CoqHammer fails at easy mathcomp goals

[aleloi]

I have tried the hammer on mathcomp lemmas and it has mostly failed. Here is a simple example: addition of algebraic complex numbers commutes. I want hammer to construct the proof term (@GRing.Theory.addrC Algebraics.Implementation.zmodType a b). The predict tool finds the correct lemma GRing.Theory.addrC, but then all external provers either time out after 10 minutes or crash after using up a few 10s of GB RAM. I think what happens is that the TPTP output fails to encode the conversion between Algebraics.Implementation.zmodType andalgC =Algebraics.Implementation.Type. The TPTP output (with a small value for the number of predictions) is uploaded here. I have tested with both few (10) predictions and many (1000). I have also tested with all the supported external provers.

Mathcomp heavily uses canonical structures. IIUC (my understanding is taken from section 6.3 of the math comp book), whenever the the unification algorithm experts a zmodType, and the term is not zmodType, it looks in a 'canonical solutions table'. If it finds that there is a canonical construction of zmodType from the type of the current term, it applies the conversion. Here is the conversion that I think predict fails to include in the TPTP output. Can it be that canonical handling is not fully handled in Coq? Or is it predict that doesn't include the right conversion?

From mathcomp Require Import algC ssralg.
From Hammer Require Import Hammer .

Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.

Local Open Scope ring_scope.

Print Algebraics.Implementation.

Lemma com_addC (a b: algC): a+b=b+a.
Proof.
  exact (@GRing.Theory.addrC Algebraics.Implementation.zmodType a b).
  Restart.
  
  predict 10. (* predicts GRing.addrC and
                 algC.Algebraics.Implementation.zmodType
                 pretty high up *)
  Set Hammer Predictions 10.
  Set Hammer GSMode 0.
  Set Hammer Debug.
  Unset Hammer Parallel.
  Set Hammer ATPLimit 600.
  hammer.

[lukaszcz]

CoqHammer was designed to work well with "standard Coq", i.e., standard-library-like developments. Poor performance on mathcomp is a known issue and an open research problem (which I personally won't work on in any near future).

One way to improve the success rate on mathcomp problems could be to preprocess mathcomp goals into a form which CoqHammer can handle better. This wouldn't actually require much modification of CoqHammer itself.

[lukaszcz]

Following up: the breflect tactic (https://coqhammer.github.io/#boolean-reflection) that comes with CoqHammer is a very basic version of such a preprocessing tactic. It converts boolean statements (arguments of is_true) into propositions in Prop. You can try it. I don't expect that much success (it doesn't convert any lemmas in the mathcomp library), but it's a start.