Commit 0a877c71 authored by Robbert Krebbers's avatar Robbert Krebbers

Make identation of solve_proper and f_equiv more consistent.

parent e81900e1
......@@ -234,40 +234,39 @@ Ltac setoid_subst :=
Ltac f_equiv :=
(* Deal with "pointwise_relation" *)
repeat lazymatch goal with
| |- pointwise_relation _ _ _ _ => intros ?
end;
| |- pointwise_relation _ _ _ _ => intros ?
end;
(* Normalize away equalities. *)
subst;
(* repeatedly apply congruence lemmas and use the equalities in the hypotheses. *)
first [ reflexivity | assumption | symmetry; assumption |
match goal with
(* We support matches on both sides, *if* they concern the same
variable.
TODO: We should support different variables, provided that we can
derive contradictions for the off-diagonal cases. *)
| |- ?R (match ?x with _ => _ end) (match ?x with _ => _ end) =>
destruct x; f_equiv
(* First assume that the arguments need the same relation as the result *)
| |- ?R (?f ?x) (?f _) =>
apply (_ : Proper (R ==> R) f); f_equiv
| |- ?R (?f ?x ?y) (?f _ _) =>
apply (_ : Proper (R ==> R ==> R) f); f_equiv
(* 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) (?f _) =>
apply (_ : Proper (_ ==> R) f); f_equiv
| |- ?R (?f ?x ?y) (?f _ _) =>
apply (_ : Proper (_ ==> _ ==> R) f); f_equiv
(* 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; f_equiv
end | idtac (* Let the user solve this goal *)
].
try match goal with
| _ => first [ reflexivity | assumption | symmetry; assumption]
(* We support matches on both sides, *if* they concern the same
variable.
TODO: We should support different variables, provided that we can
derive contradictions for the off-diagonal cases. *)
| |- ?R (match ?x with _ => _ end) (match ?x with _ => _ end) =>
destruct x; f_equiv
(* First assume that the arguments need the same relation as the result *)
| |- ?R (?f ?x) (?f _) =>
apply (_ : Proper (R ==> R) f); f_equiv
| |- ?R (?f ?x ?y) (?f _ _) =>
apply (_ : Proper (R ==> R ==> R) f); f_equiv
(* 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) (?f _) =>
apply (_ : Proper (_ ==> R) f); f_equiv
| |- ?R (?f ?x ?y) (?f _ _) =>
apply (_ : Proper (_ ==> _ ==> R) f); f_equiv
(* 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; f_equiv
end.
(** solve_proper solves goals of the form "Proper (R1 ==> R2)", for any
number of relations. All the actual work is done by f_equiv;
......@@ -277,9 +276,9 @@ Ltac solve_proper :=
(* Introduce everything *)
intros;
repeat lazymatch goal with
| |- Proper _ _ => intros ???
| |- (_ ==> _)%signature _ _ => intros ???
end;
| |- Proper _ _ => intros ???
| |- (_ ==> _)%signature _ _ => intros ???
end;
(* Unfold the head symbol, which is the one we are proving a new property about *)
lazymatch goal with
| |- ?R (?f _ _ _ _ _ _ _ _) (?f _ _ _ _ _ _ _ _) => unfold f
......
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