Commit ddfcc76c authored by Robbert Krebbers's avatar Robbert Krebbers

Move lattice related stuff up.

parent 9a1b4cde
......@@ -1158,6 +1158,49 @@ Notation "<[ k := a ]{ Γ }>" := (insertE Γ k a)
Arguments insertE _ _ _ _ _ _ !_ _ !_ / : simpl nomatch, assert.
(** * Notations for lattices. *)
(** SqSubsetEq registers the "canonical" partial order for a type, and is used
for the \sqsubseteq symbol. *)
Class SqSubsetEq A := sqsubseteq: relation A.
Hint Mode SqSubsetEq ! : typeclass_instances.
Instance: Params (@sqsubseteq) 2 := {}.
Infix "⊑" := sqsubseteq (at level 70) : stdpp_scope.
Notation "(⊑)" := sqsubseteq (only parsing) : stdpp_scope.
Notation "( x ⊑.)" := (sqsubseteq x) (only parsing) : stdpp_scope.
Notation "(.⊑ y )" := (λ x, sqsubseteq x y) (only parsing) : stdpp_scope.
Infix "⊑@{ A }" := (@sqsubseteq A _) (at level 70, only parsing) : stdpp_scope.
Notation "(⊑@{ A } )" := (@sqsubseteq A _) (only parsing) : stdpp_scope.
Instance sqsubseteq_rewrite `{SqSubsetEq A} : RewriteRelation (@{A}) := {}.
Hint Extern 0 (_ _) => reflexivity : core.
Class Meet A := meet: A A A.
Hint Mode Meet ! : typeclass_instances.
Instance: Params (@meet) 2 := {}.
Infix "⊓" := meet (at level 40) : stdpp_scope.
Notation "(⊓)" := meet (only parsing) : stdpp_scope.
Notation "( x ⊓.)" := (meet x) (only parsing) : stdpp_scope.
Notation "(.⊓ y )" := (λ x, meet x y) (only parsing) : stdpp_scope.
Class Join A := join: A A A.
Hint Mode Join ! : typeclass_instances.
Instance: Params (@join) 2 := {}.
Infix "⊔" := join (at level 50) : stdpp_scope.
Notation "(⊔)" := join (only parsing) : stdpp_scope.
Notation "( x ⊔.)" := (join x) (only parsing) : stdpp_scope.
Notation "(.⊔ y )" := (λ x, join x y) (only parsing) : stdpp_scope.
Class Top A := top : A.
Hint Mode Top ! : typeclass_instances.
Notation "⊤" := top (format "⊤") : stdpp_scope.
Class Bottom A := bottom : A.
Hint Mode Bottom ! : typeclass_instances.
Notation "⊥" := bottom (format "⊥") : stdpp_scope.
(** * Axiomatization of sets *)
(** The classes [SemiSet A C] and [Set_ A C] axiomatize sset of type [C] with
elements of type [A]. The first class, [SemiSet] does not include intersection
......@@ -1276,45 +1319,3 @@ Class Half A := half: A → A.
Hint Mode Half ! : typeclass_instances.
Notation "½" := half (format "½") : stdpp_scope.
Notation "½*" := (fmap (M:=list) half) : stdpp_scope.
(** * Notations for lattices. *)
(** SqSubsetEq registers the "canonical" partial order for a type, and is used
for the \sqsubseteq symbol. *)
Class SqSubsetEq A := sqsubseteq: relation A.
Hint Mode SqSubsetEq ! : typeclass_instances.
Instance: Params (@sqsubseteq) 2 := {}.
Infix "⊑" := sqsubseteq (at level 70) : stdpp_scope.
Notation "(⊑)" := sqsubseteq (only parsing) : stdpp_scope.
Notation "( x ⊑.)" := (sqsubseteq x) (only parsing) : stdpp_scope.
Notation "(.⊑ y )" := (λ x, sqsubseteq x y) (only parsing) : stdpp_scope.
Infix "⊑@{ A }" := (@sqsubseteq A _) (at level 70, only parsing) : stdpp_scope.
Notation "(⊑@{ A } )" := (@sqsubseteq A _) (only parsing) : stdpp_scope.
Instance sqsubseteq_rewrite `{SqSubsetEq A} : RewriteRelation (@{A}) := {}.
Hint Extern 0 (_ _) => reflexivity : core.
Class Meet A := meet: A A A.
Hint Mode Meet ! : typeclass_instances.
Instance: Params (@meet) 2 := {}.
Infix "⊓" := meet (at level 40) : stdpp_scope.
Notation "(⊓)" := meet (only parsing) : stdpp_scope.
Notation "( x ⊓.)" := (meet x) (only parsing) : stdpp_scope.
Notation "(.⊓ y )" := (λ x, meet x y) (only parsing) : stdpp_scope.
Class Join A := join: A A A.
Hint Mode Join ! : typeclass_instances.
Instance: Params (@join) 2 := {}.
Infix "⊔" := join (at level 50) : stdpp_scope.
Notation "(⊔)" := join (only parsing) : stdpp_scope.
Notation "( x ⊔.)" := (join x) (only parsing) : stdpp_scope.
Notation "(.⊔ y )" := (λ x, join x y) (only parsing) : stdpp_scope.
Class Top A := top : A.
Hint Mode Top ! : typeclass_instances.
Notation "⊤" := top (format "⊤") : stdpp_scope.
Class Bottom A := bottom : A.
Hint Mode Bottom ! : typeclass_instances.
Notation "⊥" := bottom (format "⊥") : stdpp_scope.
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