MonadLaws | funland-laws

Type-class laws for Monad, as defined in the funland sub-project, mirroring the static-land spec.

Monad inherits the laws of Applicative and of Chain and in addition must obey:

Left identity: M.chain(f, M.of(a)) <-> f(a)
Right identity: M.chain(M.of, u) <-> u
Functor's map can be derived: A.map = (f, u) => A.chain(x => A.of(f(x)), u)

Type parameters

F

Hierarchy

ApplicativeLaws<F>
- MonadLaws

Implements

ChainRecLaws<F>

Index

Constructors

constructor

Properties

F

Methods

Constructors

constructor

new MonadLaws(F: Monad<F>): MonadLaws

Overrides ApplicativeLaws.constructor
- Defined in monad.ts:26
Parameters
- F: Monad<F>
Returns MonadLaws

Properties

F

F: Monad<F>

Methods

applicativeHomomorphism

applicativeHomomorphism<A, B>(a: A, f: function): Equiv<HK<F, B>>

Inherited from ApplicativeLaws.applicativeHomomorphism
- Defined in applicative.ts:37
Type parameters
- A
- B
Parameters
- a: A
- f: function
  - - (a: A): B
    - Parameters
      - a: A
      Returns B
Returns Equiv<HK<F, B>>

applicativeIdentity

applicativeIdentity<A>(fa: HK<F, A>): Equiv<HK<F, A>>

Inherited from ApplicativeLaws.applicativeIdentity
- Defined in applicative.ts:29
Type parameters
- A
Parameters
- fa: HK<F, A>
Returns Equiv<HK<F, A>>

applicativeInterchange

applicativeInterchange<A, B>(a: A, ff: HK<F, function>): Equiv<HK<F, B>>

Inherited from ApplicativeLaws.applicativeInterchange
- Defined in applicative.ts:45
Type parameters
- A
- B
Parameters
- a: A
- ff: HK<F, function>
Returns Equiv<HK<F, B>>

applicativeMap

applicativeMap<A, B>(fa: HK<F, A>, f: function): Equiv<HK<F, B>>

Inherited from ApplicativeLaws.applicativeMap
- Defined in applicative.ts:53
Type parameters
- A
- B
Parameters
- fa: HK<F, A>
- f: function
  - - (a: A): B
    - Parameters
      - a: A
      Returns B
Returns Equiv<HK<F, B>>

applyComposition

applyComposition<A, B, C>(fa: HK<F, A>, fab: HK<F, function>, fbc: HK<F, function>): Equiv<HK<F, C>>

Inherited from ApplyLaws.applyComposition
- Defined in apply.ts:27
Type parameters
- A
- B
- C
Parameters
- fa: HK<F, A>
- fab: HK<F, function>
- fbc: HK<F, function>
Returns Equiv<HK<F, C>>

chainAssociativity

chainAssociativity<A, B, C>(fa: HK<F, A>, f: function, g: function): Equiv<HK<F, C>>

- Defined in monad.ts:54
Type parameters
- A
- B
- C
Parameters
- fa: HK<F, A>
- f: function
  - - (a: A): HK<F, B>
    - Parameters
      - a: A
      Returns HK<F, B>
- g: function
  - - (b: B): HK<F, C>
    - Parameters
      - b: B
      Returns HK<F, C>
Returns Equiv<HK<F, C>>

chainConsistentApply

chainConsistentApply<A, B>(ff: HK<F, function>, fa: HK<F, A>): Equiv<HK<F, B>>

- Defined in monad.ts:58
Type parameters
- A
- B
Parameters
- ff: HK<F, function>
- fa: HK<F, A>
Returns Equiv<HK<F, B>>

chainRecConsistency

chainRecConsistency<A>(a: A, f: function): Equiv<HK<F, A>>

- Defined in monad.ts:62
Type parameters
- A
Parameters
- a: A
- f: function
  - - (a: A): HK<F, A>
    - Parameters
      - a: A
      Returns HK<F, A>
Returns Equiv<HK<F, A>>

composition

composition<A, B, C>(fa: HK<F, A>, f: function, g: function): Equiv<HK<F, C>>

Inherited from FunctorLaws.composition
- Defined in functor.ts:28
Type parameters
- A
- B
- C
Parameters
- fa: HK<F, A>
- f: function
  - - (a: B): C
    - Parameters
      - a: B
      Returns C
- g: function
  - - (a: A): B
    - Parameters
      - a: A
      Returns B
Returns Equiv<HK<F, C>>

identity

identity<A>(fa: HK<F, A>): Equiv<HK<F, A>>

Inherited from FunctorLaws.identity
- Defined in functor.ts:24
Type parameters
- A
Parameters
- fa: HK<F, A>
Returns Equiv<HK<F, A>>

monadChainRecStackSafety

monadChainRecStackSafety(): Equiv<HK<F, number>>

- Defined in monad.ts:46
Returns Equiv<HK<F, number>>

monadLeftIdentity

monadLeftIdentity<A, B>(a: A, f: function): Equiv<HK<F, B>>

- Defined in monad.ts:31
Type parameters
- A
- B
Parameters
- a: A
- f: function
  - - (a: A): HK<F, B>
    - Parameters
      - a: A
      Returns HK<F, B>
Returns Equiv<HK<F, B>>

monadMap

monadMap<A, B>(fa: HK<F, A>, f: function): Equiv<HK<F, B>>

- Defined in monad.ts:41
Type parameters
- A
- B
Parameters
- fa: HK<F, A>
- f: function
  - - (a: A): B
    - Parameters
      - a: A
      Returns B
Returns Equiv<HK<F, B>>

monadRightIdentity

monadRightIdentity<A, B>(fa: HK<F, A>): Equiv<HK<F, A>>

- Defined in monad.ts:36
Type parameters
- A
- B
Parameters
- fa: HK<F, A>
Returns Equiv<HK<F, A>>

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