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//! Types that form a semiring with addition and multiplication operations.
//!
//! ### Examples
//!
//! ```
//! use fp_library::classes::Semiring;
//!
//! assert_eq!(i32::add(2, 3), 5);
//! assert_eq!(i32::multiply(2, 3), 6);
//! assert_eq!(i32::zero(), 0);
//! assert_eq!(i32::one(), 1);
//! ```
#[fp_macros::document_module]
mod inner {
use fp_macros::*;
/// A type class for types that form a semiring.
///
/// A semiring provides two binary operations (addition and multiplication)
/// with their respective identity elements (zero and one).
///
/// ### Laws
///
/// * Commutative monoid under addition:
/// - `add(a, add(b, c)) = add(add(a, b), c)` (associativity)
/// - `add(zero, a) = a` and `add(a, zero) = a` (identity)
/// - `add(a, b) = add(b, a)` (commutativity)
/// * Monoid under multiplication:
/// - `multiply(a, multiply(b, c)) = multiply(multiply(a, b), c)` (associativity)
/// - `multiply(one, a) = a` and `multiply(a, one) = a` (identity)
/// * Left distributivity: `multiply(a, add(b, c)) = add(multiply(a, b), multiply(a, c))`
/// * Right distributivity: `multiply(add(a, b), c) = add(multiply(a, c), multiply(b, c))`
/// * Annihilation: `multiply(zero, a) = multiply(a, zero) = zero`
///
/// **Note:** Integer types do not strictly satisfy these laws due to overflow.
#[document_examples]
///
/// ```
/// use fp_library::classes::Semiring;
///
/// // Distributivity: multiply(a, add(b, c)) = add(multiply(a, b), multiply(a, c))
/// let a = 2i32;
/// let b = 3i32;
/// let c = 4i32;
/// assert_eq!(
/// i32::multiply(a, i32::add(b, c)),
/// i32::add(i32::multiply(a, b), i32::multiply(a, c)),
/// );
/// ```
pub trait Semiring {
/// Adds two values.
#[document_signature]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The sum of the two values.")]
#[document_examples]
///
/// ```
/// use fp_library::classes::Semiring;
///
/// assert_eq!(i32::add(2, 3), 5);
/// ```
fn add(
a: Self,
b: Self,
) -> Self;
/// Returns the additive identity element.
#[document_signature]
///
#[document_returns("The additive identity (zero).")]
#[document_examples]
///
/// ```
/// use fp_library::classes::Semiring;
///
/// assert_eq!(i32::zero(), 0);
/// ```
fn zero() -> Self;
/// Multiplies two values.
#[document_signature]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The product of the two values.")]
#[document_examples]
///
/// ```
/// use fp_library::classes::Semiring;
///
/// assert_eq!(i32::multiply(2, 3), 6);
/// ```
fn multiply(
a: Self,
b: Self,
) -> Self;
/// Returns the multiplicative identity element.
#[document_signature]
///
#[document_returns("The multiplicative identity (one).")]
#[document_examples]
///
/// ```
/// use fp_library::classes::Semiring;
///
/// assert_eq!(i32::one(), 1);
/// ```
fn one() -> Self;
}
/// Adds two values.
///
/// Free function version that dispatches to [`Semiring::add`].
#[document_signature]
///
#[document_type_parameters("The semiring type.")]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The sum of the two values.")]
#[document_examples]
///
/// ```
/// use fp_library::classes::semiring::add;
///
/// assert_eq!(add(2i32, 3), 5);
/// ```
pub fn add<S: Semiring>(
a: S,
b: S,
) -> S {
S::add(a, b)
}
/// Returns the additive identity element.
///
/// Free function version that dispatches to [`Semiring::zero`].
#[document_signature]
///
#[document_type_parameters("The semiring type.")]
///
#[document_returns("The additive identity (zero).")]
#[document_examples]
///
/// ```
/// use fp_library::classes::semiring::zero;
///
/// assert_eq!(zero::<i32>(), 0);
/// ```
pub fn zero<S: Semiring>() -> S {
S::zero()
}
/// Multiplies two values.
///
/// Free function version that dispatches to [`Semiring::multiply`].
#[document_signature]
///
#[document_type_parameters("The semiring type.")]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The product of the two values.")]
#[document_examples]
///
/// ```
/// use fp_library::classes::semiring::multiply;
///
/// assert_eq!(multiply(2i32, 3), 6);
/// ```
pub fn multiply<S: Semiring>(
a: S,
b: S,
) -> S {
S::multiply(a, b)
}
/// Returns the multiplicative identity element.
///
/// Free function version that dispatches to [`Semiring::one`].
#[document_signature]
///
#[document_type_parameters("The semiring type.")]
///
#[document_returns("The multiplicative identity (one).")]
#[document_examples]
///
/// ```
/// use fp_library::classes::semiring::one;
///
/// assert_eq!(one::<i32>(), 1);
/// ```
pub fn one<S: Semiring>() -> S {
S::one()
}
macro_rules! impl_semiring_int {
($($t:ty),+) => {
$(
impl Semiring for $t {
/// Adds two values using wrapping addition.
#[document_signature]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The sum (wrapping on overflow).")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::add(2 as ", stringify!($t), ", 3 as ", stringify!($t), "), 5 as ", stringify!($t), ");")]
/// ```
fn add(
a: Self,
b: Self,
) -> Self {
a.wrapping_add(b)
}
/// Returns the additive identity (`0`).
#[document_signature]
///
#[document_returns("Zero.")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::zero(), 0 as ", stringify!($t), ");")]
/// ```
fn zero() -> Self {
0
}
/// Multiplies two values using wrapping multiplication.
#[document_signature]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The product (wrapping on overflow).")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::multiply(2 as ", stringify!($t), ", 3 as ", stringify!($t), "), 6 as ", stringify!($t), ");")]
/// ```
fn multiply(
a: Self,
b: Self,
) -> Self {
a.wrapping_mul(b)
}
/// Returns the multiplicative identity (`1`).
#[document_signature]
///
#[document_returns("One.")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::one(), 1 as ", stringify!($t), ");")]
/// ```
fn one() -> Self {
1
}
}
)+
};
}
impl_semiring_int!(i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize);
macro_rules! impl_semiring_float {
($($t:ty),+) => {
$(
impl Semiring for $t {
/// Adds two values using the `+` operator.
#[document_signature]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The sum.")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::add(2.0 as ", stringify!($t), ", 3.0 as ", stringify!($t), "), 5.0 as ", stringify!($t), ");")]
/// ```
fn add(
a: Self,
b: Self,
) -> Self {
a + b
}
/// Returns the additive identity (`0.0`).
#[document_signature]
///
#[document_returns("Zero.")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::zero(), 0.0 as ", stringify!($t), ");")]
/// ```
fn zero() -> Self {
0.0
}
/// Multiplies two values using the `*` operator.
#[document_signature]
///
#[document_parameters("The first value.", "The second value.")]
///
#[document_returns("The product.")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::multiply(2.0 as ", stringify!($t), ", 3.0 as ", stringify!($t), "), 6.0 as ", stringify!($t), ");")]
/// ```
fn multiply(
a: Self,
b: Self,
) -> Self {
a * b
}
/// Returns the multiplicative identity (`1.0`).
#[document_signature]
///
#[document_returns("One.")]
#[document_examples]
///
/// ```
#[doc = concat!("use fp_library::classes::Semiring;")]
///
#[doc = concat!("assert_eq!(<", stringify!($t), ">::one(), 1.0 as ", stringify!($t), ");")]
/// ```
fn one() -> Self {
1.0
}
}
)+
};
}
impl_semiring_float!(f32, f64);
}
pub use inner::*;