Commit 0671cb48 by Ralf Jung

### solve_proper: Do not enforce unfolding the head symbol

`It is sometimes not desirable to do so.`
parent 52b68900
Pipeline #3954 passed with stage
in 5 minutes and 19 seconds
 ... ... @@ -281,41 +281,44 @@ Ltac f_equiv := | H : ?R ?x ?y |- ?R2 (match ?x with _ => _ end) (match ?y with _ => _ end) => destruct H (* First assume that the arguments need the same relation as the result *) | |- ?R (?f ?x) _ => apply (_ : Proper (R ==> R) f) | |- ?R (?f _) _ => apply (_ : Proper (R ==> R) f) | |- ?R (?f _ _) _ => apply (_ : Proper (R ==> R ==> R) f) | |- ?R (?f _ _ _) _ => apply (_ : Proper (R ==> R ==> R ==> R) f) | |- ?R (?f _ _ _ _) _ => apply (_ : Proper (R ==> R ==> R ==> R ==> R) f) (* For the case in which R is polymorphic, or an operational type class, like equiv. *) | |- (?R _) (?f ?x) _ => apply (_ : Proper (R _ ==> _) f) | |- (?R _ _) (?f ?x) _ => apply (_ : Proper (R _ _ ==> _) f) | |- (?R _ _ _) (?f ?x) _ => apply (_ : Proper (R _ _ _ ==> _) f) | |- (?R _) (?f ?x ?y) _ => apply (_ : Proper (R _ ==> R _ ==> _) f) | |- (?R _ _) (?f ?x ?y) _ => apply (_ : Proper (R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f ?x ?y) _ => apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f) | |- (?R _) (?f _) _ => apply (_ : Proper (R _ ==> _) f) | |- (?R _ _) (?f _) _ => apply (_ : Proper (R _ _ ==> _) f) | |- (?R _ _ _) (?f _) _ => apply (_ : Proper (R _ _ _ ==> _) f) | |- (?R _) (?f _ _) _ => apply (_ : Proper (R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _) _ => apply (_ : Proper (R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _) _ => apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f) | |- (?R _) (?f _ _ _) _ => apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _ _) _ => apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _) _ => apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f) | |- (?R _) (?f _ _ _ _) _ => apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _ _ _) _ => apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _ _) _ => 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. *) (* 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 ?x) _ => apply (_ : Proper (_ ==> R) f) | |- ?R (?f ?x ?y) _ => apply (_ : Proper (_ ==> _ ==> R) f) | |- ?R (?f _) _ => apply (_ : Proper (_ ==> R) f) | |- ?R (?f _ _) _ => apply (_ : Proper (_ ==> _ ==> R) f) | |- ?R (?f _ _ _) _ => apply (_ : Proper (_ ==> _ ==> _ ==> R) f) | |- ?R (?f _ _ _ _) _ => 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. *) | H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) => apply H end; try reflexivity. (* The tactic [preprocess_solve_proper] unfolds the first head symbol, so that (* The tactic [solve_proper_unfold] unfolds the first head symbol, so that we proceed by repeatedly using [f_equiv]. *) Ltac preprocess_solve_proper := (* 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 ? end; simpl; (* Unfold the head symbol, which is the one we are proving a new property about *) Ltac solve_proper_unfold := (* Try unfolding the head symbol, which is the one we are proving a new property about *) lazymatch goal with | |- ?R (?f _ _ _ _ _ _ _ _) (?f _ _ _ _ _ _ _ _) => unfold f | |- ?R (?f _ _ _ _ _ _ _) (?f _ _ _ _ _ _ _) => unfold f ... ... @@ -325,15 +328,25 @@ Ltac preprocess_solve_proper := | |- ?R (?f _ _ _) (?f _ _ _) => unfold f | |- ?R (?f _ _) (?f _ _) => unfold f | |- ?R (?f _) (?f _) => unfold f end; simplify_eq. end; simpl. (** The tactic [solve_proper] solves goals of the form "Proper (R1 ==> R2)", for (** 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 [f_equiv]. *) Ltac solve_proper := preprocess_solve_proper; solve [repeat (f_equiv; try eassumption)]. [tac]. *) Ltac solve_proper_core tac := (* 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 ? end; simplify_eq; (* Now do the job. 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); solve [repeat first [eassumption | tac ()] ]. Ltac solve_proper := solve_proper_core ltac:(fun _ => f_equiv). (** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac, and then reverts them. *) ... ...
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