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”.

Table of contents

• BooleanAlgebra (interface)
• booleanAlgebraBoolean (constant)
• booleanAlgebraVoid (constant)
• getDualBooleanAlgebra (function)
• getFunctionBooleanAlgebra (function)

BooleanAlgebra (interface)

Signature

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

Added in v1.4.0

booleanAlgebraBoolean (constant)

Signature

export const booleanAlgebraBoolean: BooleanAlgebra<boolean> = ...

Added in v1.4.0

booleanAlgebraVoid (constant)

Signature

export const booleanAlgebraVoid: BooleanAlgebra<void> = ...

Added in v1.4.0

getDualBooleanAlgebra (function)

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

Signature

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

Added in v1.4.0

getFunctionBooleanAlgebra (function)

Signature

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

Added in v1.4.0