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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 ...
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Starting the summation from the beginning of the array yields: (((((+) +) +) +) +) +) + = Since '+' is both commutative and associative, it is a reduction operator. Therefore this reduction can be performed in parallel using several cores, where each core computes the sum of a subset of the array, and the reduction operator merges the results.
(pred array)/array or pred {⍵ /⍨ ⍺⍺ ⍵} array: The second example is an APL dop. C# 3.0 ienum.Where(pred) or The where clause: Where is an extension method ienum is an IEnumerable Similarly in all .NET languages CFML: obj.filter(func) Where obj is an array or a structure. The func receives as an argument each element's value. Clojure ...
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 evaluated.
An Array is a JavaScript object prototyped from the Array constructor specifically designed to store data values indexed by integer keys. Arrays, unlike the basic Object type, are prototyped with methods and properties to aid the programmer in routine tasks (for example, join , slice , and push ).
Given a function that accepts an array, a range query (,) on an array = [,..,] takes two indices and and returns the result of when applied to the subarray [, …,].For example, for a function that returns the sum of all values in an array, the range query (,) returns the sum of all values in the range [,].