Coq Bug: Not_focussed Error On Definition Expansion

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Coq Bug: "Not_focussed" Error on Definition Expansion

Hey everyone!

I wanted to bring up a weird bug I encountered while working with Coq, specifically when expanding definitions. It seems to lead to a frustrating "Not_focussed" error, and I'm hoping we can figure out what's going on and how to fix it. Let's dive into the details so we can better understand this issue together.

The Problem: "Not_focussed" During Expansion

The specific scenario where I ran into this was in the last exercise dealing with real numbers. When attempting to prove the forall epsilon part, things went south pretty quickly. Here's the code snippet that triggered the issue:

- We need to show that
    ∀ ε > 0, ∃ a ∈ [0, 4), 4 - ε < a.
  Take ε > 0.
  Expand All.

Now, when I executed Expand All, Coq threw this error:

Uncaught Ltac2 exception: Not_focussed;

This is super annoying, because it halts the proof and makes it difficult to proceed. Even worse, it seems to break the Help. command in these situations, making it harder to debug.

Diving Deeper: Possible Cause

After scratching my head for a bit, I suspect the issue might be related to how Coq handles unfolding methods, especially when multiple goals are opened. My current hunch is that the alt_char_sup tactic, used within one of the unfold methods, might be the culprit. It seems like applying alt_char_sup might be inadvertently opening multiple goals, which then confuses the Expand All tactic and leads to the "Not_focussed" error.

We really need to re-evaluate what the proper behavior should be when such situations arise. Should Expand All be able to handle multiple goals? Should it throw a more informative error message? Or should the alt_char_sup tactic be modified to avoid opening multiple goals in the first place?

Impact and Mitigation

The "Not_focussed" error, as discussed, interrupts the proof process. It prevents further tactic execution and renders the Help. command unusable, thereby hindering debugging. Here’s a breakdown of the immediate impact and some potential mitigation strategies we could explore:

Immediate Impact

  1. Proof Stalling: The most direct consequence is the interruption of the proof. The "Not_focussed" error halts the application of further tactics, preventing any progress until the issue is resolved.
  2. Debugging Impairment: The failure of the Help. command is a significant setback. Coq's Help. command is indispensable for understanding the current state of the proof and identifying potential tactics. Its failure leaves users without vital information needed for debugging.
  3. Increased Complexity: The error obscures the underlying issues. Without a clear understanding of the cause, users may struggle to find a workaround, increasing the time and effort required to complete the proof.

Mitigation Strategies

  1. Targeted Unfolding: Instead of using Expand All, a more targeted approach may help. By selectively unfolding specific definitions, it might be possible to avoid the problematic alt_char_sup tactic. For example, using Unfold followed by the specific definition might bypass the issue.
  2. Goal Management: Investigate whether explicit goal management tactics can help. Tactics like Focus and Solve may help manage multiple goals more explicitly, potentially avoiding the "Not_focussed" error.
  3. Debugging Tools: Employ Coq's debugging features, such as Set Debug Unfold, to gain more insight into the unfolding process. This may provide clues about why alt_char_sup is causing issues.
  4. Code Refactoring: If alt_char_sup is indeed the culprit, consider refactoring it to avoid opening multiple goals. This might involve restructuring the tactic or using alternative approaches to achieve the same result without complicating goal management.

Why This Matters: The Bigger Picture

This bug might seem like a minor inconvenience, but it highlights some important considerations for Coq's usability and robustness. When a core feature like Expand All fails unexpectedly, it can be incredibly frustrating for users, especially those who are new to the system. It erodes confidence in the tool and makes it harder to learn and use effectively.

Moreover, the fact that this bug also breaks the Help. command is a serious problem. The Help. command is essential for debugging and understanding what's going on in a proof. When it fails, users are left in the dark and have to resort to guesswork or more time-consuming debugging techniques.

Therefore, addressing this bug is crucial for improving the overall user experience and making Coq more accessible to a wider audience. By fixing the underlying issue and providing better error messages, we can make Coq a more reliable and user-friendly tool for formal verification.

Possible Solutions and Next Steps

Okay, so what can we do about this? Here are a few ideas:

  1. Investigate alt_char_sup: The first step is to dive deep into the alt_char_sup tactic and figure out why it's opening multiple goals. Is this intentional? Is there a way to modify it to avoid this behavior?
  2. Improve Expand All: We need to make Expand All more robust and able to handle situations where multiple goals are opened. Perhaps it could provide a warning message or allow the user to select which goal to focus on.
  3. Enhance Error Messages: The "Not_focussed" error message is not very informative. We should improve it to provide more context and guidance to the user. For example, it could mention which tactic is causing the problem or suggest possible solutions.
  4. Fix Help.: We absolutely need to fix the Help. command so that it doesn't fail when Expand All encounters an error. This is essential for debugging and understanding the problem.

Community Input

I'd love to hear your thoughts on this! Have you encountered this bug before? Do you have any ideas about how to fix it? Let's work together to make Coq a better tool for everyone!

Let's Discuss!

I'm really curious to hear if anyone else has encountered this specific issue or similar problems with Expand All and definition unfolding. Also, if you have any insights into how alt_char_sup works or suggestions for alternative approaches, please share them! The goal here is to collectively understand the issue and find a robust solution.

I think this discussion will be beneficial in identifying not only a fix for this particular bug but also in uncovering broader strategies for handling similar situations in the future. By working together, we can make Coq more user-friendly and efficient for everyone. Thanks for taking the time to read this, and I look forward to your contributions!