Library iris.bi.notation
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 "(⊢)".
Reserved Notation "'(⊢@{' PROP } )".
Reserved Notation "( P ⊣⊢.)".
Reserved Notation "(.⊣⊢ Q )".
Reserved Notation "P ⊣⊢ Q" (at level 95, no associativity).
Reserved Notation "P '⊣⊢@{' PROP } Q" (at level 95, no associativity).
Reserved Notation "(⊣⊢)".
Reserved Notation "'(⊣⊢@{' PROP } )".
Reserved Notation "(.⊢ Q )".
Reserved Notation "( P ⊢.)".
Reserved Notation "⊢ Q" (at level 20, Q at level 200).
Reserved Notation "'⊢@{' PROP } Q" (at level 20, Q at level 200).
Reserved Notation "P '⊢@{' PROP } Q" (at level 99, Q at level 200, right associativity).
Reserved Notation "(⊢)".
Reserved Notation "'(⊢@{' PROP } )".
Reserved Notation "( P ⊣⊢.)".
Reserved Notation "(.⊣⊢ Q )".
Reserved Notation "P ⊣⊢ Q" (at level 95, no associativity).
Reserved Notation "P '⊣⊢@{' PROP } Q" (at level 95, no associativity).
Reserved Notation "(⊣⊢)".
Reserved Notation "'(⊣⊢@{' PROP } )".
Reserved Notation "(.⊢ Q )".
Reserved Notation "( P ⊢.)".
Reserved Notation "⊢ Q" (at level 20, Q at level 200).
Reserved Notation "'⊢@{' PROP } Q" (at level 20, Q at level 200).
The definition must coincide with "'⊢@{' PROP } Q".
Reserved Notation "'(⊢@{' PROP } Q )".
Rationale:
Notation ( '⊢@{' PROP } ) prevents parsing (⊢@{PROP} Q) using the
⊢@{PROP} Q notation; since the latter parse arises from composing two
notations, it is missed by the automatic left-factorization.
To fix that, we force left-factorization by explicitly composing parentheses with
'⊢@{' PROP } Q into the new notation ( '⊢@{' PROP } Q ),
which successfully undergoes automatic left-factoring.
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, format "P ∗ '/' Q").
Reserved Notation "P -∗ Q"
(at level 99, Q at level 200, right associativity,
format "'[' P -∗ '/' '[' Q ']' ']'").
Reserved Notation "⎡ P ⎤".
Reserved Notation "'⌜' φ '⌝'" (at level 1, φ at level 200, format "⌜ φ ⌝").
Reserved Notation "P ∗ Q" (at level 80, right associativity, format "P ∗ '/' Q").
Reserved Notation "P -∗ Q"
(at level 99, Q at level 200, right associativity,
format "'[' P -∗ '/' '[' Q ']' ']'").
Reserved Notation "⎡ P ⎤".
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").
Reserved Notation "▷ P" (at level 20, right associativity).
Reserved Notation "▷? p P" (at level 20, p at level 9, P at level 20,
format "▷? p P").
Reserved Notation "▷^ n P" (at level 20, n at level 9, P at level 20,
format "▷^ n P").
Reserved Infix "∗-∗" (at level 95, no associativity).
Reserved Notation "'<affine>' P" (at level 20, right associativity).
Reserved Notation "'<affine>?' p P" (at level 20, p at level 9, P at level 20,
right associativity, format "'<affine>?' p P").
Reserved Notation "'<absorb>' P" (at level 20, right associativity).
Reserved Notation "'<absorb>?' p P" (at level 20, p at level 9, P at level 20,
right associativity, format "'<absorb>?' p P").
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").
Reserved Notation "◇ P" (at level 20, right associativity).
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").
Reserved Notation "'<obj>' P" (at level 20, right associativity).
Reserved Notation "'<subj>' 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").
Reserved Notation "▷ P" (at level 20, right associativity).
Reserved Notation "▷? p P" (at level 20, p at level 9, P at level 20,
format "▷? p P").
Reserved Notation "▷^ n P" (at level 20, n at level 9, P at level 20,
format "▷^ n P").
Reserved Infix "∗-∗" (at level 95, no associativity).
Reserved Notation "'<affine>' P" (at level 20, right associativity).
Reserved Notation "'<affine>?' p P" (at level 20, p at level 9, P at level 20,
right associativity, format "'<affine>?' p P").
Reserved Notation "'<absorb>' P" (at level 20, right associativity).
Reserved Notation "'<absorb>?' p P" (at level 20, p at level 9, P at level 20,
right associativity, format "'<absorb>?' p P").
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").
Reserved Notation "◇ P" (at level 20, right associativity).
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").
Reserved Notation "'<obj>' P" (at level 20, right associativity).
Reserved Notation "'<subj>' P" (at level 20, right associativity).
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 ']'").
Reserved Notation "|={ E1 , E2 }=> Q"
(at level 99, E1, E2 at level 50, Q at level 200,
format "'[ ' |={ E1 , E2 }=> '/' Q ']'").
Reserved Notation "P ={ E1 , E2 }=∗ Q"
(at level 99, E1,E2 at level 50, Q at level 200,
format "'[' P ={ E1 , E2 }=∗ '/' '[' Q ']' ']'").
Reserved Notation "|={ E }=> Q"
(at level 99, E at level 50, Q at level 200,
format "'[ ' |={ E }=> '/' Q ']'").
Reserved Notation "P ={ E }=∗ Q"
(at level 99, E at level 50, Q at level 200,
format "'[' P ={ E }=∗ '/' '[' Q ']' ']'").
Reserved Notation "P ==∗ Q"
(at level 99, Q at level 200, format "'[' P ==∗ '/' Q ']'").
Reserved Notation "|={ E1 , E2 }=> Q"
(at level 99, E1, E2 at level 50, Q at level 200,
format "'[ ' |={ E1 , E2 }=> '/' Q ']'").
Reserved Notation "P ={ E1 , E2 }=∗ Q"
(at level 99, E1,E2 at level 50, Q at level 200,
format "'[' P ={ E1 , E2 }=∗ '/' '[' Q ']' ']'").
Reserved Notation "|={ E }=> Q"
(at level 99, E at level 50, Q at level 200,
format "'[ ' |={ E }=> '/' Q ']'").
Reserved Notation "P ={ E }=∗ Q"
(at level 99, E at level 50, Q at level 200,
format "'[' P ={ E }=∗ '/' '[' Q ']' ']'").
Step-taking fancy updates
Reserved Notation "|={ E1 } [ E2 ]▷=> Q"
(at level 99, E1, E2 at level 50, Q at level 200,
format "'[ ' |={ E1 } [ E2 ]▷=> '/' Q ']'").
Reserved Notation "P ={ E1 } [ E2 ]▷=∗ Q"
(at level 99, E1, E2 at level 50, Q at level 200,
format "'[' P ={ E1 } [ E2 ]▷=∗ '/' '[' Q ']' ']'").
Reserved Notation "|={ E }▷=> Q"
(at level 99, E at level 50, Q at level 200,
format "'[ ' |={ E }▷=> '/' Q ']'").
Reserved Notation "P ={ E }▷=∗ Q"
(at level 99, E at level 50, Q at level 200,
format "'[' P ={ E }▷=∗ '/' '[' Q ']' ']'").
(at level 99, E1, E2 at level 50, Q at level 200,
format "'[ ' |={ E1 } [ E2 ]▷=> '/' Q ']'").
Reserved Notation "P ={ E1 } [ E2 ]▷=∗ Q"
(at level 99, E1, E2 at level 50, Q at level 200,
format "'[' P ={ E1 } [ E2 ]▷=∗ '/' '[' Q ']' ']'").
Reserved Notation "|={ E }▷=> Q"
(at level 99, E at level 50, Q at level 200,
format "'[ ' |={ E }▷=> '/' Q ']'").
Reserved Notation "P ={ E }▷=∗ Q"
(at level 99, E at level 50, Q at level 200,
format "'[' P ={ E }▷=∗ '/' '[' Q ']' ']'").
Multi-step-taking fancy updates
Reserved Notation "|={ E1 } [ E2 ]▷=>^ n Q"
(at level 99, E1, E2 at level 50, n at level 9, Q at level 200,
format "'[ ' |={ E1 } [ E2 ]▷=>^ n '/' Q ']'").
Reserved Notation "P ={ E1 } [ E2 ]▷=∗^ n Q"
(at level 99, E1, E2 at level 50, n at level 9, Q at level 200,
format "'[' P ={ E1 } [ E2 ]▷=∗^ n '/' '[' Q ']' ']'").
Reserved Notation "|={ E }▷=>^ n Q"
(at level 99, E at level 50, n at level 9, Q at level 200,
format "'[ ' |={ E }▷=>^ n '/' Q ']'").
Reserved Notation "P ={ E }▷=∗^ n Q"
(at level 99, E at level 50, n at level 9, Q at level 200,
format "'[' P ={ E }▷=∗^ n '/' '[' Q ']' ']'").
(at level 99, E1, E2 at level 50, n at level 9, Q at level 200,
format "'[ ' |={ E1 } [ E2 ]▷=>^ n '/' Q ']'").
Reserved Notation "P ={ E1 } [ E2 ]▷=∗^ n Q"
(at level 99, E1, E2 at level 50, n at level 9, Q at level 200,
format "'[' P ={ E1 } [ E2 ]▷=∗^ n '/' '[' Q ']' ']'").
Reserved Notation "|={ E }▷=>^ n Q"
(at level 99, E at level 50, n at level 9, Q at level 200,
format "'[ ' |={ E }▷=>^ n '/' Q ']'").
Reserved Notation "P ={ E }▷=∗^ n Q"
(at level 99, E at level 50, n at level 9, Q at level 200,
format "'[' P ={ E }▷=∗^ n '/' '[' Q ']' ']'").
Reserved Notation "'[∗' 'list]' k ↦ x ∈ l , P"
(at level 200, l at level 10, k binder, x binder, right associativity,
format "[∗ list] k ↦ x ∈ l , P").
Reserved Notation "'[∗' 'list]' x ∈ l , P"
(at level 200, l at level 10, x binder, right associativity,
format "[∗ list] x ∈ l , P").
Reserved Notation "'[∗' 'list]' k ↦ x1 ; x2 ∈ l1 ; l2 , P"
(at level 200, l1, l2 at level 10, k binder, x1 binder, x2 binder,
right associativity,
format "[∗ list] k ↦ x1 ; x2 ∈ l1 ; l2 , P").
Reserved Notation "'[∗' 'list]' x1 ; x2 ∈ l1 ; l2 , P"
(at level 200, l1, l2 at level 10, x1 binder, x2 binder, right associativity,
format "[∗ list] x1 ; x2 ∈ l1 ; l2 , P").
Reserved Notation "'[∗]' Ps" (at level 20).
Reserved Notation "'[∧' 'list]' k ↦ x ∈ l , P"
(at level 200, l at level 10, k binder, x binder, right associativity,
format "[∧ list] k ↦ x ∈ l , P").
Reserved Notation "'[∧' 'list]' x ∈ l , P"
(at level 200, l at level 10, x binder, 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 binder, x binder, right associativity,
format "[∨ list] k ↦ x ∈ l , P").
Reserved Notation "'[∨' 'list]' x ∈ l , P"
(at level 200, l at level 10, x binder, 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 binder, x binder, right associativity,
format "[∗ map] k ↦ x ∈ m , P").
Reserved Notation "'[∗' 'map]' x ∈ m , P"
(at level 200, m at level 10, x binder, right associativity,
format "[∗ map] x ∈ m , P").
Reserved Notation "'[∗' 'map]' k ↦ x1 ; x2 ∈ m1 ; m2 , P"
(at level 200, m1, m2 at level 10,
k binder, x1 binder, x2 binder, right associativity,
format "[∗ map] k ↦ x1 ; x2 ∈ m1 ; m2 , P").
Reserved Notation "'[∗' 'map]' x1 ; x2 ∈ m1 ; m2 , P"
(at level 200, m1, m2 at level 10, x1 binder, x2 binder, right associativity,
format "[∗ map] x1 ; x2 ∈ m1 ; m2 , P").
Reserved Notation "'[∧' 'map]' k ↦ x ∈ m , P"
(at level 200, m at level 10, k binder, x binder, right associativity,
format "[∧ map] k ↦ x ∈ m , P").
Reserved Notation "'[∧' 'map]' x ∈ m , P"
(at level 200, m at level 10, x binder, right associativity,
format "[∧ map] x ∈ m , P").
Reserved Notation "'[∗' 'set]' x ∈ X , P"
(at level 200, X at level 10, x binder, right associativity,
format "[∗ set] x ∈ X , P").
Reserved Notation "'[∗' 'mset]' x ∈ X , P"
(at level 200, X at level 10, x binder, right associativity,
format "[∗ mset] x ∈ X , P").
(at level 200, l at level 10, k binder, x binder, right associativity,
format "[∗ list] k ↦ x ∈ l , P").
Reserved Notation "'[∗' 'list]' x ∈ l , P"
(at level 200, l at level 10, x binder, right associativity,
format "[∗ list] x ∈ l , P").
Reserved Notation "'[∗' 'list]' k ↦ x1 ; x2 ∈ l1 ; l2 , P"
(at level 200, l1, l2 at level 10, k binder, x1 binder, x2 binder,
right associativity,
format "[∗ list] k ↦ x1 ; x2 ∈ l1 ; l2 , P").
Reserved Notation "'[∗' 'list]' x1 ; x2 ∈ l1 ; l2 , P"
(at level 200, l1, l2 at level 10, x1 binder, x2 binder, right associativity,
format "[∗ list] x1 ; x2 ∈ l1 ; l2 , P").
Reserved Notation "'[∗]' Ps" (at level 20).
Reserved Notation "'[∧' 'list]' k ↦ x ∈ l , P"
(at level 200, l at level 10, k binder, x binder, right associativity,
format "[∧ list] k ↦ x ∈ l , P").
Reserved Notation "'[∧' 'list]' x ∈ l , P"
(at level 200, l at level 10, x binder, 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 binder, x binder, right associativity,
format "[∨ list] k ↦ x ∈ l , P").
Reserved Notation "'[∨' 'list]' x ∈ l , P"
(at level 200, l at level 10, x binder, 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 binder, x binder, right associativity,
format "[∗ map] k ↦ x ∈ m , P").
Reserved Notation "'[∗' 'map]' x ∈ m , P"
(at level 200, m at level 10, x binder, right associativity,
format "[∗ map] x ∈ m , P").
Reserved Notation "'[∗' 'map]' k ↦ x1 ; x2 ∈ m1 ; m2 , P"
(at level 200, m1, m2 at level 10,
k binder, x1 binder, x2 binder, right associativity,
format "[∗ map] k ↦ x1 ; x2 ∈ m1 ; m2 , P").
Reserved Notation "'[∗' 'map]' x1 ; x2 ∈ m1 ; m2 , P"
(at level 200, m1, m2 at level 10, x1 binder, x2 binder, right associativity,
format "[∗ map] x1 ; x2 ∈ m1 ; m2 , P").
Reserved Notation "'[∧' 'map]' k ↦ x ∈ m , P"
(at level 200, m at level 10, k binder, x binder, right associativity,
format "[∧ map] k ↦ x ∈ m , P").
Reserved Notation "'[∧' 'map]' x ∈ m , P"
(at level 200, m at level 10, x binder, right associativity,
format "[∧ map] x ∈ m , P").
Reserved Notation "'[∗' 'set]' x ∈ X , P"
(at level 200, X at level 10, x binder, right associativity,
format "[∗ set] x ∈ X , P").
Reserved Notation "'[∗' 'mset]' x ∈ X , P"
(at level 200, X at level 10, x binder, right associativity,
format "[∗ mset] x ∈ X , P").
Define the scope
Declare Scope bi_scope.
Delimit Scope bi_scope with I.
Delimit Scope bi_scope with I.