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75236abc
Commit
75236abc
authored
May 31, 2018
by
Ralf Jung
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also pre-reserve bigops notation
parent
f9e88985
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2
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60 additions
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34 deletions
+60
-34
theories/bi/big_op.v
theories/bi/big_op.v
+20
-34
theories/bi/notation.v
theories/bi/notation.v
+40
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theories/bi/big_op.v
View file @
75236abc
...
...
@@ -5,40 +5,26 @@ Set Default Proof Using "Type".
Import
interface
.
bi
derived_laws_bi
.
bi
.
(* Notations *)
Notation
"'[∗' 'list]' k ↦ x ∈ l , P"
:
=
(
big_opL
bi_sep
(
λ
k
x
,
P
)
l
)
(
at
level
200
,
l
at
level
10
,
k
,
x
at
level
1
,
right
associativity
,
format
"[∗ list] k ↦ x ∈ l , P"
)
:
bi_scope
.
Notation
"'[∗' 'list]' x ∈ l , P"
:
=
(
big_opL
bi_sep
(
λ
_
x
,
P
)
l
)
(
at
level
200
,
l
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ list] x ∈ l , P"
)
:
bi_scope
.
Notation
"'[∗]' Ps"
:
=
(
big_opL
bi_sep
(
λ
_
x
,
x
)
Ps
)
(
at
level
20
)
:
bi_scope
.
Notation
"'[∧' 'list]' k ↦ x ∈ l , P"
:
=
(
big_opL
bi_and
(
λ
k
x
,
P
)
l
)
(
at
level
200
,
l
at
level
10
,
k
,
x
at
level
1
,
right
associativity
,
format
"[∧ list] k ↦ x ∈ l , P"
)
:
bi_scope
.
Notation
"'[∧' 'list]' x ∈ l , P"
:
=
(
big_opL
bi_and
(
λ
_
x
,
P
)
l
)
(
at
level
200
,
l
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∧ list] x ∈ l , P"
)
:
bi_scope
.
Notation
"'[∧]' Ps"
:
=
(
big_opL
bi_and
(
λ
_
x
,
x
)
Ps
)
(
at
level
20
)
:
bi_scope
.
Notation
"'[∗' 'map]' k ↦ x ∈ m , P"
:
=
(
big_opM
bi_sep
(
λ
k
x
,
P
)
m
)
(
at
level
200
,
m
at
level
10
,
k
,
x
at
level
1
,
right
associativity
,
format
"[∗ map] k ↦ x ∈ m , P"
)
:
bi_scope
.
Notation
"'[∗' 'map]' x ∈ m , P"
:
=
(
big_opM
bi_sep
(
λ
_
x
,
P
)
m
)
(
at
level
200
,
m
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ map] x ∈ m , P"
)
:
bi_scope
.
Notation
"'[∗' 'set]' x ∈ X , P"
:
=
(
big_opS
bi_sep
(
λ
x
,
P
)
X
)
(
at
level
200
,
X
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ set] x ∈ X , P"
)
:
bi_scope
.
Notation
"'[∗' 'mset]' x ∈ X , P"
:
=
(
big_opMS
bi_sep
(
λ
x
,
P
)
X
)
(
at
level
200
,
X
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ mset] x ∈ X , P"
)
:
bi_scope
.
Notation
"'[∗' 'list]' k ↦ x ∈ l , P"
:
=
(
big_opL
bi_sep
(
λ
k
x
,
P
)
l
)
:
bi_scope
.
Notation
"'[∗' 'list]' x ∈ l , P"
:
=
(
big_opL
bi_sep
(
λ
_
x
,
P
)
l
)
:
bi_scope
.
Notation
"'[∗]' Ps"
:
=
(
big_opL
bi_sep
(
λ
_
x
,
x
)
Ps
)
:
bi_scope
.
Notation
"'[∧' 'list]' k ↦ x ∈ l , P"
:
=
(
big_opL
bi_and
(
λ
k
x
,
P
)
l
)
:
bi_scope
.
Notation
"'[∧' 'list]' x ∈ l , P"
:
=
(
big_opL
bi_and
(
λ
_
x
,
P
)
l
)
:
bi_scope
.
Notation
"'[∧]' Ps"
:
=
(
big_opL
bi_and
(
λ
_
x
,
x
)
Ps
)
:
bi_scope
.
Notation
"'[∗' 'map]' k ↦ x ∈ m , P"
:
=
(
big_opM
bi_sep
(
λ
k
x
,
P
)
m
)
:
bi_scope
.
Notation
"'[∗' 'map]' x ∈ m , P"
:
=
(
big_opM
bi_sep
(
λ
_
x
,
P
)
m
)
:
bi_scope
.
Notation
"'[∗' 'set]' x ∈ X , P"
:
=
(
big_opS
bi_sep
(
λ
x
,
P
)
X
)
:
bi_scope
.
Notation
"'[∗' 'mset]' x ∈ X , P"
:
=
(
big_opMS
bi_sep
(
λ
x
,
P
)
X
)
:
bi_scope
.
(** * Properties *)
Section
bi_big_op
.
...
...
theories/bi/notation.v
View file @
75236abc
(** Just reserve the notation. *)
(** Turnstiles *)
Reserved
Notation
"P ⊢ Q"
(
at
level
99
,
Q
at
level
200
,
right
associativity
).
Reserved
Notation
"P '⊢@{' PROP } Q"
(
at
level
99
,
Q
at
level
200
,
right
associativity
).
Reserved
Notation
"('⊢@{' PROP } )"
(
at
level
99
).
Reserved
Notation
"P ⊣⊢ Q"
(
at
level
95
,
no
associativity
).
Reserved
Notation
"P '⊣⊢@{' PROP } Q"
(
at
level
95
,
no
associativity
).
Reserved
Notation
"('⊣⊢@{' PROP } )"
(
at
level
95
).
(** BI connectives *)
Reserved
Notation
"'emp'"
.
Reserved
Notation
"'⌜' φ '⌝'"
(
at
level
1
,
φ
at
level
200
,
format
"⌜ φ ⌝"
).
Reserved
Notation
"P ∗ Q"
(
at
level
80
,
right
associativity
).
Reserved
Notation
"P -∗ Q"
(
at
level
99
,
Q
at
level
200
,
right
associativity
).
(** Modalities *)
Reserved
Notation
"'<pers>' P"
(
at
level
20
,
right
associativity
).
Reserved
Notation
"'<pers>?' p P"
(
at
level
20
,
p
at
level
9
,
P
at
level
20
,
right
associativity
,
format
"'<pers>?' p P"
).
...
...
@@ -38,6 +43,7 @@ Reserved Notation "■ P" (at level 20, right associativity).
Reserved
Notation
"■? p P"
(
at
level
20
,
p
at
level
9
,
P
at
level
20
,
right
associativity
,
format
"■? p P"
).
(** Update modalities *)
Reserved
Notation
"|==> Q"
(
at
level
99
,
Q
at
level
200
,
format
"|==> Q"
).
Reserved
Notation
"P ==∗ Q"
(
at
level
99
,
Q
at
level
200
,
format
"P ==∗ Q"
).
...
...
@@ -68,5 +74,39 @@ Reserved Notation "P ={ E }▷=∗ Q"
(
at
level
99
,
E
at
level
50
,
Q
at
level
200
,
format
"P ={ E }▷=∗ Q"
).
(** Big Ops *)
Reserved
Notation
"'[∗' 'list]' k ↦ x ∈ l , P"
(
at
level
200
,
l
at
level
10
,
k
,
x
at
level
1
,
right
associativity
,
format
"[∗ list] k ↦ x ∈ l , P"
).
Reserved
Notation
"'[∗' 'list]' x ∈ l , P"
(
at
level
200
,
l
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ list] x ∈ l , P"
).
Reserved
Notation
"'[∗]' Ps"
(
at
level
20
).
Reserved
Notation
"'[∧' 'list]' k ↦ x ∈ l , P"
(
at
level
200
,
l
at
level
10
,
k
,
x
at
level
1
,
right
associativity
,
format
"[∧ list] k ↦ x ∈ l , P"
).
Reserved
Notation
"'[∧' 'list]' x ∈ l , P"
(
at
level
200
,
l
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∧ list] x ∈ l , P"
).
Reserved
Notation
"'[∧]' Ps"
(
at
level
20
).
Reserved
Notation
"'[∗' 'map]' k ↦ x ∈ m , P"
(
at
level
200
,
m
at
level
10
,
k
,
x
at
level
1
,
right
associativity
,
format
"[∗ map] k ↦ x ∈ m , P"
).
Reserved
Notation
"'[∗' 'map]' x ∈ m , P"
(
at
level
200
,
m
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ map] x ∈ m , P"
).
Reserved
Notation
"'[∗' 'set]' x ∈ X , P"
(
at
level
200
,
X
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ set] x ∈ X , P"
).
Reserved
Notation
"'[∗' 'mset]' x ∈ X , P"
(
at
level
200
,
X
at
level
10
,
x
at
level
1
,
right
associativity
,
format
"[∗ mset] x ∈ X , P"
).
(** Define the scope *)
Delimit
Scope
bi_scope
with
I
.
Write
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