Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
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
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[6]
[11]
[12]
[3]
[2]
[4]
[10]
[1]
[5]
[8]
[7]
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.
Received March 6, 1990
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