This coq library aims to formalize a substantial body of mathematics using the univalent point of view.
UniMath uses both ASCII and Unicode notation. Below we give an overview of the most important symbols.
To see how to input a specific Unicode character, type
C-u C-x =
(meaning: hold CTRL, then press u and x; release CTRL, press =) while hovering over that character.
Below is a partial list of Unicode symbols and identifiers used in UniMath.
Item | UniMath symbol | Unicode input | UniMath ASCII alternative |
---|---|---|---|
Type and term constructors | |||
Product type | ∏ (x : A), B |
\prod |
forall x : A, B |
Function type | A → B |
\to |
A -> B |
Lambda abstraction | λ x, e |
\lambda |
fun x => e |
Sigma type | ∑ (x : A), B |
\sum |
total2 (fun x => B) |
Cartesian product type | X × Y |
\times |
dirprod X Y |
Pair term | a,,b |
a,,b |
|
Coproduct type | X ⨿ Y |
\union then select from menu |
coprod X Y |
Identity type | a = b |
a = b |
|
Univalent logic in hProp |
|||
Conjunction | A ∧ B |
\and |
hconj A B |
Disjunction | A ∨ B |
\or |
hdisj A B |
Implication | A ⇒ B |
\=> |
himpl A B |
Negation | ¬ X |
\neg |
hneg X |
Universal quantification | ∀ x , P x |
\forall |
forall_hProp A |
Existential quantification | ∃ x, P x |
\ex |
hexists P |
Propositional truncation | ∥ A ∥ |
\\|\| |
ishinh A |
Category theory | |||
Object type of C |
ob C or C |
||
Morphisms | C⟦a,b⟧ |
\[[ and \]] |
a --> b |
Functor F on objects |
F a |
||
Functor F on morphisms |
#F f |