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This property is inherited from lambda calculus, where multi-argument functions are usually represented in curried form. Currying is related to, but not the same as partial application . [ 1 ] [ 2 ] In practice, the programming technique of closures can be used to perform partial application and a kind of currying, by hiding arguments in an ...
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.
In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages.
The generalized curry function is given an uncurried function f and its arity (say, 3), and it returns the value of (lambda (v1) (lambda (v2) (lambda (v3) (f v1 v2 v3)))). This example is due to Olivier Danvy and was worked out in the mid-1980s. [13] Here is a unit-test function to illustrate what the generalized curry function is expected to do:
(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 ...
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
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.
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