Commit 0671cb48 authored by Ralf Jung's avatar Ralf Jung

solve_proper: Do not enforce unfolding the head symbol

It is sometimes not desirable to do so.
parent 52b68900
......@@ -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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