- In mathematics, a
setoid (X, ~) is a set (or type) X
equipped with an
equivalence relation ~. A
setoid may also be
called E-set,
Bishop set, or extensional...
-
equipped with an
equivalence relation or a
partition is
sometimes called a
setoid,
typically in type
theory and
proof theory. A
partition of a set X is a...
-
equivalence relation –
Generalization of
equivalence classes to
scheme theory Setoid –
Mathematical construction of a set with an
equivalence relation Transversal...
-
given two elements. This
definition is
equivalent to a
partial order on a
setoid,
where equality is
taken to be a
defined equivalence relation rather than...
- {\displaystyle X}
together with the
relation ∼ {\displaystyle \,\sim \,} is
called a
setoid. The
equivalence class of a {\displaystyle a}
under ∼ , {\displaystyle \...
- types,
setoids (sets
explicitly equipped with an
equivalence relation) are
often used
instead of
quotient types. However,
unlike with
setoids, many type...
- → C {\displaystyle h\circ g:A\rightarrow C} .
Special cases include:
Setoids: sets that come with an
equivalence relation, G-sets: sets
equipped with...
-
apartness relation is
known as a
constructive setoid. A
function f : A → B {\displaystyle f:A\to B}
between such
setoids A {\displaystyle A} and B {\displaystyle...
- may be
modeled by
refinement types, and
quotient sets may be
replaced by
setoids.) The
characteristic function F {\displaystyle F} of a set S {\displaystyle...
- more
commonly used,
particularly to
define setoids,
sometimes called partial setoids.
Forming a
partial setoid from a type and a PER is
analogous to forming...
