Commit dcc164e3 authored by Robbert Krebbers's avatar Robbert Krebbers
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Also specialize big ops on CMRAs to gmap.

parent 5726049c
From algebra Require Export cmra.
From prelude Require Import fin_maps.
From prelude Require Import gmap.
Fixpoint big_op {A : cmraT} `{Empty A} (xs : list A) : A :=
match xs with [] => | x :: xs => x big_op xs end.
Arguments big_op _ _ !_ /.
Instance: Params (@big_op) 2.
Definition big_opM {A : cmraT} `{FinMapToList K A M, Empty A} (m : M) : A :=
Definition big_opM `{Countable K} {A : cmraT} `{Empty A} (m : gmap K A) : A :=
big_op (snd <$> map_to_list m).
Instance: Params (@big_opM) 5.
......@@ -34,33 +34,31 @@ Proof.
Lemma big_op_contains xs ys : xs `contains` ys big_op xs big_op ys.
induction 1 as [|x xs ys|x y xs|x xs ys|xs ys zs]; rewrite //=.
- by apply cmra_preserving_l.
- by rewrite !assoc (comm _ y).
- by transitivity (big_op ys); last apply cmra_included_r.
- by transitivity (big_op ys).
intros [xs' ->]%contains_Permutation.
rewrite big_op_app; apply cmra_included_l.
Lemma big_op_delete xs i x :
xs !! i = Some x x big_op (delete i xs) big_op xs.
Proof. by intros; rewrite {2}(delete_Permutation xs i x). Qed.
Context `{FinMap K M}.
Lemma big_opM_empty : big_opM ( : M A) .
Context `{Countable K}.
Implicit Types m : gmap K A.
Lemma big_opM_empty : big_opM ( : gmap K A) .
Proof. unfold big_opM. by rewrite map_to_list_empty. Qed.
Lemma big_opM_insert (m : M A) i x :
Lemma big_opM_insert m i x :
m !! i = None big_opM (<[i:=x]> m) x big_opM m.
Proof. intros ?; by rewrite /big_opM map_to_list_insert. Qed.
Lemma big_opM_delete (m : M A) i x :
Lemma big_opM_delete m i x :
m !! i = Some x x big_opM (delete i m) big_opM m.
intros. by rewrite -{2}(insert_delete m i x) // big_opM_insert ?lookup_delete.
Lemma big_opM_singleton i x : big_opM ({[i := x]} : M A) x.
Lemma big_opM_singleton i x : big_opM ({[i := x]} : gmap K A) x.
rewrite -insert_empty big_opM_insert /=; last auto using lookup_empty.
by rewrite big_opM_empty right_id.
Global Instance big_opM_proper : Proper (() ==> ()) (big_opM : M A _).
Global Instance big_opM_proper : Proper (() ==> ()) (big_opM : gmap K A _).
intros m1; induction m1 as [|i x m1 ? IH] using map_ind.
{ by intros m2; rewrite (symmetry_iff ()) map_equiv_empty; intros ->. }
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