 It is defined by

for formula_23 from formula_3 and formula_29 from formula_4.We then also write

Uncurrying is the reverse transformation, and is most easily understood in terms of its right adjoint, the function formula_64

In set theory, the notation formula_65 is used to denote the set of functions from the set formula_3 to the set formula_4.Currying is the natural bijection between the set formula_68 of functions from formula_69 to formula_70, and the set formula_71 of functions from formula_72 to the set of functions from formula_73 to formula_70.