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92 lines
3.3 KiB
Swift
92 lines
3.3 KiB
Swift
// Copyright © 2015 GitHub. All rights reserved.
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/// The cofree comonad over `Syntax`.
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///
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/// 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.
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///
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/// 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.
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public enum Cofree<A, B> {
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case Unroll(B, () -> Syntax<Cofree, A>)
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public var unwrap: Syntax<Cofree, A> {
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switch self {
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case let .Unroll(_, rest):
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return rest()
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}
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}
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/// Recursively copies a `Fix<A>` into a `Cofree<A, B>` with a function assigning `B` for every `Fix<A>`.
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public init(_ fix: Fix<A>, _ annotate: Fix<A> -> B) {
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self = Cofree<A, Fix<A>>.coiterate { $0.out } (fix).map(annotate)
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}
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/// Constructs a cofree by coiteration.
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///
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/// 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.
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///
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/// 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.
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public static func coiterate(annotate: B -> Syntax<B, A>)(_ seed: B) -> Cofree {
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return .Unroll(seed, { annotate(seed).map(coiterate(annotate)) })
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}
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}
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// MARK: - Functor
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extension Cofree {
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public func map<Other>(transform: B -> Other) -> Cofree<A, Other> {
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return .Unroll(transform(extract), { self.unwrap.map { $0.map(transform) } })
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}
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}
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// MARK: - Comonad
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extension Cofree {
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/// Returns the value annotating the syntax tree at this node.
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public var extract: B {
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switch self {
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case let .Unroll(b, _):
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return b
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}
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}
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/// Returns a new `Cofree` by recursively applying `transform` to each node, producing the annotations for the copy.
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public func extend<Other>(transform: Cofree -> Other) -> Cofree<A, Other> {
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return .Unroll(transform(self), { self.unwrap.map { $0.extend(transform) } })
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}
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/// Returns a new `Cofree` constructed by recursively annotating each subtree with itself.
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public var duplicate: Cofree<A, Cofree<A, B>> {
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return extend(id)
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}
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}
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// MARK: - Equality
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extension Cofree {
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public static func equals(annotation annotation: (B, B) -> Bool, leaf: (A, A) -> Bool)(_ left: Cofree, _ right: Cofree) -> Bool {
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return annotation(left.extract, right.extract)
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&& Syntax.equals(ifLeaf: leaf, ifRecur: Cofree.equals(annotation: annotation, leaf: leaf))(left.unwrap, right.unwrap)
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}
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}
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public func == <A: Equatable, B: Equatable> (left: Cofree<A, B>, right: Cofree<A, B>) -> Bool {
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return Cofree.equals(annotation: ==, leaf: ==)(left, right)
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}
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// MARK: - Hashing
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extension Cofree {
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public func hash(annotation annotation: B -> Hash, leaf: A -> Hash) -> Hash {
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return .Ordered([ annotation(extract), unwrap.hash(ifLeaf: leaf, ifRecur: { $0.hash(annotation: annotation, leaf: leaf) }) ])
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}
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}
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import Prelude
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