fp_library/types/

option.rs

//! Functional programming trait implementations for the standard library [`Option`] type.
//!
//! Extends `Option` with [`Functor`](crate::classes::Functor), [`Monad`](crate::classes::semimonad::Semimonad), [`Foldable`](crate::classes::Foldable), [`Traversable`](crate::classes::Traversable), [`Filterable`](crate::classes::Filterable), and [`Witherable`](crate::classes::Witherable) instances.

#[fp_macros::document_module]
mod inner {
	use {
		crate::{
			Apply,
			brands::OptionBrand,
			classes::{
				Applicative,
				ApplyFirst,
				ApplySecond,
				CloneableFn,
				Compactable,
				Filterable,
				Foldable,
				Functor,
				Lift,
				Monoid,
				ParFoldable,
				Pointed,
				Semiapplicative,
				Semimonad,
				SendCloneableFn,
				Traversable,
				Witherable,
				foldable_with_index::FoldableWithIndex,
				functor_with_index::FunctorWithIndex,
				traversable_with_index::TraversableWithIndex,
			},
			impl_kind,
			kinds::*,
		},
		fp_macros::*,
	};

	impl_kind! {
		for OptionBrand {
			type Of<'a, A: 'a>: 'a = Option<A>;
		}
	}

	impl Functor for OptionBrand {
		/// Maps a function over the value in the option.
		///
		/// This method applies a function to the value inside the option, producing a new option with the transformed value. If the option is `None`, it returns `None`.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the value.",
			"The type of the value inside the option.",
			"The type of the result of applying the function."
		)]
		///
		#[document_parameters("The function to apply to the value.", "The option to map over.")]
		///
		#[document_returns(
			"A new option containing the result of applying the function, or `None`."
		)]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let y = map::<OptionBrand, _, _>(|i| i * 2, x);
		/// assert_eq!(y, Some(10));
		/// ```
		fn map<'a, A: 'a, B: 'a>(
			func: impl Fn(A) -> B + 'a,
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>) {
			fa.map(func)
		}
	}

	impl Lift for OptionBrand {
		/// Lifts a binary function into the option context.
		///
		/// This method lifts a binary function to operate on values within the option context.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The type of the first option's value.",
			"The type of the second option's value.",
			"The return type of the function."
		)]
		///
		#[document_parameters(
			"The binary function to apply.",
			"The first option.",
			"The second option."
		)]
		///
		#[document_returns("`Some(f(a, b))` if both options are `Some`, otherwise `None`.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(1);
		/// let y = Some(2);
		/// let z = lift2::<OptionBrand, _, _, _>(|a, b| a + b, x, y);
		/// assert_eq!(z, Some(3));
		/// ```
		fn lift2<'a, A, B, C>(
			func: impl Fn(A, B) -> C + 'a,
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
			fb: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>),
		) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, C>)
		where
			A: 'a,
			B: 'a,
			C: 'a, {
			fa.zip(fb).map(|(a, b)| func(a, b))
		}
	}

	impl Pointed for OptionBrand {
		/// Wraps a value in an option.
		///
		/// This method wraps a value in an option context.
		#[document_signature]
		///
		#[document_type_parameters("The lifetime of the value.", "The type of the value to wrap.")]
		///
		#[document_parameters("The value to wrap.")]
		///
		#[document_returns("`Some(a)`.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	functions::*,
		/// };
		///
		/// let x = pure::<OptionBrand, _>(5);
		/// assert_eq!(x, Some(5));
		/// ```
		fn pure<'a, A: 'a>(a: A) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>) {
			Some(a)
		}
	}

	impl ApplyFirst for OptionBrand {}
	impl ApplySecond for OptionBrand {}

	impl Semiapplicative for OptionBrand {
		/// Applies a wrapped function to a wrapped value.
		///
		/// This method applies a function wrapped in an option to a value wrapped in an option.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The brand of the cloneable function wrapper.",
			"The type of the input value.",
			"The type of the output value."
		)]
		///
		#[document_parameters(
			"The option containing the function.",
			"The option containing the value."
		)]
		///
		#[document_returns("`Some(f(a))` if both are `Some`, otherwise `None`.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	classes::*,
		/// 	functions::*,
		/// };
		///
		/// let f = Some(cloneable_fn_new::<RcFnBrand, _, _>(|x: i32| x * 2));
		/// let x = Some(5);
		/// let y = apply::<RcFnBrand, OptionBrand, _, _>(f, x);
		/// assert_eq!(y, Some(10));
		/// ```
		fn apply<'a, FnBrand: 'a + CloneableFn, A: 'a + Clone, B: 'a>(
			ff: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, <FnBrand as CloneableFn>::Of<'a, A, B>>),
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>) {
			match (ff, fa) {
				(Some(f), Some(a)) => Some(f(a)),
				_ => None,
			}
		}
	}

	impl Semimonad for OptionBrand {
		/// Chains option computations.
		///
		/// This method chains two option computations, where the second computation depends on the result of the first.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The type of the result of the first computation.",
			"The type of the result of the second computation."
		)]
		///
		#[document_parameters(
			"The first option.",
			"The function to apply to the value inside the option."
		)]
		///
		#[document_returns(
			"The result of applying `f` to the value if `ma` is `Some`, otherwise `None`."
		)]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let y = bind::<OptionBrand, _, _>(x, |i| Some(i * 2));
		/// assert_eq!(y, Some(10));
		/// ```
		fn bind<'a, A: 'a, B: 'a>(
			ma: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
			func: impl Fn(A) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>) + 'a,
		) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>) {
			ma.and_then(func)
		}
	}

	impl Foldable for OptionBrand {
		/// Folds the option from the right.
		///
		/// This method performs a right-associative fold of the option. If the option is `Some(a)`, it applies the function to `a` and the initial value. If `None`, it returns the initial value.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The brand of the cloneable function to use.",
			"The type of the elements in the structure.",
			"The type of the accumulator."
		)]
		///
		#[document_parameters("The folding function.", "The initial value.", "The option to fold.")]
		///
		#[document_returns("`func(a, initial)` if `fa` is `Some(a)`, otherwise `initial`.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// 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: CloneableFn + 'a, {
			match fa {
				Some(a) => func(a, initial),
				None => initial,
			}
		}

		/// Folds the option from the left.
		///
		/// This method performs a left-associative fold of the option. If the option is `Some(a)`, it applies the function to the initial value and `a`. If `None`, it returns the initial value.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"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 option to fold."
		)]
		///
		#[document_returns("`f(initial, a)` if `fa` is `Some(a)`, otherwise `initial`.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// 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: CloneableFn + 'a, {
			match fa {
				Some(a) => func(initial, a),
				None => initial,
			}
		}

		/// Maps the value to a monoid and returns it, or returns empty.
		///
		/// This method maps the element of the option to a monoid. If the option is `None`, it returns the monoid's identity element.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The brand of the cloneable function to use.",
			"The type of the elements in the structure.",
			"The type of the monoid."
		)]
		///
		#[document_parameters("The mapping function.", "The option to fold.")]
		///
		#[document_returns("`func(a)` if `fa` is `Some(a)`, otherwise `M::empty()`.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// 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: CloneableFn + 'a, {
			match fa {
				Some(a) => func(a),
				None => M::empty(),
			}
		}
	}

	impl Traversable for OptionBrand {
		/// Traverses the option with an applicative function.
		///
		/// This method maps the element of the option to a computation, evaluates it, and wraps the result in the applicative context. If `None`, it returns `pure(None)`.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The type of the elements in the traversable structure.",
			"The type of the elements in the resulting traversable structure.",
			"The applicative context."
		)]
		///
		#[document_parameters(
			"The function to apply to each element, returning a value in an applicative context.",
			"The option to traverse."
		)]
		///
		#[document_returns("The option wrapped in the applicative context.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let y = traverse::<OptionBrand, _, _, OptionBrand>(|a| Some(a * 2), x);
		/// assert_eq!(y, Some(Some(10)));
		/// ```
		fn traverse<'a, A: 'a + Clone, B: 'a + Clone, F: Applicative>(
			func: impl Fn(A) -> Apply!(<F as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>) + 'a,
			ta: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> Apply!(<F as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>)>)
		where
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>): Clone, {
			match ta {
				Some(a) => F::map(|b| Some(b), func(a)),
				None => F::pure(None),
			}
		}

		/// Sequences an option of applicative.
		///
		/// This method evaluates the computation inside the option and wraps the result in the applicative context. If `None`, it returns `pure(None)`.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The type of the elements in the traversable structure.",
			"The applicative context."
		)]
		///
		#[document_parameters("The option containing the applicative value.")]
		///
		#[document_returns("The result of the traversal.")]
		///
		/// # Returns
		///
		/// The option wrapped in the applicative context.
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(Some(5));
		/// let y = sequence::<OptionBrand, _, OptionBrand>(x);
		/// assert_eq!(y, Some(Some(5)));
		/// ```
		fn sequence<'a, A: 'a + Clone, F: Applicative>(
			ta: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Apply!(<F as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>)>)
		) -> Apply!(<F as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>)>)
		where
			Apply!(<F as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>): Clone,
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>): Clone, {
			match ta {
				Some(fa) => F::map(|a| Some(a), fa),
				None => F::pure(None),
			}
		}
	}

	impl FunctorWithIndex<()> for OptionBrand {
		/// Maps a function over the value in the option, providing the index `()`.
		#[document_signature]
		#[document_type_parameters(
			"The lifetime of the value.",
			"The type of the value inside the option.",
			"The type of the result of applying the function."
		)]
		#[document_parameters(
			"The function to apply to the value and its index.",
			"The option to map over."
		)]
		#[document_returns(
			"A new option containing the result of applying the function, or `None`."
		)]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	classes::functor_with_index::FunctorWithIndex,
		/// 	functions::*,
		/// };
		/// let x = Some(5);
		/// let y = <OptionBrand as FunctorWithIndex<()>>::map_with_index(|_, i| i * 2, x);
		/// assert_eq!(y, Some(10));
		/// ```
		fn map_with_index<'a, A: 'a, B: 'a>(
			f: impl Fn((), A) -> B + 'a,
			fa: Option<A>,
		) -> Option<B> {
			fa.map(|a| f((), a))
		}
	}

	impl FoldableWithIndex<()> for OptionBrand {
		/// Folds the option using a monoid, providing the index `()`.
		#[document_signature]
		#[document_type_parameters(
			"The lifetime of the value.",
			"The type of the value inside the option.",
			"The monoid type."
		)]
		#[document_parameters(
			"The function to apply to the value and its index.",
			"The option to fold."
		)]
		#[document_returns("The monoid value.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	classes::foldable_with_index::FoldableWithIndex,
		/// 	functions::*,
		/// };
		/// let x = Some(5);
		/// let y =
		/// 	<OptionBrand as FoldableWithIndex<()>>::fold_map_with_index(|_, i: i32| i.to_string(), x);
		/// assert_eq!(y, "5".to_string());
		/// ```
		fn fold_map_with_index<'a, A: 'a, R: Monoid>(
			f: impl Fn((), A) -> R + 'a,
			fa: Option<A>,
		) -> R {
			match fa {
				Some(a) => f((), a),
				None => R::empty(),
			}
		}
	}

	impl TraversableWithIndex<()> for OptionBrand {
		/// Traverses the option with an applicative function, providing the index `()`.
		#[document_signature]
		#[document_type_parameters(
			"The lifetime of the value.",
			"The type of the value inside the option.",
			"The type of the result.",
			"The applicative context."
		)]
		#[document_parameters(
			"The function to apply to the value and its index, returning a value in an applicative context.",
			"The option to traverse."
		)]
		#[document_returns("The option wrapped in the applicative context.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	classes::traversable_with_index::TraversableWithIndex,
		/// 	functions::*,
		/// };
		/// let x = Some(5);
		/// let y = <OptionBrand as TraversableWithIndex<()>>::traverse_with_index::<i32, i32, OptionBrand>(
		/// 	|_, i| Some(i * 2),
		/// 	x,
		/// );
		/// assert_eq!(y, Some(Some(10)));
		/// ```
		fn traverse_with_index<'a, A: 'a, B: 'a + Clone, M: Applicative>(
			f: impl Fn((), A) -> M::Of<'a, B> + 'a,
			ta: Option<A>,
		) -> M::Of<'a, Option<B>> {
			match ta {
				Some(a) => M::map(|b| Some(b), f((), a)),
				None => M::pure(None),
			}
		}
	}

	impl ParFoldable for OptionBrand {
		/// Maps the value to a monoid and returns it, or returns empty, in parallel.
		///
		/// This method maps the element of the option to a monoid. Since `Option` contains at most one element, no actual parallelism occurs, but the interface is satisfied.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The brand of the cloneable function wrapper.",
			"The element type.",
			"The monoid type."
		)]
		///
		#[document_parameters("The mapping function.", "The option to fold.")]
		///
		#[document_returns("The combined monoid value.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(1);
		/// let f = send_cloneable_fn_new::<ArcFnBrand, _, _>(|x: i32| x.to_string());
		/// let y = par_fold_map::<ArcFnBrand, OptionBrand, _, _>(f, x);
		/// assert_eq!(y, "1".to_string());
		/// ```
		fn par_fold_map<'a, FnBrand, A, M>(
			func: <FnBrand as SendCloneableFn>::SendOf<'a, A, M>,
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> M
		where
			FnBrand: 'a + SendCloneableFn,
			A: 'a + Clone + Send + Sync,
			M: Monoid + Send + Sync + 'a, {
			match fa {
				Some(a) => func(a),
				None => M::empty(),
			}
		}
	}

	impl Compactable for OptionBrand {
		/// Compacts a nested option.
		///
		/// This method flattens a nested option.
		#[document_signature]
		///
		#[document_type_parameters("The lifetime of the values.", "The type of the elements.")]
		///
		#[document_parameters("The nested option.")]
		///
		#[document_returns("The flattened option.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(Some(5));
		/// let y = compact::<OptionBrand, _>(x);
		/// assert_eq!(y, Some(5));
		/// ```
		fn compact<'a, A: 'a>(
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<
			'a,
			Apply!(<OptionBrand as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		>)
		) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>) {
			fa.flatten()
		}

		/// Separates an option of result.
		///
		/// This method separates an option of result into a pair of options.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The type of the error value.",
			"The type of the success value."
		)]
		///
		#[document_parameters("The option of result.")]
		///
		#[document_returns("A pair of options.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x: Option<Result<i32, &str>> = Some(Ok(5));
		/// let (errs, oks) = separate::<OptionBrand, _, _>(x);
		/// assert_eq!(oks, Some(5));
		/// assert_eq!(errs, None);
		/// ```
		fn separate<'a, E: 'a, O: 'a>(
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Result<O, E>>)
		) -> (
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, E>),
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, O>),
		) {
			match fa {
				Some(Ok(o)) => (None, Some(o)),
				Some(Err(e)) => (Some(e), None),
				None => (None, None),
			}
		}
	}

	impl Filterable for OptionBrand {
		/// Partitions an option based on a function that returns a result.
		///
		/// This method partitions an option based on a function that returns a result.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The type of the input value.",
			"The type of the error value.",
			"The type of the success value."
		)]
		///
		#[document_parameters("The function to apply.", "The option to partition.")]
		///
		#[document_returns("A pair of options.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let (errs, oks) =
		/// 	partition_map::<OptionBrand, _, _, _>(|a| if a > 2 { Ok(a) } else { Err(a) }, x);
		/// assert_eq!(oks, Some(5));
		/// assert_eq!(errs, None);
		/// ```
		fn partition_map<'a, A: 'a, E: 'a, O: 'a>(
			func: impl Fn(A) -> Result<O, E> + 'a,
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> (
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, E>),
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, O>),
		) {
			match fa {
				Some(a) => match func(a) {
					Ok(o) => (None, Some(o)),
					Err(e) => (Some(e), None),
				},
				None => (None, None),
			}
		}

		/// Partitions an option based on a predicate.
		///
		/// This method partitions an option based on a predicate.
		#[document_signature]
		///
		#[document_type_parameters("The lifetime of the values.", "The type of the elements.")]
		///
		#[document_parameters("The predicate.", "The option to partition.")]
		///
		#[document_returns("A pair of options.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let (not_satisfied, satisfied) = partition::<OptionBrand, _>(|a| a > 2, x);
		/// assert_eq!(satisfied, Some(5));
		/// assert_eq!(not_satisfied, None);
		/// ```
		fn partition<'a, A: 'a + Clone>(
			func: impl Fn(A) -> bool + 'a,
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> (
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) {
			match fa {
				Some(a) =>
					if func(a.clone()) {
						(None, Some(a))
					} else {
						(Some(a), None)
					},
				None => (None, None),
			}
		}

		/// Maps a function over an option and filters out `None` results.
		///
		/// This method maps a function over an option and filters out `None` results.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The type of the input value.",
			"The type of the result of applying the function."
		)]
		///
		#[document_parameters("The function to apply.", "The option to filter and map.")]
		///
		#[document_returns("The filtered and mapped option.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let y = filter_map::<OptionBrand, _, _>(|a| if a > 2 { Some(a * 2) } else { None }, x);
		/// assert_eq!(y, Some(10));
		/// ```
		fn filter_map<'a, A: 'a, B: 'a>(
			func: impl Fn(A) -> Option<B> + 'a,
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>) {
			fa.and_then(func)
		}

		/// Filters an option based on a predicate.
		///
		/// This method filters an option based on a predicate.
		#[document_signature]
		///
		#[document_type_parameters("The lifetime of the values.", "The type of the elements.")]
		///
		#[document_parameters("The predicate.", "The option to filter.")]
		///
		#[document_returns("The filtered option.")]
		///
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::OptionBrand,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let y = filter::<OptionBrand, _>(|a| a > 2, x);
		/// assert_eq!(y, Some(5));
		/// ```
		fn filter<'a, A: 'a + Clone>(
			func: impl Fn(A) -> bool + 'a,
			fa: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>) {
			fa.filter(|a| func(a.clone()))
		}
	}

	impl Witherable for OptionBrand {
		/// Partitions an option based on a function that returns a result in an applicative context.
		///
		/// This method partitions an option based on a function that returns a result in an applicative context.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The applicative context.",
			"The type of the elements in the input structure.",
			"The type of the error values.",
			"The type of the success values."
		)]
		///
		#[document_parameters(
			"The function to apply to each element, returning a `Result` in an applicative context.",
			"The option to partition."
		)]
		///
		#[document_returns("The partitioned option wrapped in the applicative context.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let y =
		/// 	wilt::<OptionBrand, OptionBrand, _, _, _>(|a| Some(if a > 2 { Ok(a) } else { Err(a) }), x);
		/// assert_eq!(y, Some((None, Some(5))));
		/// ```
		fn wilt<'a, M: Applicative, A: 'a + Clone, E: 'a + Clone, O: 'a + Clone>(
			func: impl Fn(A) -> Apply!(<M as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Result<O, E>>)
			+ 'a,
			ta: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> Apply!(<M as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<
		'a,
		(
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, E>),
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, O>),
		),
	>)
		where
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Result<O, E>>): Clone,
			Apply!(<M as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Result<O, E>>): Clone, {
			match ta {
				Some(a) => M::map(
					|res| match res {
						Ok(o) => (None, Some(o)),
						Err(e) => (Some(e), None),
					},
					func(a),
				),
				None => M::pure((None, None)),
			}
		}

		/// Maps a function over an option and filters out `None` results in an applicative context.
		///
		/// This method maps a function over an option and filters out `None` results in an applicative context.
		#[document_signature]
		///
		#[document_type_parameters(
			"The lifetime of the values.",
			"The applicative context.",
			"The type of the elements in the input structure.",
			"The type of the result of applying the function."
		)]
		///
		#[document_parameters(
			"The function to apply to each element, returning an `Option` in an applicative context.",
			"The option to filter and map."
		)]
		///
		#[document_returns("The filtered and mapped option wrapped in the applicative context.")]
		#[document_examples]
		///
		/// ```
		/// use fp_library::{
		/// 	brands::*,
		/// 	functions::*,
		/// };
		///
		/// let x = Some(5);
		/// let y = wither::<OptionBrand, OptionBrand, _, _>(
		/// 	|a| Some(if a > 2 { Some(a * 2) } else { None }),
		/// 	x,
		/// );
		/// assert_eq!(y, Some(Some(10)));
		/// ```
		fn wither<'a, M: Applicative, A: 'a + Clone, B: 'a + Clone>(
			func: impl Fn(A) -> Apply!(<M as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Option<B>>) + 'a,
			ta: Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, A>),
		) -> Apply!(<M as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<
		'a,
		Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, B>),
	>)
		where
			Apply!(<Self as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Option<B>>): Clone,
			Apply!(<M as Kind!( type Of<'a, T: 'a>: 'a; )>::Of<'a, Option<B>>): Clone, {
			match ta {
				Some(a) => func(a),
				None => M::pure(None),
			}
		}
	}
}

#[cfg(test)]
mod tests {

	use {
		crate::{
			brands::*,
			classes::CloneableFn,
			functions::*,
		},
		quickcheck_macros::quickcheck,
	};

	// Functor Laws

	/// Tests the identity law for Functor.
	#[quickcheck]
	fn functor_identity(x: Option<i32>) -> bool {
		map::<OptionBrand, _, _>(identity, x) == x
	}

	/// Tests the composition law for Functor.
	#[quickcheck]
	fn functor_composition(x: Option<i32>) -> bool {
		let f = |x: i32| x.wrapping_add(1);
		let g = |x: i32| x.wrapping_mul(2);
		map::<OptionBrand, _, _>(compose(f, g), x)
			== map::<OptionBrand, _, _>(f, map::<OptionBrand, _, _>(g, x))
	}

	// Applicative Laws

	/// Tests the identity law for Applicative.
	#[quickcheck]
	fn applicative_identity(v: Option<i32>) -> bool {
		apply::<RcFnBrand, OptionBrand, _, _>(
			pure::<OptionBrand, _>(<RcFnBrand as CloneableFn>::new(identity)),
			v,
		) == v
	}

	/// Tests the homomorphism law for Applicative.
	#[quickcheck]
	fn applicative_homomorphism(x: i32) -> bool {
		let f = |x: i32| x.wrapping_mul(2);
		apply::<RcFnBrand, OptionBrand, _, _>(
			pure::<OptionBrand, _>(<RcFnBrand as CloneableFn>::new(f)),
			pure::<OptionBrand, _>(x),
		) == pure::<OptionBrand, _>(f(x))
	}

	/// Tests the composition law for Applicative.
	#[quickcheck]
	fn applicative_composition(
		w: Option<i32>,
		u_is_some: bool,
		v_is_some: bool,
	) -> bool {
		let v_fn = |x: i32| x.wrapping_mul(2);
		let u_fn = |x: i32| x.wrapping_add(1);

		let v = if v_is_some {
			pure::<OptionBrand, _>(<RcFnBrand as CloneableFn>::new(v_fn))
		} else {
			None
		};
		let u = if u_is_some {
			pure::<OptionBrand, _>(<RcFnBrand as CloneableFn>::new(u_fn))
		} else {
			None
		};

		// RHS: u <*> (v <*> w)
		let vw = apply::<RcFnBrand, OptionBrand, _, _>(v.clone(), w);
		let rhs = apply::<RcFnBrand, OptionBrand, _, _>(u.clone(), vw);

		// LHS: pure(compose) <*> u <*> v <*> w
		// equivalent to (u . v) <*> w
		let uv = match (u, v) {
			(Some(uf), Some(vf)) => {
				let composed = move |x| uf(vf(x));
				Some(<RcFnBrand as CloneableFn>::new(composed))
			}
			_ => None,
		};

		let lhs = apply::<RcFnBrand, OptionBrand, _, _>(uv, w);

		lhs == rhs
	}

	/// Tests the interchange law for Applicative.
	#[quickcheck]
	fn applicative_interchange(y: i32) -> bool {
		// u <*> pure y = pure ($ y) <*> u
		let f = |x: i32| x.wrapping_mul(2);
		let u = pure::<OptionBrand, _>(<RcFnBrand as CloneableFn>::new(f));

		let lhs = apply::<RcFnBrand, OptionBrand, _, _>(u.clone(), pure::<OptionBrand, _>(y));

		let rhs_fn =
			<RcFnBrand as CloneableFn>::new(move |f: std::rc::Rc<dyn Fn(i32) -> i32>| f(y));
		let rhs = apply::<RcFnBrand, OptionBrand, _, _>(pure::<OptionBrand, _>(rhs_fn), u);

		lhs == rhs
	}

	// Monad Laws

	/// Tests the left identity law for Monad.
	#[quickcheck]
	fn monad_left_identity(a: i32) -> bool {
		let f = |x: i32| Some(x.wrapping_mul(2));
		bind::<OptionBrand, _, _>(pure::<OptionBrand, _>(a), f) == f(a)
	}

	/// Tests the right identity law for Monad.
	#[quickcheck]
	fn monad_right_identity(m: Option<i32>) -> bool {
		bind::<OptionBrand, _, _>(m, pure::<OptionBrand, _>) == m
	}

	/// Tests the associativity law for Monad.
	#[quickcheck]
	fn monad_associativity(m: Option<i32>) -> bool {
		let f = |x: i32| Some(x.wrapping_mul(2));
		let g = |x: i32| Some(x.wrapping_add(1));
		bind::<OptionBrand, _, _>(bind::<OptionBrand, _, _>(m, f), g)
			== bind::<OptionBrand, _, _>(m, |x| bind::<OptionBrand, _, _>(f(x), g))
	}

	// Edge Cases

	/// Tests `map` on `None`.
	#[test]
	fn map_none() {
		assert_eq!(map::<OptionBrand, _, _>(|x: i32| x + 1, None), None);
	}

	/// Tests `bind` on `None`.
	#[test]
	fn bind_none() {
		assert_eq!(bind::<OptionBrand, _, _>(None, |x: i32| Some(x + 1)), None);
	}

	/// Tests `bind` returning `None`.
	#[test]
	fn bind_returning_none() {
		assert_eq!(bind::<OptionBrand, _, _>(Some(5), |_| None::<i32>), None);
	}

	/// Tests `fold_right` on `None`.
	#[test]
	fn fold_right_none() {
		assert_eq!(
			crate::classes::foldable::fold_right::<RcFnBrand, OptionBrand, _, _>(
				|x: i32, acc| x + acc,
				0,
				None
			),
			0
		);
	}

	/// Tests `fold_left` on `None`.
	#[test]
	fn fold_left_none() {
		assert_eq!(
			crate::classes::foldable::fold_left::<RcFnBrand, OptionBrand, _, _>(
				|acc, x: i32| acc + x,
				0,
				None
			),
			0
		);
	}

	/// Tests `traverse` on `None`.
	#[test]
	fn traverse_none() {
		assert_eq!(
			crate::classes::traversable::traverse::<OptionBrand, _, _, OptionBrand>(
				|x: i32| Some(x + 1),
				None
			),
			Some(None)
		);
	}

	/// Tests `traverse` returning `None`.
	#[test]
	fn traverse_returning_none() {
		assert_eq!(
			crate::classes::traversable::traverse::<OptionBrand, _, _, OptionBrand>(
				|_: i32| None::<i32>,
				Some(5)
			),
			None
		);
	}

	// ParFoldable Tests

	/// Tests `par_fold_map` on `None`.
	#[test]
	fn par_fold_map_none() {
		let x: Option<i32> = None;
		let f = send_cloneable_fn_new::<ArcFnBrand, _, _>(|x: i32| x.to_string());
		assert_eq!(par_fold_map::<ArcFnBrand, OptionBrand, _, _>(f, x), "".to_string());
	}

	/// Tests `par_fold_map` on `Some`.
	#[test]
	fn par_fold_map_some() {
		let x = Some(5);
		let f = send_cloneable_fn_new::<ArcFnBrand, _, _>(|x: i32| x.to_string());
		assert_eq!(par_fold_map::<ArcFnBrand, OptionBrand, _, _>(f, x), "5".to_string());
	}

	/// Tests `par_fold_right` on `Some`.
	#[test]
	fn par_fold_right_some() {
		let x = Some(5);
		let f = send_cloneable_fn_new::<ArcFnBrand, _, _>(|(a, b): (i32, i32)| a + b);
		assert_eq!(par_fold_right::<ArcFnBrand, OptionBrand, _, _>(f, 10, x), 15);
	}

	// Filterable Laws

	/// Tests `filterMap identity ≡ compact`.
	#[quickcheck]
	fn filterable_filter_map_identity(x: Option<Option<i32>>) -> bool {
		filter_map::<OptionBrand, _, _>(identity, x) == compact::<OptionBrand, _>(x)
	}

	/// Tests `filterMap Just ≡ identity`.
	#[quickcheck]
	fn filterable_filter_map_just(x: Option<i32>) -> bool {
		filter_map::<OptionBrand, _, _>(Some, x) == x
	}

	/// Tests `filterMap (l <=< r) ≡ filterMap l <<< filterMap r`.
	#[quickcheck]
	fn filterable_filter_map_composition(x: Option<i32>) -> bool {
		let r = |i: i32| if i % 2 == 0 { Some(i) } else { None };
		let l = |i: i32| if i > 5 { Some(i) } else { None };
		let composed = |i| r(i).and_then(l);

		filter_map::<OptionBrand, _, _>(composed, x)
			== filter_map::<OptionBrand, _, _>(l, filter_map::<OptionBrand, _, _>(r, x))
	}

	/// Tests `filter ≡ filterMap <<< maybeBool`.
	#[quickcheck]
	fn filterable_filter_consistency(x: Option<i32>) -> bool {
		let p = |i: i32| i % 2 == 0;
		let maybe_bool = |i| if p(i) { Some(i) } else { None };

		filter::<OptionBrand, _>(p, x) == filter_map::<OptionBrand, _, _>(maybe_bool, x)
	}

	/// Tests `partitionMap identity ≡ separate`.
	#[quickcheck]
	fn filterable_partition_map_identity(x: Option<Result<i32, i32>>) -> bool {
		partition_map::<OptionBrand, _, _, _>(identity, x) == separate::<OptionBrand, _, _>(x)
	}

	/// Tests `partitionMap Right ≡ identity` (on the right side).
	#[quickcheck]
	fn filterable_partition_map_right_identity(x: Option<i32>) -> bool {
		let (_, oks) = partition_map::<OptionBrand, _, _, _>(Ok::<_, i32>, x);
		oks == x
	}

	/// Tests `partitionMap Left ≡ identity` (on the left side).
	#[quickcheck]
	fn filterable_partition_map_left_identity(x: Option<i32>) -> bool {
		let (errs, _) = partition_map::<OptionBrand, _, _, _>(Err::<i32, _>, x);
		errs == x
	}

	/// Tests `f <<< partition ≡ partitionMap <<< eitherBool`.
	#[quickcheck]
	fn filterable_partition_consistency(x: Option<i32>) -> bool {
		let p = |i: i32| i % 2 == 0;
		let either_bool = |i| if p(i) { Ok(i) } else { Err(i) };

		let (not_satisfied, satisfied) = partition::<OptionBrand, _>(p, x);
		let (errs, oks) = partition_map::<OptionBrand, _, _, _>(either_bool, x);

		satisfied == oks && not_satisfied == errs
	}

	// Witherable Laws

	/// Tests `wither (pure <<< Just) ≡ pure`.
	#[quickcheck]
	fn witherable_identity(x: Option<i32>) -> bool {
		wither::<OptionBrand, OptionBrand, _, _>(|i| Some(Some(i)), x) == Some(x)
	}

	/// Tests `wilt p ≡ map separate <<< traverse p`.
	#[quickcheck]
	fn witherable_wilt_consistency(x: Option<i32>) -> bool {
		let p = |i: i32| Some(if i % 2 == 0 { Ok(i) } else { Err(i) });

		let lhs = wilt::<OptionBrand, OptionBrand, _, _, _>(p, x);
		let rhs = map::<OptionBrand, _, _>(
			separate::<OptionBrand, _, _>,
			traverse::<OptionBrand, _, _, OptionBrand>(p, x),
		);

		lhs == rhs
	}

	/// Tests `wither p ≡ map compact <<< traverse p`.
	#[quickcheck]
	fn witherable_wither_consistency(x: Option<i32>) -> bool {
		let p = |i: i32| Some(if i % 2 == 0 { Some(i) } else { None });

		let lhs = wither::<OptionBrand, OptionBrand, _, _>(p, x);
		let rhs = map::<OptionBrand, _, _>(
			compact::<OptionBrand, _>,
			traverse::<OptionBrand, _, _, OptionBrand>(p, x),
		);

		lhs == rhs
	}

	// Edge Cases

	/// Tests `compact` on `Some(None)`.
	#[test]
	fn compact_some_none() {
		assert_eq!(compact::<OptionBrand, _>(Some(None::<i32>)), None);
	}

	/// Tests `compact` on `Some(Some(x))`.
	#[test]
	fn compact_some_some() {
		assert_eq!(compact::<OptionBrand, _>(Some(Some(5))), Some(5));
	}

	/// Tests `compact` on `None`.
	#[test]
	fn compact_none() {
		assert_eq!(compact::<OptionBrand, _>(None::<Option<i32>>), None);
	}

	/// Tests `separate` on `Some(Ok(x))`.
	#[test]
	fn separate_some_ok() {
		let (errs, oks) = separate::<OptionBrand, _, _>(Some(Ok::<i32, &str>(5)));
		assert_eq!(oks, Some(5));
		assert_eq!(errs, None);
	}

	/// Tests `separate` on `Some(Err(e))`.
	#[test]
	fn separate_some_err() {
		let (errs, oks) = separate::<OptionBrand, _, _>(Some(Err::<i32, &str>("error")));
		assert_eq!(oks, None);
		assert_eq!(errs, Some("error"));
	}

	/// Tests `separate` on `None`.
	#[test]
	fn separate_none() {
		let (errs, oks) = separate::<OptionBrand, _, _>(None::<Result<i32, &str>>);
		assert_eq!(oks, None);
		assert_eq!(errs, None);
	}

	/// Tests `partition_map` on `None`.
	#[test]
	fn partition_map_none() {
		let (errs, oks) =
			partition_map::<OptionBrand, _, _, _>(|x: i32| Ok::<i32, i32>(x), None::<i32>);
		assert_eq!(oks, None);
		assert_eq!(errs, None);
	}

	/// Tests `partition` on `None`.
	#[test]
	fn partition_none() {
		let (not_satisfied, satisfied) = partition::<OptionBrand, _>(|x: i32| x > 0, None::<i32>);
		assert_eq!(satisfied, None);
		assert_eq!(not_satisfied, None);
	}

	/// Tests `filter_map` on `None`.
	#[test]
	fn filter_map_none() {
		assert_eq!(filter_map::<OptionBrand, _, _>(|x: i32| Some(x), None::<i32>), None);
	}

	/// Tests `filter` on `None`.
	#[test]
	fn filter_none() {
		assert_eq!(filter::<OptionBrand, _>(|x: i32| x > 0, None::<i32>), None);
	}

	/// Tests `wilt` on `None`.
	#[test]
	fn wilt_none() {
		let res = wilt::<OptionBrand, OptionBrand, _, _, _>(
			|x: i32| Some(Ok::<i32, i32>(x)),
			None::<i32>,
		);
		assert_eq!(res, Some((None, None)));
	}

	/// Tests `wither` on `None`.
	#[test]
	fn wither_none() {
		let res = wither::<OptionBrand, OptionBrand, _, _>(|x: i32| Some(Some(x)), None::<i32>);
		assert_eq!(res, Some(None));
	}
}