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Therefore, compilers will attempt to transform the first form into the second; this type of optimization is known as map fusion and is the functional analog of loop fusion. [2] Map functions can be and often are defined in terms of a fold such as foldr, which means one can do a map-fold fusion: foldr f z . map g is equivalent to foldr (f .
In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function. Higher-order functions should not be confused with other uses of the word "functor" throughout mathematics, see Functor (disambiguation).
Neural operators are a class of deep learning architectures designed to learn maps between infinite-dimensional function spaces.Neural operators represent an extension of traditional artificial neural networks, marking a departure from the typical focus on learning mappings between finite-dimensional Euclidean spaces or finite sets.
In Python, functions are first-class objects that can be created and passed around dynamically. 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:
MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. [1] [2] [3]A MapReduce program is composed of a map procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a reduce method, which performs a summary ...
The distinction between the two is subtle: "higher-order" describes a mathematical concept of functions that operate on other functions, while "first-class" is a computer science term for programming language entities that have no restriction on their use (thus first-class functions can appear anywhere in the program that other first-class ...
A simple example of a higher-ordered function is the map function, which takes, as its arguments, a function and a list, and returns the list formed by applying the function to each member of the list. For a language to support map, it must support passing a function as an argument.
Some parallel programming systems, such as OpenMP and Cilk, have language support for the map pattern in the form of a parallel for loop; [2] languages such as OpenCL and CUDA support elemental functions (as "kernels") at the language level. The map pattern is typically combined with other parallel design patterns.