56 lines
1.5 KiB
TypeScript
56 lines
1.5 KiB
TypeScript
/**
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* Boolean algebras are Heyting algebras with the additional constraint that the law of the excluded middle is true
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* (equivalently, double-negation is true).
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*
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* Instances should satisfy the following laws in addition to the `HeytingAlgebra` laws:
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*
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* - Excluded middle: `a ∨ ¬a <-> 1`
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*
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* Boolean algebras generalize classical logic: one is equivalent to "true" and zero is equivalent to "false".
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*
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* @since 2.0.0
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*/
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import { HeytingAlgebra } from './HeytingAlgebra'
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/**
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* @category model
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* @since 2.0.0
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*/
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export interface BooleanAlgebra<A> extends HeytingAlgebra<A> {}
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/**
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* Every boolean algebras has a dual algebra, which involves reversing one/zero as well as join/meet.
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*
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* @since 2.10.0
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*/
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export declare const reverse: <A>(B: BooleanAlgebra<A>) => BooleanAlgebra<A>
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/**
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* @category instances
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* @since 2.0.0
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*/
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export declare const booleanAlgebraVoid: BooleanAlgebra<void>
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/**
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* Use [`reverse`](#reverse) instead.
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*
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* @category zone of death
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* @since 2.0.0
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* @deprecated
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*/
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export declare const getDualBooleanAlgebra: <A>(B: BooleanAlgebra<A>) => BooleanAlgebra<A>
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/**
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* Use [`BooleanAlgebra`](./boolean.ts.html#booleanalgebra) instead.
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*
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* @category zone of death
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* @since 2.0.0
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* @deprecated
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*/
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export declare const booleanAlgebraBoolean: BooleanAlgebra<boolean>
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/**
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* Use [`getBooleanAlgebra`](./function.ts.html#getbooleanalgebra) instead.
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*
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* @category zone of death
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* @since 2.0.0
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* @deprecated
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*/
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export declare const getFunctionBooleanAlgebra: <B>(
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B: BooleanAlgebra<B>
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) => <A = never>() => BooleanAlgebra<(a: A) => B>
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