the novel design. Cleanly separating between the interface and implementation of simplification modules provides two new modularity axes. First, simplification modules share thousands of lines of infrastructure code dealing with term-representation, pretty-printing, certification, and macros/reflection. Second, new simplification modules can reuse existing ones. We demonstrate this design by developing simplification modules for monoid varieties: ordinary, commutative, and involutive. We implemented this design in the new Idris2 dependently-typed programming language, and in Agda.
Subjects: Programming Languages (cs.PL); Logic in Computer Science (cs.LO); Symbolic Computation (cs.SC)
Cite as: arXiv:2306.15375 [cs.PL]
  (or arXiv:2306.15375v1 [cs.PL] for this version)
  https://doi.org/10.48550/arXiv.2306.15375

Submission history

From: Jeremy Yallop [view email]
[v1] Tue, 27 Jun 2023 10:47:22 UTC (547 KB)
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