Commit d101c562 authored by Robbert Krebbers's avatar Robbert Krebbers
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Indexed map function for finite maps.

parent c5bdf622
......@@ -104,6 +104,12 @@ index contains a value in the second map as well. *)
Instance map_difference `{Merge M} {A} : Difference (M A) :=
difference_with (λ _ _, None).
(** A stronger variant of map that allows the mapped function to use the index
of the elements. Implemented by conversion to lists, so not very efficient. *)
Definition map_imap `{ A, Insert K A (M A), A, Empty (M A),
A, FinMapToList K A (M A)} {A B} (f : K A option B) (m : M A) : M B :=
map_of_list (omap (λ ix, (fst ix,) <$> curry f ix) (map_to_list m)).
(** * Theorems *)
Section theorems.
Context `{FinMap K M}.
......@@ -585,6 +591,23 @@ Proof.
exists i x. rewrite <-elem_of_map_to_list, Hm. by left.
(** Properties of the imap function *)
Lemma lookup_imap {A B} (f : K A option B) m i :
map_imap f m !! i = m !! i = f i.
unfold map_imap; destruct (m !! i = f i) as [y|] eqn:Hi; simpl.
* destruct (m !! i) as [x|] eqn:?; simplify_equality'.
apply elem_of_map_of_list_1_help.
{ apply elem_of_list_omap; exists (i,x); split;
[by apply elem_of_map_to_list|by simplify_option_equality]. }
intros y'; rewrite elem_of_list_omap; intros ([i' x']&Hi'&?).
by rewrite elem_of_map_to_list in Hi'; simplify_option_equality.
* apply not_elem_of_map_of_list; rewrite elem_of_list_fmap.
intros ([i' x]&->&Hi'); simplify_equality'.
rewrite elem_of_list_omap in Hi'; destruct Hi' as ([j y]&Hj&?).
rewrite elem_of_map_to_list in Hj; simplify_option_equality.
(** ** Properties of conversion from collections *)
Lemma lookup_map_of_collection {A} `{FinCollection K C}
(f : K option A) X i x :
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