foldr和foldr1 Haskell

时间:2018-02-04 19:01:04

标签: haskell fold

我正试图深入研究,认为这对我来说似乎是一个非常强大的资产。但是,你能帮我解决这个问题:

foldr  (/) 2 [1,2,3] -- (1/(2/(3/2))), result 0,75 {where 2 is base)
foldr1 (/)   [2,2,3] -- (1/(2/(3/2))), result 3.00 {where 2 is base)

我认为我正在认真监督褶皱之间的本质区别。 THX

2 个答案:

答案 0 :(得分:6)

foldr :: (a -> b -> b) -> b -> [a] -> b具有实施方式:

foldr :: (a -> b -> b) -> b -> [a] -> b
foldr _ z [] = z
foldr f z (x:xs) = f x (foldr f z xs)

这意味着如果我们输入foldr f z [x1, x2, x3],那么它将被评估为:

   foldr f z [x1, x2, x3]
-> f x1 (foldr f z [x2, x3])
-> f x1 (f x2 (foldr f z [x3]))
-> f x1 (f x2 (f x3 (foldr f z [])))
-> f x1 (f x2 (f x3 z))

因此,您的示例将评估为:

  (/) 1 ((/) 2 ((/) 3 2))
= 1 / (2 / (3 / 2))
= 1 / (2 / 1.5)
= 1 / 1.33333...
= 0.75

foldr1 :: (a -> a -> a) -> [a] -> a函数几乎类似,除非我们看到1元素列表,我们返回该元素,因此区别为:

foldr1 :: (a -> a -> a) -> [a] -> a
foldr1 _ [x] = x
foldr f (x:xs) = f x (foldr1 f xs)

这意味着我们得到foldr1 f [x1, x2, x3]

   foldr1 f [x1, x2, x3]
-> f x1 (foldr1 f [x2, x3])
-> f x1 (f x2 (foldr1 f [x3]))
-> f x1 (f x2 x3))

因此,对于样本输入,我们得到:

  (/) 2 ((/) 2 3)
= 2 / (2 / 3)
= 2 / 0.6666...
= 3.0

因此,如果zxi具有相同的类型,则foldr f z [x1, ..., xn]等于foldr1 f [x1, ..., xn, z]

答案 1 :(得分:6)

一般

foldr1 op [y1, ..., yn, x]

基本相同
foldr op x [y1, ..., yn]

只要n >= 1。也就是说,在你的特殊情况下

foldr1 (/) [2, 2, 3]

将评估为2/(2/3) = 3

使用除法运算符,它有点无聊,因为

foldr1 (/) [y, y, x1, ... , xn]
  = y/(y/(foldr1 (/) [x1, ..., xn]))
  = foldr1 (/) [x1, ..., xn]

适用于所有n >= 1。因此,在您的示例中,它应该只返回

的结果
foldr1 (/) [3]

当然是3.0,它确实评估为3.0

这是一个不太简洁的例子:

foldr1 (/) [2, 3, 5, 7] --  evals to 0.47619047619047616

这里,它给出了与2 / (3 / (5 / 7))相同的结果,而foldr (/) 7 [2, 3, 5] 依次为$(document).ready(function () { var ds = new kendo.data.DataSource({ type: "aspnetmvc-ajax", transport: { read: "http://localhost:51618/Home/Customers_Read", dataType: "json", type: "POST" }, pageSize: 20, serverPaging: true, serverFiltering: true, serverSorting: true, }); $("#grid").kendoGrid({ dataSource: ds, height: 550, groupable: true, filterable:true, sortable: true, pageable: { refresh: true, pageSizes: true, buttonCount: 5 }, columns: [{ template: "<div class='customer-photo'" + "style='background-image: url(../content/web/Customers/#:data.CustomerID#.jpg);'></div>" + "<div class='customer-name'>#: ContactName #</div>", field: "ContactName", title: "Contact Name", width: 240 }, { field: "ContactTitle", title: "Contact Title" }, { field: "CompanyName", title: "Company Name" }, { field: "Country", width: 150 }] }); });

相同
FileReader

我希望它能稍微澄清一下评估的顺序。