### Merge branch 'ralf/solve_proper' into 'master'

```Factor out solve_proper_prepare

See merge request robbertkrebbers/coq-stdpp!19```
parents e1fff8e2 e1c92aa2
 ... ... @@ -304,18 +304,18 @@ Ltac f_equiv := | |- (?R _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> R _ _ _ ==> _) f) (* Next, try to infer the relation. Unfortunately, there is an instance of Proper for (eq ==> _), which will always be matched. *) (* Next, try to infer the relation. Unfortunately, very often, it will turn the goal into a Leibniz equality so we get stuck. *) (* TODO: Can we exclude that instance? *) (* TODO: If some of the arguments are the same, we could also query for "pointwise_relation"'s. But that leads to a combinatorial explosion about which arguments are and which are not the same. *) | |- ?R (?f _) _ => simple apply (_ : Proper (_ ==> R) f) | |- ?R (?f _ _) _ => simple apply (_ : Proper (_ ==> _ ==> R) f) | |- ?R (?f _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> R) f) | |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> R) f) (* In case the function symbol differs, but the arguments are the same, maybe we have a pointwise_relation in our context. *) (* In case the function symbol differs, but the arguments are the same, maybe we have a pointwise_relation in our context. *) (* TODO: If only some of the arguments are the same, we could also query for "pointwise_relation"'s. But that leads to a combinatorial explosion about which arguments are and which are not the same. *) | H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) => simple apply H end; try simple apply reflexivity. ... ... @@ -335,23 +335,30 @@ Ltac solve_proper_unfold := | |- ?R (?f _ _) (?f _ _) => unfold f | |- ?R (?f _) (?f _) => unfold f end. (** The tactic [solve_proper_core tac] solves goals of the form "Proper (R1 ==> R2)", for any number of relations. The actual work is done by repeatedly applying [tac]. *) Ltac solve_proper_core tac := (* [solve_proper_prepare] does some preparation work before the main [solve_proper] loop. Having this as a separate tactic is useful for debugging [solve_proper] failure. *) Ltac solve_proper_prepare := (* Introduce everything *) intros; repeat lazymatch goal with | |- Proper _ _ => intros ??? | |- (_ ==> _)%signature _ _ => intros ??? | |- pointwise_relation _ _ _ _ => intros ? | |- ?R ?f _ => try let f' := constr:(λ x, f x) in intros ? | |- ?R ?f _ => let f' := constr:(λ x, f x) in intros ? end; simplify_eq; (* Now do the job. We try with and without unfolding. We have to backtrack on (* We try with and without unfolding. We have to backtrack on that because unfolding may succeed, but then the proof may fail. *) (solve_proper_unfold + idtac); simpl; (solve_proper_unfold + idtac); simpl. (** The tactic [solve_proper_core tac] solves goals of the form "Proper (R1 ==> R2)", for any number of relations. The actual work is done by repeatedly applying [tac]. *) Ltac solve_proper_core tac := solve_proper_prepare; (* Now do the job. *) solve [repeat first [eassumption | tac ()] ]. (** Finally, [solve_proper] tries to apply [f_equiv] in a loop. *) Ltac solve_proper := solve_proper_core ltac:(fun _ => f_equiv). (** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac, ... ...
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