fp_library/classes/
monoid.rs

1//! A type class for types that have an identity element and an associative binary operation.
2//!
3//! ### Examples
4//!
5//! ```
6//! use fp_library::functions::*;
7//!
8//! let x: String = empty();
9//! assert_eq!(x, "".to_string());
10//! ```
11
12use super::semigroup::Semigroup;
13
14/// A type class for types that have an identity element and an associative binary operation.
15///
16/// ### Laws
17///
18/// `Monoid` instances must satisfy the identity laws:
19/// * Left Identity: `append(empty(), a) = a`.
20/// * Right Identity: `append(a, empty()) = a`.
21pub trait Monoid: Semigroup {
22	/// The identity element.
23	///
24	/// This method returns the identity element of the monoid.
25	///
26	/// ### Type Signature
27	///
28	/// `forall m. Monoid m => () -> m`
29	///
30	/// ### Returns
31	///
32	/// The identity element.
33	///
34	/// ### Examples
35	///
36	/// ```
37	/// use fp_library::functions::*;
38	///
39	/// let x: String = empty();
40	/// assert_eq!(x, "".to_string());
41	/// ```
42	fn empty() -> Self;
43}
44
45/// The identity element.
46///
47/// Free function version that dispatches to [the type class' associated function][`Monoid::empty`].
48///
49/// ### Type Signature
50///
51/// `forall m. Monoid m => () -> m`
52///
53/// ### Type Parameters
54///
55/// * `M`: The type of the monoid.
56///
57/// ### Returns
58///
59/// The identity element.
60///
61/// ### Examples
62///
63/// ```
64/// use fp_library::functions::*;
65///
66/// let x: String = empty();
67/// assert_eq!(x, "".to_string());
68/// ```
69pub fn empty<M: Monoid>() -> M {
70	M::empty()
71}
fp_library/classes/monoid.rs

fp_library/classes/
monoid.rs
