kex docs Standard Library

Algebra

Algebraic structures: combining values associatively.

Kex traits do not inherit from one another, so concrete types explicitly implement every structure whose laws they satisfy.

Monoid is "these two values combine, and there is a neutral one". Numbers, strings and lists all satisfy it, which is what lets repeat be written once:

"ab".repeat(3)   # => "ababab"
[1].repeat(2)    # => [1, 1]
5.repeat(3)      # => 15

Ordering and comparison (Ordering, Comparable) live in comparable.kex.

trait Monoid

Types whose values combine associatively and have a neutral element.

Implemented by Integer (addition), String and List (concatenation), Map and both Set flavours (union), and Ordering ("first decision wins" — declared beside Ordering in comparable.kex).

Implemented by Integer, String, [A], Ordering, Map<K, V>, Queue<A>, Set<A>, UnorderedSet<A>, Stack<A>.

Required functions

An implementor writes these.

identity

identity : This

The neutral element: combining it with any value gives that value back.

combine must be associative and identity neutral on both sides.

Returns the identity

Examples
Integer.identity   # => 0
String.identity    # => ""

combine

combine(other: This) -> This

Combines this value with other.

Must be associative: a.combine(b).combine(c) and a.combine(b.combine(c)) have to agree.

Parameters
other
the value to combine with

Returns the combined value

Examples
5.combine(3)          # => 8
"ab".combine("cd")    # => "abcd"
[1].combine([2])      # => [1, 2]

Folding a list of values into one

parts.reduce(String.identity) { |acc, s| acc.combine(s) }

Provided functions

Every implementor gets these, written in terms of the required functions.

repeat

repeat(n: Integer) -> This

Combines this value with itself n times.

Repeating zero times gives the identity: "" for a string, 0 for an integer, [] for a list. A negative count is invalid and ends the program.

Parameters
n
how many copies to combine; must not be negative

Returns the repeated value

Examples
"ab".repeat(3)   # => "ababab"
[1].repeat(2)    # => [1, 1]
5.repeat(3)      # => 15
"x".repeat(0)    # => ""

Drawing a separator line

IO.printLine("-".repeat(40))

trait Group

A Monoid in which every value has an inverse that combines with it to give the identity.

Implemented by Integer, where the inverse is negation.

Implemented by Integer.

Required functions

An implementor writes these.

identity

identity : This

The neutral element.

Returns the identity

combine

combine : This -> This

Combines this value with other.

Returns the combined value

inverse

inverse : This

The value that combines with this one to give the identity.

Returns the inverse

Examples
5.inverse             # => -5
5.combine(5.inverse)  # => 0

extends Integer

More functions for Integer, added by this module.

Implements Monoid, Group.

Implements Monoid, Group over Integer for addition.

identity Monoid Group

0: the neutral element for addition.

Returns Integer — zero

Examples
Integer.identity   # => 0

combine Monoid Group

combine(other: This) -> This

Adds other to this integer. Addition is the monoid operation for Integer.

Parameters
other
the integer to add

Returns the sum

Examples
5.combine(3)   # => 8

inverse Group

inverse : This

The additive inverse: this integer negated.

Returns the negation

Examples
5.inverse    # => -5
(-5).inverse # => 5

extends String

More functions for String, added by this module.

Implements Monoid.

Implements Monoid over String for concatenation.

identity Monoid

"": the neutral element for concatenation.

Returns String — the empty string

Examples
String.identity   # => ""

combine Monoid

combine(other: This) -> This

Concatenates other onto this string. Concatenation is the monoid operation for String.

Parameters
other
the string to append

Returns the concatenation

Examples
"ab".combine("cd")   # => "abcd"

extends [A]

More functions for List, added by this module.

Implements Monoid.

Implements Monoid over List<A> for concatenation.

identity Monoid

[]: the neutral element for concatenation.

Returns [A] — the empty list

Examples
[1].combine(List.identity)   # => [1]

combine Monoid

combine(other: This) -> This

Concatenates other onto this list. Concatenation is the monoid operation for List.

Parameters
other
the list to append

Returns the concatenation

Examples
[1].combine([2, 3])   # => [1, 2, 3]

Flattening a list of lists

groups.reduce([]) { |acc, g| acc.combine(g) }