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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.
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 ...
Introduced in Python 2.2 as an optional feature and finalized in version 2.3, generators are Python's mechanism for lazy evaluation of a function that would otherwise return a space-prohibitive or computationally intensive list. This is an example to lazily generate the prime numbers:
(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 ...
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. It must first be retrieved into a Method or Proc object to be used as first-class data. The syntax for ...
The three axes of the cube correspond to three different augmentations of the simply typed lambda calculus: the addition of dependent types, the addition of polymorphism, and the addition of higher kinded type constructors (functions from types to types, for example). The lambda cube is generalized further by pure type systems.
The examples 1 and 2 denote different terms, differing only in where the parentheses are placed. They have different meanings: example 1 is a function definition, while example 2 is a function application. The lambda variable x is a placeholder in both examples. Here, example 1 defines a function .