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Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
evaluates to the list 2, 4, …, 10 by applying the predicate even to every element of the list of integers 1, 2, …, 10 in that order and creating a new list of those elements for which the predicate returns the Boolean value true, thereby giving a list containing only the even members of that list. Conversely, the code example
In languages which support first-class functions and currying, map may be partially applied to lift a function that works on only one value to an element-wise equivalent that works on an entire container; for example, map square is a Haskell function which squares each element of a list.
Variables in standard JavaScript have no type attached, so any value (each value has a type) can be stored in any variable. Starting with ES6, the 6th version of the language, variables could be declared with var for function scoped variables, and let or const which are for block level variables.
Although has a fixed value, it is possible to logically group elements of a vector together and reduce . For example, a problem instance with vectors of size four can be handled by splitting the vectors into the first two and last two elements, which are always transmitted and computed together.
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returns a function or value as its result. All other functions are first-order functions. 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.
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