fp_library/typeclasses/
monoid.rs

1use crate::{hkt::Apply0, typeclasses::Semigroup};
2
3/// A typeclass for monoids.
4///
5/// `Monoid` extends [`Semigroup`] with an identity element. A monoid is a set
6/// equipped with an associative binary operation and an identity element.
7///
8/// In functional programming, monoids are useful for combining values in
9/// a consistent way, especially when accumulating results or folding
10/// collections.
11///
12/// # Laws
13///
14/// Monoid instances must satisfy the following laws:
15/// * Left identity: `append(empty(), x) = x`.
16/// * Right identity: `append(x, empty()) = x`.
17/// * Associativity: `append(append(x, y), z) = append(x, append(y, z))`.
18///
19/// # Examples
20///
21/// Common monoids include:
22/// * Strings with concatenation and empty string.
23/// * Numbers with addition and zero.
24/// * Numbers with multiplication and one.
25/// * Lists with concatenation and empty list.
26pub trait Monoid<'a>: Semigroup<'a> {
27	/// Returns the identity element for the monoid.
28	///
29	/// # Type Signature
30	///
31	/// `forall a. Monoid a => () -> a`
32	///
33	/// # Returns
34	///
35	/// The identity element which, when combined with any other element
36	/// using the semigroup operation, leaves the other element unchanged.
37	fn empty() -> Apply0<Self>;
38}
39
40/// Returns the identity element for the monoid.
41///
42/// Free function version that dispatches to [the typeclass' associated function][`Monoid::empty`].
43///
44/// # Type Signature
45///
46/// `forall a. Monoid a => () -> a`
47///
48/// # Returns
49///
50/// The identity element which, when combined with any other element
51/// using the semigroup operation, leaves the other element unchanged.
52///
53/// # Examples
54///
55/// ```
56/// use fp_library::{brands::StringBrand, functions::empty};
57///
58/// assert_eq!(empty::<StringBrand>(), "".to_string());
59/// ```
60pub fn empty<'a, Brand: Monoid<'a>>() -> Apply0<Brand> {
61	Brand::empty()
62}
fp_library/typeclasses/monoid.rs

fp_library/typeclasses/
monoid.rs
