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In my coq development I am learning how to create new tactics tailored to my problem domain, a la Prof. Adam Chlipala. On that page he describes how to create powerful custom tactics by e.g. combining repeat with match.

Now, I already have a powerful one-shot tactic in use, auto. It strings together chains of steps found from hint databases. I have invested some effort in curating those hint databases, so I'd like to continue using it as well.

However this presents a problem. It isn't clear what the "right" way is to incorporate auto's functionality into customized tactics.

For example, since (per its page) auto always either solves the goal or does nothing, putting it inside a loop is no more powerful than calling it once after the loop.

To see why this isn't ideal, consider a hypothetical way to directly call a single "step" of auto, which succeeds if it could make a change (as opposed to only when it solved the goal) and fails otherwise. Such single-steps could be interleaved with custom behavior in a match repeat loop, allowing us to e.g. try contradiction or try congruence at intermediate points within the search tree.

Are there good design patterns for incorporating auto's functionality into custom tactics?

Can auto's behavior be decomposed into "single step" tactics that we can use?

phs
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What I would do instead would be to incorporate other tactics within auto. You can do so by using the Hint Extern num pat => mytactic : mybase command where num is a priority number (0 being the highest priority), pat a pattern to filter when the hint should be used and mytactic and mybase are of course the tactic you want to apply and the base you want to add the hint to (do not use the default core; build up your custom base instead and call it with auto with mybase; if you do not want to include the lemmas from the core base in the search, add the fake base nocore: auto with mybase nocore).

If you start relying on auto very much, I would switch instead to the almost equivalent but better behaved typeclasses eauto with mybase. Contrary to what its name suggests, it is a general purpose tactic that has nothing to do with type classes (as long as you explicitly provide the hint base on which it should be working). One of the main behavior difference to know is that the search depth is unbounded by default. So beware of possible infinite loops or fix a finite limit with the variant typeclasses eauto num with mybase.

Zimm i48
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  • How would this allow us to combine auto-like searching with, say, `congruence` or other solvers for restricted fragments? – phs Dec 17 '16 at 17:50
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    @phs: What I'm suggesting is calling congruence and such *from* the auto tactic. – Zimm i48 Dec 17 '16 at 19:24
  • Ah, I see. Do you know of a variant of `typeclasses eauto` similar to `auto using ...`, where explicit terms can be added to the search? If it's in the manual, it's not somewhere I could see. – phs Dec 17 '16 at 23:30
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    No unfortunately this syntax is not available yet for typeclasses eauto although you can get the same result using singleton hint bases that you add to the with clause (`typeclasses eauto with mybase mysingletonbase`). – Zimm i48 Dec 17 '16 at 23:37
  • Fair enough. I might try scripting up automatic creation/population/use/disposal of hint dbs for that purpose. Perhaps it won't be very expensive? – phs Dec 17 '16 at 23:43
  • Nope, removing hintdbs is apparently not a possible operation, nor is calling gallina commands from within the tactics grammar. – phs Dec 17 '16 at 23:48
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    Right, the vernacular commands can't be scripted. Ltac is just for scripting tactics. It might be that you are better off sticking to auto until typeclasses eauto accepts the using clause (that should be the case in the next 8.7 release...) – Zimm i48 Dec 18 '16 at 00:03