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Просмотр файла: BooleanAlgebra.js
/**
* 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".
*
* @since 2.0.0
*/
import { getBooleanAlgebra } from './function';
// -------------------------------------------------------------------------------------
// combinators
// -------------------------------------------------------------------------------------
/**
* Every boolean algebras has a dual algebra, which involves reversing one/zero as well as join/meet.
*
* @since 2.10.0
*/
export var reverse = function (B) { return ({
meet: function (x, y) { return B.join(x, y); },
join: function (x, y) { return B.meet(x, y); },
zero: B.one,
one: B.zero,
implies: function (x, y) { return B.join(B.not(x), y); },
not: B.not
}); };
// -------------------------------------------------------------------------------------
// instances
// -------------------------------------------------------------------------------------
/**
* @category instances
* @since 2.0.0
*/
export var booleanAlgebraVoid = {
meet: function () { return undefined; },
join: function () { return undefined; },
zero: undefined,
one: undefined,
implies: function () { return undefined; },
not: function () { return undefined; }
};
// -------------------------------------------------------------------------------------
// deprecated
// -------------------------------------------------------------------------------------
/**
* Use [`reverse`](#reverse) instead.
*
* @category zone of death
* @since 2.0.0
* @deprecated
*/
export var getDualBooleanAlgebra = reverse;
/**
* Use [`BooleanAlgebra`](./boolean.ts.html#booleanalgebra) instead.
*
* @category zone of death
* @since 2.0.0
* @deprecated
*/
export var booleanAlgebraBoolean = {
meet: function (x, y) { return x && y; },
join: function (x, y) { return x || y; },
zero: false,
one: true,
implies: function (x, y) { return !x || y; },
not: function (x) { return !x; }
};
/**
* Use [`getBooleanAlgebra`](./function.ts.html#getbooleanalgebra) instead.
*
* @category zone of death
* @since 2.0.0
* @deprecated
*/
export var getFunctionBooleanAlgebra = getBooleanAlgebra;
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