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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 .
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 ...
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.
(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 ...
This can be done either explicitly, by using a higher-order function – passing in a function as an argument and calling it – or implicitly, via reflection features which allow one to access certain functions depending on the current context, especially "the current function" or sometimes "the calling function of the current function".
To apply such a function object, one must use the funcall function: (funcall #'foo bar baz). Python Explicit partial application with functools.partial since version 2.5, and operator.methodcaller since version 2.6. Ruby The identifier of a regular "function" in Ruby (which is really a method) cannot be used as a value or passed.
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.
Many dynamic languages, such as JavaScript, Lua, Python, Perl [1] [2] and PHP, allow a function object to be passed. CLI languages such as C# and VB.NET provide a type-safe encapsulating function reference known as delegate. Events and event handlers, as used in .NET languages, provide for callbacks.