Curried and Uncurried Functions

Grzegorz Bancerek

Warsaw University, Bialystok

Summary.

In the article following functors are introduced: the projections of subsets of the Cartesian product, the functor which for every function $f:X \times Y \to Z$ gives some curried function ($X \to(Y \to Z)$), and the functor which from curried functions makes uncurried functions. Some of their properties and some properties of the set of all functions from a set into a set are also shown.

MML Identifier: FUNCT_5

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. Zermelo theorem and axiom of choice. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.

[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[7] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.

[8] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.

[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[10] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.