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//! Data structures that can be folded into a single value from the left or right.
//!
//! ### Examples
//!
//! ```
//! use fp_library::{
//! brands::*,
//! functions::explicit::*,
//! };
//!
//! let x = Some(5);
//! let y = fold_right::<RcFnBrand, OptionBrand, _, _, _, _>(|a, b| a + b, 10, x);
//! assert_eq!(y, 15);
//! ```
#[fp_macros::document_module]
mod inner {
use {
crate::{
classes::*,
kinds::*,
types::*,
},
fp_macros::*,
};
/// A type class for structures that can be folded to a single value.
///
/// A `Foldable` represents a structure that can be folded over to combine its elements
/// into a single result.
///
/// ### Minimal Implementation
///
/// A minimal implementation of `Foldable` requires implementing either [`Foldable::fold_right`] or [`Foldable::fold_map`].
///
/// * If [`Foldable::fold_right`] is implemented, [`Foldable::fold_map`] and [`Foldable::fold_left`] are derived from it.
/// * If [`Foldable::fold_map`] is implemented, [`Foldable::fold_right`] is derived from it, and [`Foldable::fold_left`] is derived from the derived [`Foldable::fold_right`].
///
/// Note that [`Foldable::fold_left`] is not sufficient on its own because the default implementations of [`Foldable::fold_right`] and [`Foldable::fold_map`] do not depend on it.
///
/// ### Laws
///
/// `Foldable` instances must be internally consistent:
/// * fold_map/fold_right consistency: `fold_map(f, fa) = fold_right(|a, m| append(f(a), m), empty(), fa)`.
#[document_examples]
///
/// Foldable laws for [`Vec`]:
///
/// ```
/// use fp_library::{
/// brands::*,
/// functions::{
/// explicit::{
/// fold_map,
/// fold_right,
/// },
/// *,
/// },
/// };
///
/// let xs = vec![1, 2, 3];
/// let f = |a: i32| a.to_string();
///
/// // fold_map/fold_right consistency:
/// // fold_map(f, fa) = fold_right(|a, m| append(f(a), m), empty(), fa)
/// assert_eq!(
/// fold_map::<RcFnBrand, VecBrand, _, _, _, _>(f, xs.clone()),
/// fold_right::<RcFnBrand, VecBrand, _, _, _, _>(
/// |a: i32, m: String| append(f(a), m),
/// empty::<String>(),
/// xs,
/// ),
/// );
/// ```
#[kind(type Of<'a, A: 'a>: 'a;)]
pub trait Foldable {
/// Folds the structure by applying a function from right to left.
///
/// This method performs a right-associative fold of the structure.
#[document_signature]
///
#[document_type_parameters(
"The lifetime of the elements.",
"The brand of the cloneable function to use.",
"The type of the elements in the structure.",
"The type of the accumulator."
)]
///
#[document_parameters(
"The function to apply to each element and the accumulator.",
"The initial value of the accumulator.",
"The structure to fold."
)]
///
#[document_returns("The final accumulator value.")]
#[document_examples]
///
/// ```
/// use fp_library::{
/// brands::*,
/// functions::explicit::*,
/// };
///
/// let x = Some(5);
/// let y = fold_right::<RcFnBrand, OptionBrand, _, _, _, _>(|a, b| a + b, 10, x);
/// assert_eq!(y, 15);
/// ```
fn fold_right<'a, FnBrand, A: 'a + Clone, B: 'a>(
func: impl Fn(A, B) -> B + 'a,
initial: B,
fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
) -> B
where
FnBrand: LiftFn + 'a, {
let f = <FnBrand as LiftFn>::new(move |(a, b)| func(a, b));
let m = Self::fold_map::<FnBrand, A, Endofunction<FnBrand, B>>(
move |a: A| {
let f = f.clone();
Endofunction::<FnBrand, B>::new(<FnBrand as LiftFn>::new(move |b| {
f((a.clone(), b))
}))
},
fa,
);
m.0(initial)
}
/// Folds the structure by applying a function from left to right.
///
/// This method performs a left-associative fold of the structure.
#[document_signature]
///
#[document_type_parameters(
"The lifetime of the elements.",
"The brand of the cloneable function to use.",
"The type of the elements in the structure.",
"The type of the accumulator."
)]
///
#[document_parameters(
"The function to apply to the accumulator and each element.",
"The initial value of the accumulator.",
"The structure to fold."
)]
///
#[document_returns("The final accumulator value.")]
#[document_examples]
///
/// ```
/// use fp_library::{
/// brands::*,
/// functions::explicit::*,
/// };
///
/// let x = Some(5);
/// let y = fold_left::<RcFnBrand, OptionBrand, _, _, _, _>(|b, a| b + a, 10, x);
/// assert_eq!(y, 15);
/// ```
fn fold_left<'a, FnBrand, A: 'a + Clone, B: 'a>(
func: impl Fn(B, A) -> B + 'a,
initial: B,
fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
) -> B
where
FnBrand: LiftFn + 'a, {
let f = <FnBrand as LiftFn>::new(move |(b, a)| func(b, a));
let m = Self::fold_right::<FnBrand, A, Endofunction<FnBrand, B>>(
move |a: A, k: Endofunction<'a, FnBrand, B>| {
let f = f.clone();
// k is the "rest" of the computation.
// We want to perform "current" (f(b, a)) then "rest".
// Endofunction composition is f . g (f after g).
// So we want k . current.
// append(k, current).
let current =
Endofunction::<FnBrand, B>::new(<FnBrand as LiftFn>::new(move |b| {
f((b, a.clone()))
}));
Semigroup::append(k, current)
},
Endofunction::<FnBrand, B>::empty(),
fa,
);
m.0(initial)
}
/// Maps values to a monoid and combines them.
///
/// This method maps each element of the structure to a monoid and then combines the results using the monoid's `append` operation.
#[document_signature]
///
#[document_type_parameters(
"The lifetime of the elements.",
"The brand of the cloneable function to use.",
"The type of the elements in the structure.",
"The type of the monoid."
)]
///
#[document_parameters(
"The function to map each element to a monoid.",
"The structure to fold."
)]
///
#[document_returns("The combined monoid value.")]
#[document_examples]
///
/// ```
/// use fp_library::{
/// brands::*,
/// functions::explicit::*,
/// };
///
/// let x = Some(5);
/// let y = fold_map::<RcFnBrand, OptionBrand, _, _, _, _>(|a: i32| a.to_string(), x);
/// assert_eq!(y, "5".to_string());
/// ```
fn fold_map<'a, FnBrand, A: 'a + Clone, M>(
func: impl Fn(A) -> M + 'a,
fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
) -> M
where
M: Monoid + 'a,
FnBrand: LiftFn + 'a, {
Self::fold_right::<FnBrand, A, M>(move |a, m| M::append(func(a), m), M::empty(), fa)
}
}
}
pub use inner::*;