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BooleanAlgebra.d.ts 1.5 KiB

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  1. /**
  2. * Boolean algebras are Heyting algebras with the additional constraint that the law of the excluded middle is true
  3. * (equivalently, double-negation is true).
  4. *
  5. * Instances should satisfy the following laws in addition to the `HeytingAlgebra` laws:
  6. *
  7. * - Excluded middle: `a ∨ ¬a <-> 1`
  8. *
  9. * Boolean algebras generalize classical logic: one is equivalent to "true" and zero is equivalent to "false".
  10. *
  11. * @since 2.0.0
  12. */
  13. import { HeytingAlgebra } from './HeytingAlgebra'
  14. /**
  15. * @category model
  16. * @since 2.0.0
  17. */
  18. export interface BooleanAlgebra<A> extends HeytingAlgebra<A> {}
  19. /**
  20. * Every boolean algebras has a dual algebra, which involves reversing one/zero as well as join/meet.
  21. *
  22. * @since 2.10.0
  23. */
  24. export declare const reverse: <A>(B: BooleanAlgebra<A>) => BooleanAlgebra<A>
  25. /**
  26. * @category instances
  27. * @since 2.0.0
  28. */
  29. export declare const booleanAlgebraVoid: BooleanAlgebra<void>
  30. /**
  31. * Use [`reverse`](#reverse) instead.
  32. *
  33. * @category zone of death
  34. * @since 2.0.0
  35. * @deprecated
  36. */
  37. export declare const getDualBooleanAlgebra: <A>(B: BooleanAlgebra<A>) => BooleanAlgebra<A>
  38. /**
  39. * Use [`BooleanAlgebra`](./boolean.ts.html#booleanalgebra) instead.
  40. *
  41. * @category zone of death
  42. * @since 2.0.0
  43. * @deprecated
  44. */
  45. export declare const booleanAlgebraBoolean: BooleanAlgebra<boolean>
  46. /**
  47. * Use [`getBooleanAlgebra`](./function.ts.html#getbooleanalgebra) instead.
  48. *
  49. * @category zone of death
  50. * @since 2.0.0
  51. * @deprecated
  52. */
  53. export declare const getFunctionBooleanAlgebra: <B>(
  54. B: BooleanAlgebra<B>
  55. ) => <A = never>() => BooleanAlgebra<(a: A) => B>