Question

The typical academic example is to sum a list. Are there real world examples of the use of fold that will shed light on its utility ?

Answer 1

<条码>倍也许是顺序上最基本的操作。寻求其效用,就象要求使用一种必要语言的<条码>。

Given a list (or array, or tree, or ..), a starting value, and a function, the fold operator reduces the list to a single result. It is also the natural catamorphism (destructor) for lists.

Any operations that take a list as input, and produce an output after inspecting the elements of the list can be encoded as folds. E.g.

sum      = fold (+) 0

length   = fold (λx n → 1 + n) 0

reverse  = fold (λx xs → xs ++ [x]) []

map f    = fold (λx ys → f x : ys) []

filter p = fold (λx xs → if p x then x : xs else xs) []

组合操作者并不具体列出清单,但可以统一归纳为“常规”数据类型。

因此,作为各种数据类型的最基本业务之一,它当然会有一些用途。能够承认何时算法可以被描述为一重,是一种有用的技能,可形成更清洁的法典。

参考资料:

Answer 2

Lots And Lots Of raftLeft /a>列出了以下职能:

sum
product
count
average
last
penultimate
contains
get
to string
reverse
unique
to set
double
insertion sort
pivot (part of quicksort)
encode (count consecutive elements)
decode (generate consecutive elements)
group (into sublists of even sizes)

Answer 3

我的回答是:

foldr is for reducing the problem to the primitive case and then assembling back up (behaves as a non tail-recursion)
foldl is for reducing the problem and assembling the solution at every step, where at the primitive case you have the solution ready (bahaves as a tail recursion / iteration)

This question reminded me immediately of a talk by Ralf Lämmel Going Bananas (as the rfold operator notation looks like a banana (| and |)). There are quite illustrative examples of mapping recursion to folds and even one fold to the other.

传统文件(第一是相当困难的)是http://eprints.eemcs.utrome.nl/7281/01/db-utrome-40501F46.pdf” rel=“nofollow” 班纳、Lenses、Envelopes和Barbed 的实用规划,在其他运营商的监视下命名。

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