Tactics and Certificates in Meta Dedukti

Cauderlier, Raphaël

doi:10.1007/978-3-319-94821-8_9

Cited by 2 publications

(2 citation statements)

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“…In Mtac2, we can write this as split &> [m: tacP | tacQ] &> tacB. In the system presented by [Cauderlier 2018], however, this is written roughly as split (tacP; tacB) (tacQ; tacB) (where we use ; to signify the bind operation). Note that the tacB tactic has to be repeated in both continuations since there is no way to merge the proof script after splitting.…”

Section: :28mentioning

confidence: 99%

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Mtac2: typed tactics for backward reasoning in Coq

Kaiser

Ziliani

Krebbers

et al. 2018

Proc. ACM Program. Lang.

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Coq supports a range of built-in tactics, which are engineered primarily to support backward reasoning. Starting from a desired goal, the Coq programmer can use these tactics to manipulate the proof state interactively, applying axioms or lemmas to break the goal into subgoals until all subgoals have been solved. Additionally, it provides support for tactic programming via OCaml and Ltac, so that users can roll their own custom proof automation routines. Unfortunately, though, these tactic languages share a significant weakness. They do not offer the tactic programmer any static guarantees about the soundness of their custom tactics, making large tactic developments difficult to maintain. To address this limitation, Ziliani et al. previously proposed Mtac, a new typed approach to custom proof automation in Coq which provides the static guarantees that OCaml and Ltac are missing. However, despite its name, Mtac is really more of a metaprogramming language than it is a full-blown tactic language: it misses an essential feature of tactic programming, namely the ability to directly manipulate Coq's proof state and perform backward reasoning on it. In this paper, we present Mtac2, a next-generation version of Mtac that combines its support for typed metaprogramming with additional support for the programming of backward-reasoning tactics in the style of Ltac. In so doing, Mtac2 introduces a novel feature in tactic programming languagesÐwhat we call typed backward reasoning. With this feature, Mtac2 is capable of statically ruling out several classes of errors that would otherwise remain undetected at tactic definition time. We demonstrate the utility of Mtac2's typed tactics by porting several tactics from a large Coq development, the Iris Proof Mode, from Ltac to Mtac2.

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Section: :28mentioning

confidence: 99%

“…When compared to Mtac, the expressiveness of Cauderlier [2018] is somewhat limited. For a start, Meta Dedukti has no notion of meta-variables, and they cannot support the kind of dynamic checks we use in Mtac, which limits the kind of primitives that can be coded.…”

Section: :28mentioning

confidence: 99%