 Under the Curry–Howard correspondence, the existence of currying and uncurrying is equivalent to the logical theorem formula_135, as tuples (product type) corresponds to conjunction in logic, and function type corresponds to implication.The exponential object formula_136 in the category of Heyting algebras is normally written as material implication formula_137.Distributive Heyting algebras are Boolean algebras, and the exponential object has the explicit form formula_138, thus making it clear that the exponential object really is material implication.