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In mathematics and computer science, currying is the technique of translating a function that takes multiple arguments into a sequence of families of functions, each taking a single argument. In the prototypical example, one begins with a function : that takes two arguments, one from and one from , and produces objects in .
A higher-order function is a function that takes a function as an argument or returns one as a result. This is commonly used to customize the behavior of a generically defined function, often a looping construct or recursion scheme. Anonymous functions are a convenient way to specify such function arguments. The following examples are in Python 3.
The term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
In this Erlang example, the higher-order function or_else/2 takes a list of functions (Fs) and argument (X). It evaluates the function F with the argument X as argument. If the function F returns false then the next function in Fs will be evaluated. If the function F returns {false, Y} then the next function in Fs with argument Y will be
Lambda lifting is expensive on processing time for the compiler. An efficient implementation of lambda lifting is () on processing time for the compiler. [2] In the untyped lambda calculus, where the basic types are functions, lifting may change the result of beta reduction of a lambda expression. The resulting functions will have the same ...
Anonymous recursion is primarily of use in allowing recursion for anonymous functions, particularly when they form closures or are used as callbacks, to avoid having to bind the name of the function.
For example, in higher-order programming, one can pass functions as arguments to other functions and functions can be the return value of other functions (such as in macros or for interpreting). This style of programming is mostly used in functional programming , but it can also be very useful in object-oriented programming .
(Here we use the standard notations and conventions of lambda calculus: Y is a function that takes one argument f and returns the entire expression following the first period; the expression . ( ) denotes a function that takes one argument x, thought of as a function, and returns the expression ( ), where ( ) denotes x applied to itself ...