Skip to main content Link Search Menu Expand Document (external link)

BooleanAlgebra overview

Boolean algebras are Heyting algebras with the additional constraint that the law of the excluded middle is true (equivalently, double-negation is true).

Instances should satisfy the following laws in addition to the HeytingAlgebra laws:

  • Excluded middle: a ∨ ¬a <-> 1

Boolean algebras generalize classical logic: one is equivalent to “true” and zero is equivalent to “false”.

Added in v2.0.0


Table of contents


instances

booleanAlgebraVoid

Signature

export declare const booleanAlgebraVoid: BooleanAlgebra<void>

Added in v2.0.0

model

BooleanAlgebra (interface)

Signature

export interface BooleanAlgebra<A> extends HeytingAlgebra<A> {}

Added in v2.0.0

utils

reverse

Every boolean algebras has a dual algebra, which involves reversing one/zero as well as join/meet.

Signature

export declare const reverse: <A>(B: BooleanAlgebra<A>) => BooleanAlgebra<A>

Added in v2.10.0

zone of death

booleanAlgebraBoolean

Use BooleanAlgebra instead.

Signature

export declare const booleanAlgebraBoolean: BooleanAlgebra<boolean>

Added in v2.0.0

getDualBooleanAlgebra

Use reverse instead.

Signature

export declare const getDualBooleanAlgebra: <A>(B: BooleanAlgebra<A>) => BooleanAlgebra<A>

Added in v2.0.0

getFunctionBooleanAlgebra

Use getBooleanAlgebra instead.

Signature

export declare const getFunctionBooleanAlgebra: <B>(
  B: BooleanAlgebra<B>
) => <A = never>() => BooleanAlgebra<(a: A) => B>

Added in v2.0.0