# Finite¶

The category of domains composed of a finite set of elements. We include the functions lookup and index to give a bijection between the finite set and an initial segment of positive integers.

=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
convert: % -> InputForm
from ConvertibleTo InputForm
enumerate: () -> List %
enumerate() returns list of elements of the set.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
index: PositiveInteger -> %
index(i) takes a positive integer i less than or equal to size() and returns the i-th element of the set. This operation establishes a bijection between the elements of the finite set and 1..size().
latex: % -> String
from SetCategory
lookup: % -> PositiveInteger
lookup(x) returns a positive integer such that x = index lookup x.
random: () -> %
random() returns a random element from the set.
size: () -> NonNegativeInteger
size() returns the number of elements in the set.
smaller?: (%, %) -> Boolean
from Comparable

BasicType

Comparable

SetCategory