Abstract
Matching logic (ML) is a formalism for specifying and reasoning about mathematical structures by means of patterns and pattern matching. Previously, it has been used to capture a number of other logics, e.g., separation logic with recursive definitions and linear temporal logic. ML has also been formalized in the Coq Proof Assistant, and the soundness of its Hilbert-style proof system has been mechanized.
However, using a Hilbert-style system for interactive reasoning is challenging—even more so in ML, which lacks a general deduction theorem. Therefore, we propose a single-conclusion sequent calculus for ML that is more amenable to interactive proving. Based on this sequent calculus, we implement a proof mode for interactive reasoning in ML, which significantly simplifies the construction of ML proofs in Coq. The proof mode is a mechanism for displaying intermediate proof states and an extensible set of proof tactics that implement the rules of the sequent calculus. We evaluate our proof mode on a collection of examples, showing a substantial improvement in proof script size and readability.
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Notes
- 1.
This is done without modifications to Coq. In particular, MLPM is not a Coq plugin.
- 2.
We expand on the preliminary implementation reported in [4].
- 3.
[1,
:
,
,
,
]. - 4.
We plan to extend \(\vdash _{\mathcal {S}}\) with fixpoint and frame reasoning capabilities in the future.
- 5.
The application context of the framing rules are decomposed into two separate rules in [4].
- 6.
- 7.
In the implementation we allow only (co-)finite sets of variables for the components of a constraint.
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We warmly thank Runtime Verification Inc. for their generous funding support.
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Tušil, J., Bereczky, P., Horpácsi, D. (2023). Interactive Matching Logic Proofs in Coq. In: Ábrahám, E., Dubslaff, C., Tarifa, S.L.T. (eds) Theoretical Aspects of Computing – ICTAC 2023. ICTAC 2023. Lecture Notes in Computer Science, vol 14446. Springer, Cham. https://doi.org/10.1007/978-3-031-47963-2_10
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