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stdpp
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ddfcc76c
Commit
ddfcc76c
authored
Feb 17, 2020
by
Robbert Krebbers
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Move lattice related stuff up.
parent
9a1b4cde
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-42
theories/base.v
theories/base.v
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-42
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theories/base.v
View file @
ddfcc76c
...
...
@@ -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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