Higher-Order Functions
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Higher-Order Functions: Fold

Higher-Order Functions: Fold


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In functional programming, fold, also known variously as reduce, accumulate, compress or inject, is a family of higher-order functions that iterate an arbitrary function over a data structure in some order and build up a return value. Typically, a fold deals with two things: a combining function and a list of elements of some data structure. The fold then proceeds to combine elements of the data structure using the function in some systematic way. Folds are in a sense dual to unfolds, which take a starting value of some other type and apply a function recursively to decide how to construct a data structure, whereas a fold recursively breaks that structure down, replacing it with other functions and values (anamorphism as opposed to catamorphism). The folding of the list with the addition operator would result in 15, the sum of the elements of the list . To a rough approximation, one can think of this fold as replacing the commas in the list with the + operation, giving 1 + 2 + 3 + 4 + 5. In the example above, + is an associative operation, so it is irrelevant how the addition is parenthesized. In the general case of non-associative binary functions, the order in which the elements are combined matters. On lists, there are two obvious ways to carry this out: either by recursively combining the first element with the results of combining the rest (called a right fold) or by recursively combining the results of combining all but the last element with the last one (called a left fold). With a right fold, the sum would be parenthesized as 1 + (2 + (3 + (4 + 5))), whereas with a left fold it would be parenthesized as (((1 + 2) + 3) + 4) + 5. In practice, it is convenient and natural to have an initial value which in the case of a right fold is use... More: http://booksllc.net/?id=6364389


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Product Details
  • ISBN-13: 9781156181331
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Fold
  • Width: 229 mm
  • ISBN-10: 115618133X
  • Publisher Date: 31 May 2010
  • Binding: Paperback
  • Spine Width: 3 mm
  • Weight: 73 gr


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