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Tree overview

Multi-way trees (aka rose trees) and forests, where a forest is

type Forest<A> = Array<Tree<A>>

Added in v2.0.0


Table of contents


Apply

ap

Apply a function to an argument under a type constructor.

Signature

export declare const ap: <A>(fa: Tree<A>) => <B>(fab: Tree<(a: A) => B>) => Tree<B>

Added in v2.0.0

Extend

extend

Signature

export declare const extend: <A, B>(f: (wa: Tree<A>) => B) => (wa: Tree<A>) => Tree<B>

Added in v2.0.0

Extract

extract

Signature

export declare const extract: <A>(wa: Tree<A>) => A

Added in v2.6.2

Foldable

foldMap

Signature

export declare const foldMap: <M>(M: Monoid<M>) => <A>(f: (a: A) => M) => (fa: Tree<A>) => M

Added in v2.0.0

reduce

Signature

export declare const reduce: <A, B>(b: B, f: (b: B, a: A) => B) => (fa: Tree<A>) => B

Added in v2.0.0

reduceRight

Signature

export declare const reduceRight: <A, B>(b: B, f: (a: A, b: B) => B) => (fa: Tree<A>) => B

Added in v2.0.0

Functor

map

map can be used to turn functions (a: A) => B into functions (fa: F<A>) => F<B> whose argument and return types use the type constructor F to represent some computational context.

Signature

export declare const map: <A, B>(f: (a: A) => B) => (fa: Tree<A>) => Tree<B>

Added in v2.0.0

Monad

chain

Composes computations in sequence, using the return value of one computation to determine the next computation.

Signature

export declare const chain: <A, B>(f: (a: A) => Tree<B>) => (ma: Tree<A>) => Tree<B>

Added in v2.0.0

Pointed

of

Signature

export declare const of: <A>(a: A) => Tree<A>

Added in v2.7.0

combinators

apFirst

Combine two effectful actions, keeping only the result of the first.

Derivable from Apply.

Signature

export declare const apFirst: <B>(second: Tree<B>) => <A>(first: Tree<A>) => Tree<A>

Added in v2.0.0

apSecond

Combine two effectful actions, keeping only the result of the second.

Derivable from Apply.

Signature

export declare const apSecond: <B>(second: Tree<B>) => <A>(first: Tree<A>) => Tree<B>

Added in v2.0.0

chainFirst

Composes computations in sequence, using the return value of one computation to determine the next computation and keeping only the result of the first.

Derivable from Chain.

Signature

export declare const chainFirst: <A, B>(f: (a: A) => Tree<B>) => (first: Tree<A>) => Tree<A>

Added in v2.0.0

duplicate

Derivable from Extend.

Signature

export declare const duplicate: <A>(wa: Tree<A>) => Tree<Tree<A>>

Added in v2.0.0

flap

Derivable from Functor.

Signature

export declare const flap: <A>(a: A) => <B>(fab: Tree<(a: A) => B>) => Tree<B>

Added in v2.10.0

flatten

Derivable from Chain.

Signature

export declare const flatten: <A>(mma: Tree<Tree<A>>) => Tree<A>

Added in v2.0.0

constructors

make

Signature

export declare function make<A>(value: A, forest: Forest<A> = []): Tree<A>

Added in v2.0.0

unfoldForest

Build a (possibly infinite) forest from a list of seed values in breadth-first order.

Signature

export declare function unfoldForest<A, B>(bs: Array<B>, f: (b: B) => [A, Array<B>]): Forest<A>

Added in v2.0.0

unfoldForestM

Monadic forest builder, in depth-first order

Signature

export declare function unfoldForestM<M extends URIS4>(
  M: Monad4<M>
): <S, R, E, A, B>(bs: Array<B>, f: (b: B) => Kind4<M, S, R, E, [A, Array<B>]>) => Kind4<M, S, R, E, Forest<A>>
export declare function unfoldForestM<M extends URIS3>(
  M: Monad3<M>
): <R, E, A, B>(bs: Array<B>, f: (b: B) => Kind3<M, R, E, [A, Array<B>]>) => Kind3<M, R, E, Forest<A>>
export declare function unfoldForestM<M extends URIS3, E>(
  M: Monad3C<M, E>
): <R, A, B>(bs: Array<B>, f: (b: B) => Kind3<M, R, E, [A, Array<B>]>) => Kind3<M, R, E, Forest<A>>
export declare function unfoldForestM<M extends URIS2>(
  M: Monad2<M>
): <R, E, B>(bs: Array<B>, f: (b: B) => Kind2<M, R, [E, Array<B>]>) => Kind2<M, R, Forest<E>>
export declare function unfoldForestM<M extends URIS2, E>(
  M: Monad2C<M, E>
): <A, B>(bs: Array<B>, f: (b: B) => Kind2<M, E, [A, Array<B>]>) => Kind2<M, E, Forest<A>>
export declare function unfoldForestM<M extends URIS>(
  M: Monad1<M>
): <A, B>(bs: Array<B>, f: (b: B) => Kind<M, [A, Array<B>]>) => Kind<M, Forest<A>>
export declare function unfoldForestM<M>(
  M: MonadHKT<M>
): <A, B>(bs: Array<B>, f: (b: B) => HKT<M, [A, Array<B>]>) => HKT<M, Forest<A>>

Added in v2.0.0

unfoldTree

Build a (possibly infinite) tree from a seed value in breadth-first order.

Signature

export declare function unfoldTree<A, B>(b: B, f: (b: B) => [A, Array<B>]): Tree<A>

Added in v2.0.0

unfoldTreeM

Monadic tree builder, in depth-first order

Signature

export declare function unfoldTreeM<M extends URIS4>(
  M: Monad4<M>
): <S, R, E, A, B>(b: B, f: (b: B) => Kind4<M, S, R, E, [A, Array<B>]>) => Kind4<M, S, R, E, Tree<A>>
export declare function unfoldTreeM<M extends URIS3>(
  M: Monad3<M>
): <R, E, A, B>(b: B, f: (b: B) => Kind3<M, R, E, [A, Array<B>]>) => Kind3<M, R, E, Tree<A>>
export declare function unfoldTreeM<M extends URIS3, E>(
  M: Monad3C<M, E>
): <R, A, B>(b: B, f: (b: B) => Kind3<M, R, E, [A, Array<B>]>) => Kind3<M, R, E, Tree<A>>
export declare function unfoldTreeM<M extends URIS2>(
  M: Monad2<M>
): <E, A, B>(b: B, f: (b: B) => Kind2<M, E, [A, Array<B>]>) => Kind2<M, E, Tree<A>>
export declare function unfoldTreeM<M extends URIS2, E>(
  M: Monad2C<M, E>
): <A, B>(b: B, f: (b: B) => Kind2<M, E, [A, Array<B>]>) => Kind2<M, E, Tree<A>>
export declare function unfoldTreeM<M extends URIS>(
  M: Monad1<M>
): <A, B>(b: B, f: (b: B) => Kind<M, [A, Array<B>]>) => Kind<M, Tree<A>>
export declare function unfoldTreeM<M>(
  M: MonadHKT<M>
): <A, B>(b: B, f: (b: B) => HKT<M, [A, Array<B>]>) => HKT<M, Tree<A>>

Added in v2.0.0

destructors

fold

Fold a tree into a “summary” value in depth-first order.

For each node in the tree, apply f to the value and the result of applying f to each forest.

This is also known as the catamorphism on trees.

Signature

export declare function fold<A, B>(f: (a: A, bs: Array<B>) => B): (tree: Tree<A>) => B

Example

import { fold, make } from 'fp-ts/Tree'
import { concatAll } from 'fp-ts/Monoid'
import { MonoidSum } from 'fp-ts/number'

const t = make(1, [make(2), make(3)])

const sum = concatAll(MonoidSum)

// Sum the values in a tree:
assert.deepStrictEqual(fold((a: number, bs: Array<number>) => a + sum(bs))(t), 6)

// Find the maximum value in the tree:
assert.deepStrictEqual(fold((a: number, bs: Array<number>) => bs.reduce((b, acc) => Math.max(b, acc), a))(t), 3)

// Count the number of leaves in the tree:
assert.deepStrictEqual(fold((_: number, bs: Array<number>) => (bs.length === 0 ? 1 : sum(bs)))(t), 2)

Added in v2.6.0

instances

Applicative

Signature

export declare const Applicative: Applicative1<'Tree'>

Added in v2.7.0

Apply

Signature

export declare const Apply: Apply1<'Tree'>

Added in v2.10.0

Chain

Signature

export declare const Chain: Chain1<'Tree'>

Added in v2.10.0

Comonad

Signature

export declare const Comonad: Comonad1<'Tree'>

Added in v2.7.0

Foldable

Signature

export declare const Foldable: Foldable1<'Tree'>

Added in v2.7.0

Functor

Signature

export declare const Functor: Functor1<'Tree'>

Added in v2.7.0

Monad

Signature

export declare const Monad: Monad1<'Tree'>

Added in v2.7.0

Pointed

Signature

export declare const Pointed: Pointed1<'Tree'>

Added in v2.10.0

Traversable

Signature

export declare const Traversable: Traversable1<'Tree'>

Added in v2.7.0

URI

Signature

export declare const URI: 'Tree'

Added in v2.0.0

URI (type alias)

Signature

export type URI = typeof URI

Added in v2.0.0

getEq

Signature

export declare function getEq<A>(E: Eq<A>): Eq<Tree<A>>

Added in v2.0.0

getShow

Signature

export declare function getShow<A>(S: Show<A>): Show<Tree<A>>

Added in v2.0.0

tree

Use small, specific instances instead.

Signature

export declare const tree: Monad1<'Tree'> & Foldable1<'Tree'> & Traversable1<'Tree'> & Comonad1<'Tree'>

Added in v2.0.0

model

Forest (type alias)

Signature

export type Forest<A> = Array<Tree<A>>

Added in v2.0.0

Tree (interface)

Signature

export interface Tree<A> {
  readonly value: A
  readonly forest: Forest<A>
}

Added in v2.0.0

utils

Do

Signature

export declare const Do: Tree<{}>

Added in v2.9.0

apS

Signature

export declare const apS: <N, A, B>(
  name: Exclude<N, keyof A>,
  fb: Tree<B>
) => (fa: Tree<A>) => Tree<{ readonly [K in N | keyof A]: K extends keyof A ? A[K] : B }>

Added in v2.8.0

bind

Signature

export declare const bind: <N, A, B>(
  name: Exclude<N, keyof A>,
  f: (a: A) => Tree<B>
) => (ma: Tree<A>) => Tree<{ readonly [K in N | keyof A]: K extends keyof A ? A[K] : B }>

Added in v2.8.0

bindTo

Signature

export declare const bindTo: <N>(name: N) => <A>(fa: Tree<A>) => Tree<{ readonly [K in N]: A }>

Added in v2.8.0

drawForest

Neat 2-dimensional drawing of a forest

Signature

export declare function drawForest(forest: Forest<string>): string

Added in v2.0.0

drawTree

Neat 2-dimensional drawing of a tree

Signature

export declare function drawTree(tree: Tree<string>): string

Example

import { make, drawTree } from 'fp-ts/Tree'

const fa = make('a', [make('b'), make('c'), make('d', [make('e'), make('f')])])

assert.strictEqual(
  drawTree(fa),
  `a
├─ b
├─ c
└─ d
   ├─ e
   └─ f`
)

Added in v2.0.0

elem

Signature

export declare function elem<A>(E: Eq<A>): (a: A, fa: Tree<A>) => boolean

Added in v2.0.0

sequence

Signature

export declare const sequence: Sequence1<'Tree'>

Added in v2.6.3

traverse

Signature

export declare const traverse: PipeableTraverse1<'Tree'>

Added in v2.6.3