How to Try a Tactic in Ltac Without Failure

Discover how to effectively use Ltac tactics in Coq to try rewriting and applying lemmas seamlessly while ensuring your proof continues even if the rewrite fails.
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This video is based on the question https://stackoverflow.com/q/69859421/ asked by the user 'sdpoll' ( https://stackoverflow.com/u/12288637/ ) and on the answer https://stackoverflow.com/a/69860249/ provided by the user 'Andrey' ( https://stackoverflow.com/u/2066615/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Understanding Tactic Application in Ltac

When working with Coq, a proof assistant, we often face situations where we want to execute multiple tactics efficiently. One common scenario is wanting to perform an action that might fail (like a rewrite) but still ensures that we can move forward with a fallback tactic (like applying a lemma). This post will help you navigate this situation effectively in Ltac, Coq's tactic language.

The Problem Explained

Imagine you have a proof that involves two cases, where the tactics applied may look like this:

[[See Video to Reveal this Text or Code Snippet]]

In essence, your intention is to combine these two cases into a single tactic. Specifically, you want to try to rewrite using a hypothesis (H), and if that attempt fails, you want to move on to applying lemma1 without causing any interruptions.

Key Questions

How can I try executing a tactic while ensuring that if it fails, the proof process continues without error?

Is there a tactic in Ltac that performs "nothing," allowing me to fail gracefully?

The Solution

Leveraging the try Tactic

Interestingly, in Ltac, you do not need a specific "do nothing" tactic. The try tactic itself handles this requirement perfectly. The try tactic will attempt to execute the tactic you provide. If it fails, it simply does nothing and moves on to the next line of code.

The Ideal Implementation

To achieve your goal effectively, you can use the following simplified tactic:

[[See Video to Reveal this Text or Code Snippet]]

Here's an explanation of what happens:

try rewrite H: This attempts to rewrite using the hypothesis H.

If it is successful, the next tactic apply lemma1 will be executed.

If rewrite H fails (perhaps H does not apply in that context), it just stops and skips to the next tactic without throwing an error.

apply lemma1: This will always attempt to apply lemma1, regardless of whether the rewrite was successful or not.

Why try Works in Your Scenario

The beauty of using try in Ltac is its simplicity and functionality:

It lets you handle potential failures gracefully.

You can ensure that the flow of your proof continues unimpeded, focusing on what you need to achieve.

Conclusion

In summary, if you need to execute a tactic that might fail but you want to keep the proof process going, using the try tactic in Ltac is your best bet. The syntax:

[[See Video to Reveal this Text or Code Snippet]]

not only simplifies your proof but also enhances clarity, allowing you to focus on the logic of the proof rather than the technicalities of error handling.

Final Thoughts

Experimentation with Ltac can seem daunting at first, but taking advantage of its intuitive tactics like try can significantly ease the proof-writing process. Happy proving!