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Some programming languages almost always use curried functions to achieve multiple arguments; notable examples are ML and Haskell, where in both cases all functions have exactly one argument. This property is inherited from lambda calculus, where multi-argument functions are usually represented in curried form.
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.
Python's limited support for anonymous functions is the lambda construct. An example is the anonymous function which squares its input, called with the argument of 5: An example is the anonymous function which squares its input, called with the argument of 5:
What is thought of as functions with multiple parameters is usually represented in lambda calculus as a function which takes the first argument, and returns a function which takes the rest of the arguments; this is a transformation known as currying. Some programming languages, like ML and Haskell, follow this scheme.
(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 ...
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
It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higher-order functions. A programming language can be considered higher-order if components, such as procedures or labels, can be used just like data. For example, these elements could be used in the same way as arguments or ...
In typed lambda calculus, functions can be applied only if they are capable of accepting the given input's "type" of data. Typed lambda calculi are strictly weaker than the untyped lambda calculus, which is the primary subject of this article, in the sense that typed lambda calculi can express less than the untyped calculus can. On the other ...