Isabelle / HOL中的错误消息

Question

When applying the wrong tactic or the wrong deduction rule, the error message is usually too general:

Failed to apply initial proof method⌂

I am using Isabelle to teach natural deduction. When Isabelle complains, some students change the rule/tactic arbitrary without reflecting on the possible causes of the error. A more detailed error message could be part of the learning process of Isabelle, I think.

How to make those error messages student friendly? Does that require editing the source code or can it be managed by defining more expressive tactics of natural deduction?

Answer 1

Tactics in Isabelle can be thought of as chainable non-deterministic transformations of the goal state. That means that the question of what specifically caused a tactic to fail is difficult to answer in general, and there is no mechanism to track such information in Isabelle's tactic system. However, one could relatively easily modify existing tactics such that they can optionally output some tracing information.

However, I have no idea what this information should be. There are simple tactics such as rule where the reason why applying it fails is always that the rule that it is given cannot be unified with the goal (and possibly chained facts), and there are similarly simple tactics like intro , drule , frule , erule , and elim . Such unification-related problems can be debugged quite well sometimes using declare [[unify_trace_failure]] , which prints some tracing information every time a unification fails.

With simp and auto , the situation is much less clear because of how many different things these methods can do. Essentially, when the proof method could not be applied at all, it means that 'none of the things that simp and auto can do worked for this goal'. For simp , this includes simplification, splitting, linear arithmetic, and probably a lot more things that I forgot. For auto , it additionally includes classical reasoning with a certain search depth. One cannot really say easily what specific thing went wrong when these methods fail.

Some specialised tactics do print more specific error messages if something goes wrong, eg sat and smt sometimes print a special error message when they have found a counterexample to the goal, but I cannot even imagine what more helpful output for something like simp or auto would look like. If you have an idea, please do tell me.

I think this problem cannot really be solved with error messages; one must simply get to know the system and the tactics one uses better and understand what they do and when they fail. Perhaps it would be good to have a kind of catalogue of commonly-used tactics that mentions these things.