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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.
Using a higher-order function so the top-level function recurses anonymously on an argument, but still needing the standard recursive function as an argument: def fact0 ( n0 ): if n0 == 0 : return 1 return n0 * fact0 ( n0 - 1 ) fact1 = lambda f , n1 : 1 if n1 == 0 else n1 * f ( n1 - 1 ) fact = lambda n : fact1 ( fact0 , n )
Java has no first-class functions, so function objects are usually expressed by an interface with a single method (most commonly the Callable interface), typically with the implementation being an anonymous inner class, or, starting in Java 8, a lambda. For an example from Java's standard library, java.util.Collections.sort() takes a List and a ...
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 PHP and other languages, the lambda is an alternative. A function is defined in a code statement rather than declared with the usual function syntax. It has no name but is callable via a function reference. Such functions can be defined inside of a function as well as in other scopes. To use local variables in the anonymous function, use ...
The free variables in the sub expression are the parameters to the function call. Lambda lifts may be used on individual functions, in code refactoring, to make a function usable outside the scope in which it was written. Such lifts may also be repeated, until the expression has no lambda abstractions, in order to transform the program.
The function that accepts a callback may be designed to store the callback so that it can be called back after returning which is known as asynchronous, non-blocking or deferred. Programming languages support callbacks in different ways such as function pointers, lambda expressions and blocks.
There are other common notational differences as well; for example Apply is often called Eval, [6] even though in computer science, these are not the same thing, with eval distinguished from Apply, as being the evaluation of the quoted string form of a function with its arguments, rather than the application of a function to some arguments.