A typed tactic language for Coq.

Copyright (c) 2020 Jan-Oliver Kaiser [email protected] Beta Ziliani [email protected]

Distributed under the terms of the MIT License, see LICENSE for details. Accepted contributions will be held under scrutiny to ensure they do not incur in a copyright infringement.

This repository contains a plugin for Coq with the tactic language described in the paper Mtac2: Typed Tactics for Backward Reasoning in Coq.

The project has 3 subdirectories:

• src contains the code of the plugin.

  • run.ml is the interpreter.

• theories contains support Coq files for the plugin.

  • Mtac2.v declares the plugin on the Coq side and imports all the required theories.
  • The intf folder contains the basics: the M monad with its operations documented, exceptions, etc.
  • The folder tactics contains everything relating to tactics:
    • Tactics.v defines the tactic type and several tactics and combinators.
    • Ttactics.v defines the type for typed tactics and combinators.
    • IntroPatt.v defines intro patterns.
    • ConstrSelector.v defines a selector based on the indices of an inductive type's constructors.

• examples contains simple examples to show the different features of Mtac2.

  • tactics.v shows how to standard, Ltac's like, proving. But with some interesting features not present in Ltac.
  • tauto.v shows many different ways to code a simple tautology prover, with different degrees of certainty and verboseness.

• test-suite contains several tests, including some uses of the plugin.

The plugin works currently with Coq v8.7 (and any minor version). It requires UniCoq to be installed. Mtac2 will be available in OPAM soon. For the moment you should have coqc, ocamlc and make in your path. Then simply do:

 coq_makefile -f _CoqProject -o Makefile

To generate a makefile from the description in _CoqProject, then make. This will consecutively build the plugin and the supporting theories.

You can then either make install the plugin or leave it in its current directory. To be able to import it from anywhere in Coq, simply add the following to ~/.coqrc:

Add LoadPath "path_to_mtac2/theories" as Mtac2.
Add ML Path "path_to_mtac2/src".

Once installed, you can Require Import Mtac2.Mtac2 to load the plugin. The plugin defines a tactic mrun t to execute code t and a proof mode MProof where Mtac2's tactic can be executed directly.