compiler/edu.cornell.cs.apl.viaduct.algebra/HeytingAlgebra

HeytingAlgebra

interface HeytingAlgebra<T : HeytingAlgebra<T>> : Lattice<T>
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A Heyting algebra is a bounded lattice that supports an implication operation → where A → B is the greatest element x that satisfies A ∧ x ≤ B.

This is also called an implicated lattice.

See also

Functions

imply
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abstract fun imply(that: T): T
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this.imply(that) is the greatest solution to this.meet(x) ≤ that.

join
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abstract fun join(that: T): T
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The least upper bound of this and that.

lessThanOrEqualTo
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abstract fun lessThanOrEqualTo(that: T): Boolean
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Returns true if this is ordered before that.

meet
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abstract fun meet(that: T): T
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The greatest lower bound of this and that.

Inheritors

FreeDistributiveLattice
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