Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# Library Coq.Init.Notations

These are the notations whose level and associativity are imposed by Coq
Notations for propositional connectives
Reserved Notation "x -> y" (at level 99, right associativity, y at level 200).
Reserved Notation "x <-> y" (at level 95, no associativity).
Reserved Notation "x /\ y" (at level 80, right associativity).
Reserved Notation "x \/ y" (at level 85, right associativity).
Reserved Notation "~ x" (at level 75, right associativity).
Notations for equality and inequalities
Reserved Notation "x = y :> T"
(at level 70, y at next level, no associativity).
Reserved Notation "x = y" (at level 70, no associativity).
Reserved Notation "x = y = z"
(at level 70, no associativity, y at next level).
Reserved Notation "x <> y :> T"
(at level 70, y at next level, no associativity).
Reserved Notation "x <> y" (at level 70, no associativity).
Reserved Notation "x <= y" (at level 70, no associativity).
Reserved Notation "x < y" (at level 70, no associativity).
Reserved Notation "x >= y" (at level 70, no associativity).
Reserved Notation "x > y" (at level 70, no associativity).
Reserved Notation "x <= y <= z" (at level 70, y at next level).
Reserved Notation "x <= y < z" (at level 70, y at next level).
Reserved Notation "x < y < z" (at level 70, y at next level).
Reserved Notation "x < y <= z" (at level 70, y at next level).
Arithmetical notations (also used for type constructors)
Reserved Notation "x + y" (at level 50, left associativity).
Reserved Notation "x - y" (at level 50, left associativity).
Reserved Notation "x * y" (at level 40, left associativity).
Reserved Notation "x / y" (at level 40, left associativity).
Reserved Notation "- x" (at level 35, right associativity).
Reserved Notation "/ x" (at level 35, right associativity).
Reserved Notation "x ^ y" (at level 30, right associativity).
Notations for booleans
Reserved Notation "x || y" (at level 50, left associativity).
Reserved Notation "x && y" (at level 40, left associativity).
Notations for pairs
Reserved Notation "( x , y , .. , z )"
(at level 0, format "( '[' x , '/' y , '/' .. , '/' z ']' )").
Notation "{ x }" is reserved and has a special status as component of other notations such as "{ A } + { B }" and "A + { B }" (which are at the same level as "x + y"); "{ x }" is at level 0 to factor with "{ x : A | P }"
Reserved Notation "{ x }" (at level 0, x at level 99).
Notations for sigma-types or subsets
#[warning="-closed-notation-not-level-0"]
Reserved Notation "{ A } + { B }" (at level 50, left associativity).
#[warning="-postfix-notation-not-level-1"]
Reserved Notation "A + { B }" (at level 50, left associativity).
Reserved Notation "{ x | P }" (at level 0, x at level 99).
Reserved Notation "{ x | P & Q }" (at level 0, x at level 99).
Reserved Notation "{ x : A | P }" (at level 0, x at level 99).
Reserved Notation "{ x : A | P & Q }" (at level 0, x at level 99).
Reserved Notation "{ x & P }" (at level 0, x at level 99).
Reserved Notation "{ x & P & Q }" (at level 0, x at level 99).
Reserved Notation "{ x : A & P }" (at level 0, x at level 99).
Reserved Notation "{ x : A & P & Q }" (at level 0, x at level 99).
Reserved Notation "{ ' pat | P }"
(at level 0, pat strict pattern, format "{ ' pat | P }").
Reserved Notation "{ ' pat | P & Q }"
(at level 0, pat strict pattern, format "{ ' pat | P & Q }").
Reserved Notation "{ ' pat : A | P }"
(at level 0, pat strict pattern, format "{ ' pat : A | P }").
Reserved Notation "{ ' pat : A | P & Q }"
(at level 0, pat strict pattern, format "{ ' pat : A | P & Q }").
Reserved Notation "{ ' pat & P }"
(at level 0, pat strict pattern, format "{ ' pat & P }").
Reserved Notation "{ ' pat & P & Q }"
(at level 0, pat strict pattern, format "{ ' pat & P & Q }").
Reserved Notation "{ ' pat : A & P }"
(at level 0, pat strict pattern, format "{ ' pat : A & P }").
Reserved Notation "{ ' pat : A & P & Q }"
(at level 0, pat strict pattern, format "{ ' pat : A & P & Q }").
Support for Gonthier-Ssreflect's "if c is pat then u else v"
Module IfNotations.
Notation "'if' c 'is' p 'then' u 'else' v" :=
(match c with p => u | _ => v end)
(at level 200, p pattern at level 100).
End IfNotations.
Notations for first and second projections
Reserved Notation "p .1" (at level 1, left associativity, format "p .1").
Reserved Notation "p .2" (at level 1, left associativity, format "p .2").
Scopes
Declare Scope core_scope.
Delimit Scope core_scope with core.
Declare Scope function_scope.
Delimit Scope function_scope with function.
Bind Scope function_scope with Funclass.
Declare Scope type_scope.
Delimit Scope type_scope with type.
Bind Scope type_scope with Sortclass.
Open Scope core_scope.
Open Scope function_scope.
Open Scope type_scope.