Commit e20e49c6 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Simplify big_opM again (revert e760dfb5).

parent 785b2175
...@@ -55,9 +55,9 @@ Fixpoint big_op `{Op A, Empty A} (xs : list A) : A := ...@@ -55,9 +55,9 @@ Fixpoint big_op `{Op A, Empty A} (xs : list A) : A :=
Arguments big_op _ _ _ !_ /. Arguments big_op _ _ _ !_ /.
Instance: Params (@big_op) 3. Instance: Params (@big_op) 3.
Definition big_opM `{FinMapToList K A M, Op B, Empty B} Definition big_opM `{FinMapToList K A M, Op A, Empty A} (m : M) : A :=
(f : K A list B) (m : M) : B := big_op (map_to_list m = curry f). big_op (snd <$> map_to_list m).
Instance: Params (@big_opM) 4. Instance: Params (@big_opM) 6.
(** Updates *) (** Updates *)
Definition ra_update_set `{Op A, Valid A} (x : A) (P : A Prop) := Definition ra_update_set `{Op A, Valid A} (x : A) (P : A Prop) :=
...@@ -141,26 +141,21 @@ Proof. ...@@ -141,26 +141,21 @@ Proof.
Qed. Qed.
Context `{FinMap K M}. Context `{FinMap K M}.
Context `{Equiv B} `{!Equivalence (() : relation B)} (f : K B list A). Lemma big_opM_empty : big_opM ( : M A) .
Lemma big_opM_empty : big_opM f ( : M B) . Proof. unfold big_opM. by rewrite map_to_list_empty. Qed.
Proof. by unfold big_opM; rewrite map_to_list_empty. Qed. Lemma big_opM_insert (m : M A) i x :
Lemma big_opM_insert (m : M B) i (y : B) : m !! i = None big_opM (<[i:=x]> m) x big_opM m.
m !! i = None big_opM f (<[i:=y]> m) big_op (f i y) big_opM f m. Proof. intros ?; unfold big_opM. by rewrite map_to_list_insert by done. Qed.
Proof. Lemma big_opM_singleton i x : big_opM ({[i,x]} : M A) x.
intros ?; unfold big_opM.
by rewrite map_to_list_insert, bind_cons, big_op_app by done.
Qed.
Lemma big_opM_singleton i (y : B) : big_opM f ({[i,y]} : M B) big_op (f i y).
Proof. Proof.
unfold singleton, map_singleton. unfold singleton, map_singleton.
rewrite big_opM_insert by auto using lookup_empty; simpl. rewrite big_opM_insert by auto using lookup_empty; simpl.
by rewrite big_opM_empty, (right_id _ _). by rewrite big_opM_empty, (right_id _ _).
Qed. Qed.
Global Instance big_opM_proper : Global Instance big_opM_proper : Proper (() ==> ()) (big_opM : M A _).
( i, Proper (() ==> ()) (f i)) Proper (() ==> ()) (big_opM f: M B A).
Proof. Proof.
intros Hf m1; induction m1 as [|i x m1 ? IH] using map_ind. intros m1; induction m1 as [|i x m1 ? IH] using map_ind.
{ by intros m2; rewrite (symmetry_iff () ), map_equiv_empty; intros ->. } { by intros m2; rewrite (symmetry_iff ()), map_equiv_empty; intros ->. }
intros m2 Hm2; rewrite big_opM_insert by done. intros m2 Hm2; rewrite big_opM_insert by done.
rewrite (IH (delete i m2)) by (by rewrite <-Hm2, delete_insert). rewrite (IH (delete i m2)) by (by rewrite <-Hm2, delete_insert).
destruct (map_equiv_lookup (<[i:=x]> m1) m2 i x) destruct (map_equiv_lookup (<[i:=x]> m1) m2 i x)
......
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