/// The cofree comonad over `Syntax`.
///
/// This is “free” in the sense of “unconstrained” rather than “zero-cost”; it’s the comonad obtained by taking a functor (in this case `Syntax`) and adding the minimum necessary details (the `B` paired with it) to satisfy the comonad laws.
///
/// This type is dual to `Free`. Where `Free` is inhabited by syntax trees where some terms are replaced with `B`s, `Cofree` is inhabited by syntax trees where all terms are annotated with `B`s. In Doubt, this allows us to e.g. annotate terms with source range information, categorization, etc.
public enum Cofree<A, B> {
	indirect case Unroll(B, Syntax<Cofree, A>)

	public var unwrap: Syntax<Cofree, A> {
		switch self {
		case let .Unroll(_, rest):
			return rest
		}
	}


	public init(_ annotation: B, _ syntax: Syntax<Cofree, A>) {
		self = .Unroll(annotation, syntax)
	}


	/// Constructs a cofree by coiteration.
	///
	/// The initial seed is used as the annotation of the returned value. The continuation of the structure is unpacked by applying `annotate` to the seed and mapping the resulting syntax’s values recursively. In this manner, the structure is unfolded bottom-up, starting with `seed` and ending at the leaves.
	///
	/// As this is the dual of `Free.iterate`, it’s unsurprising that we have a similar guarantee: coiteration is linear in the size of the constructed tree.
	public static func coiterate(annotate: B -> Syntax<B, A>)(_ seed: B) -> Cofree {
		return .Unroll(seed, annotate(seed).map(coiterate(annotate)))
	}
}


// MARK: - CustomDebugStringConvertible

extension Cofree: CustomDebugStringConvertible {
	public var debugDescription: String {
		return "(\(String(reflecting: extract)), \(String(reflecting: unwrap)))"
	}
}


// MARK: - Functor

extension Cofree {
	public func map<Other>(transform: B -> Other) -> Cofree<A, Other> {
		return .Unroll(transform(extract), unwrap.map { $0.map(transform) })
	}
}


// MARK: - Comonad

extension Cofree {
	/// Returns the value annotating the syntax tree at this node.
	public var extract: B {
		switch self {
		case let .Unroll(b, _):
			return b
		}
	}

	/// Returns a new `Cofree` by recursively applying `transform` to each node, producing the annotations for the copy.
	public func extend<Other>(transform: Cofree -> Other) -> Cofree<A, Other> {
		return .Unroll(transform(self), unwrap.map { $0.extend(transform) })
	}

	/// Returns a new `Cofree` constructed by recursively annotating each subtree with itself.
	public var duplicate: Cofree<A, Cofree<A, B>> {
		return extend(id)
	}
}


// MARK: - Equality

extension Cofree {
	public static func equals(annotation annotation: (B, B) -> Bool, leaf: (A, A) -> Bool)(_ left: Cofree, _ right: Cofree) -> Bool {
		return annotation(left.extract, right.extract)
			&& Syntax.equals(ifLeaf: leaf, ifRecur: Cofree.equals(annotation: annotation, leaf: leaf))(left.unwrap, right.unwrap)
	}
}

public func == <A: Equatable, B: Equatable> (left: Cofree<A, B>, right: Cofree<A, B>) -> Bool {
	return Cofree.equals(annotation: ==, leaf: ==)(left, right)
}


// MARK: - JSON

extension Cofree {
	public func JSON(annotation annotation: B -> Doubt.JSON, leaf: A -> Doubt.JSON) -> Doubt.JSON {
		return [
			"extract": annotation(extract),
			"unwrap": unwrap.JSON(ifLeaf: leaf, ifRecur: { $0.JSON(annotation: annotation, leaf: leaf) })
		]
	}
}

extension Cofree where A: CustomJSONConvertible, B: CustomJSONConvertible {
	public var JSON: Doubt.JSON {
		return JSON(annotation: { $0.JSON }, leaf: { $0.JSON })
	}
}


// MARK: - Categorizable

extension Cofree where B: Categorizable {
	var categories: Set<B.Category> {
		return extract.categories
	}
}


import Prelude