mirror of
https://github.com/achlipala/frap.git
synced 2024-11-28 07:16:20 +00:00
Merge branch 'master' of ssh://schizomaniac.net//home/adamc/git-root/frap
This commit is contained in:
commit
48e75a5ab5
1 changed files with 16 additions and 3 deletions
19
Map.v
19
Map.v
|
@ -6,11 +6,13 @@ Module Type S.
|
|||
Parameter fmap : Type -> Type -> Type.
|
||||
|
||||
Parameter empty : forall A B, fmap A B.
|
||||
Parameter lookup : forall A B, fmap A B -> A -> option B.
|
||||
Parameter add : forall A B, fmap A B -> A -> B -> fmap A B.
|
||||
|
||||
Parameter remove : forall A B, fmap A B -> A -> fmap A B.
|
||||
Parameter join : forall A B, fmap A B -> fmap A B -> fmap A B.
|
||||
Parameter merge : forall A B, (option B -> option B -> option B) -> fmap A B -> fmap A B -> fmap A B.
|
||||
Parameter lookup : forall A B, fmap A B -> A -> option B.
|
||||
Parameter restrict : forall A B, (A -> bool) -> fmap A B -> fmap A B.
|
||||
Parameter includes : forall A B, fmap A B -> fmap A B -> Prop.
|
||||
|
||||
Notation "$0" := (empty _ _).
|
||||
|
@ -119,6 +121,9 @@ Module Type S.
|
|||
Axiom dom_add : forall A B (m : fmap A B) (k : A) (v : B),
|
||||
dom (add m k v) = {k} \cup dom m.
|
||||
|
||||
Axiom lookup_restrict : forall A B (f : A -> bool) (m : fmap A B) k,
|
||||
lookup (restrict f m) k = if f k then lookup m k else None.
|
||||
|
||||
Hint Extern 1 => match goal with
|
||||
| [ H : lookup (empty _ _) _ = Some _ |- _ ] =>
|
||||
rewrite lookup_empty in H; discriminate
|
||||
|
@ -127,7 +132,7 @@ Module Type S.
|
|||
Hint Resolve includes_lookup includes_add empty_includes.
|
||||
|
||||
Hint Rewrite lookup_empty lookup_add_eq lookup_add_ne lookup_remove_eq lookup_remove_ne
|
||||
lookup_merge using congruence.
|
||||
lookup_merge lookup_restrict using congruence.
|
||||
|
||||
Hint Rewrite dom_empty dom_add.
|
||||
|
||||
|
@ -182,6 +187,8 @@ Module M : S.
|
|||
Definition merge A B f (m1 m2 : fmap A B) : fmap A B :=
|
||||
fun k => f (m1 k) (m2 k).
|
||||
Definition lookup A B (m : fmap A B) (k : A) := m k.
|
||||
Definition restrict A B (f : A -> bool) (m : fmap A B) : fmap A B :=
|
||||
fun k => if f k then m k else None.
|
||||
Definition includes A B (m1 m2 : fmap A B) :=
|
||||
forall k v, m1 k = Some v -> m2 k = Some v.
|
||||
|
||||
|
@ -405,7 +412,13 @@ Module M : S.
|
|||
Proof.
|
||||
unfold lookup, add; simpl; intros.
|
||||
destruct (decide (k' = k)); intuition congruence.
|
||||
Qed.
|
||||
Qed.
|
||||
|
||||
Theorem lookup_restrict : forall A B (f : A -> bool) (m : fmap A B) k,
|
||||
lookup (restrict f m) k = if f k then lookup m k else None.
|
||||
Proof.
|
||||
auto.
|
||||
Qed.
|
||||
End M.
|
||||
|
||||
Export M.
|
||||
|
|
Loading…
Reference in a new issue