In programming language theory and type theory, polymorphism is the provision of a single interface to entities of different types or the use of a single symbol to represent multiple different types. The concept is borrowed from a principle in biology where an organism or species can have many different forms or stages. The most commonly recognized major classes of polymorphism are: Ad hoc polymorphism: defines a common interface for an arbitrary set of individually specified types.
In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism.
Template metaprogramming (TMP) is a metaprogramming technique in which templates are used by a compiler to generate temporary source code, which is merged by the compiler with the rest of the source code and then compiled. The output of these templates can include compile-time constants, data structures, and complete functions. The use of templates can be thought of as compile-time polymorphism. The technique is used by a number of languages, the best-known being C++, but also Curl, D, Nim, and XL.
Generic programming is a style of computer programming in which algorithms are written in terms of data types to-be-specified-later that are then instantiated when needed for specific types provided as parameters. This approach, pioneered by the ML programming language in 1973, permits writing common functions or types that differ only in the set of types on which they operate when used, thus reducing duplicate code. Generics was introduced to the main-stream programming with Ada in 1977 and then with templates in C++ it became part of the repertoire of professional library design.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.