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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 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:
It will not work, however, if passed as an argument to another function, e.g. lapply, inside the anonymous function definition. In this case, sys.function(0) can be used. [8] For example, the code below squares a list recursively:
(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 ...
va_start takes two arguments, a va_list object and a reference to the function's last parameter (the one before the ellipsis; the macro uses this to get its bearings). In C23, the second argument will no longer be required and variadic functions will no longer need a named parameter before the ellipsis.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
The following REBOL/Red code demonstrates callback use. As alert requires a string, form produces a string from the result of calculate; The get-word! values (i.e., :calc-product and :calc-sum) trigger the interpreter to return the code of the function rather than evaluate with the function. The datatype! references in a block!