R语言中的函数式数据结构：高级统计编程

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"Functional Data Structures in R - Advanced Statistical Programming in R" 本书主要探讨的是函数式数据结构在R语言中的应用，这是统计编程的一个高级主题。在传统的数据结构中，很多依赖于可变性，例如可以更新搜索树、改变链表中的链接或者重排向量中的值。然而，在函数式语言中，以及R编程语言的一般规则下，数据是不可变的。这意味着你不能修改已存在的数据。这就意味着用于优化算法编程的数据结构修改技术在R中不适用。在R中，函数式数据结构强调的是不可变性，这带来了一系列独特的挑战和优势。例如，通过创建新的数据结构而不是修改旧的，可以更容易地跟踪数据的变化历史，这对于理解和调试代码特别有用。此外，不可变性还支持并行计算，因为不同线程或进程可以安全地操作同一数据，无需担心数据同步问题。书中可能涵盖了如下知识点： 1. Lambda函数和高阶函数：在R中，函数被视为一等公民，可以作为参数传递给其他函数，也可以作为函数的返回值。Lambda函数（匿名函数）和map、reduce等高阶函数是函数式编程的核心工具，它们可以用来处理数据集而不直接改变它。 2. 列表和向量：R中的向量是基本的数据结构，但它们通常是不可变的。这意味着你不能更改向量中的单个元素。相反，函数式编程通常会返回一个新的向量，这个新向量基于原始向量但有必要的变化。 3. 数据框和tibbles：在R中，data.frame是最常用的数据结构之一，用于存储表格型数据。在函数式编程中，tibbles（tidyverse的一部分）提供了更严格的规则，使得它们在操作时更加一致且不易出错。 4. 管道操作符%>%：这个操作符允许将一系列操作串联起来，形成一个清晰的数据处理流程，而不会污染全局环境或产生中间变量。 5. 函数式编程库：如purrr库提供了丰富的函数式编程工具，包括映射、过滤、组合等，方便进行数据处理。 6. 递归：在不可变数据的世界里，递归是一种强大的解决问题的工具。书中可能讲解如何在R中使用递归来处理数据结构。 7. 尾递归优化：R支持尾递归优化，这意味着在某些情况下，递归函数可以避免栈溢出，从而处理大规模数据。 8. 闭包和环境：理解R中的闭包和环境是深入学习函数式编程的关键，它们在函数式编程中起到重要的作用，特别是在处理副作用和状态管理时。 9. 函数式数据结构的性能：虽然不可变性可能会导致额外的内存开销，但通过合理的数据结构设计和算法选择，可以在保持函数式编程风格的同时实现高效计算。《Functional Data Structures in R - Advanced Statistical Programming in R》这本书旨在帮助读者掌握如何在R中利用函数式数据结构进行高效、清晰且可靠的统计编程。通过对这些概念的深入理解和实践，读者可以提升R编程能力，尤其是在处理复杂数据分析任务时。

Abstract Data Structures inR

If we define abstract data structures by the operations they provide, it is

natural to represent them in R by a set of generic functions. In this book,

I will use the S3 object system for this.

Let’s say we want a data structure that represents sets, and we need

two operations on it: we want to be able to insert elements into the set, and

we want to be able to check if an element is found in the set. The generic

interface for such a data structure could look like this:

insert <- function(set, elem) UseMethod("insert")

member <- function(set, elem) UseMethod("member")

Using generic functions, we can replace one implementation with

another with little hassle. We just need one place to specify which

concrete implementation we will use for an object we will otherwise only

access through the abstract interface. Each implementation we write will

have one function for constructing an empty data structure. This empty

structure sets the class for the concrete implementation, and from here on

we can access the data structure through generic functions. We can write a

simple list-based implementation of the set data structure like this:

empty_list_set <- function() {

structure(c(), class = "list_set")

}

insert.list_set <- function(set, elem) {

structure(c(elem, set), class = "list_set")

}

If you are unfamiliar with generic functions and the S3 system, you can check out

my book Advanced Object-Oriented Programming in R book (Apress, 2017), where

I explain all this.

Chapter 2 abstraCt Data struCtures

The reason for this is simple: our functions can’t have side effects. If a

“pop” function takes a stack as an argument, it cannot modify this stack. It

can give you the top element of the stack, and it can give you a new stack

where the top element is removed, but it cannot give you the top element

and then modify the stack as a side effect. Whenever we want to modify

a data structure, what we have to do in a functional language, is to create

a new structure instead. And we need to return this new structure to the

caller. Instead of wrapping query answers and new (or “modified”) data

structures in lists so we can return multiple values, it is much easier to

keep the two operations separate.

Another rule of thumb for interfaces that I will stick to in this book,

with one exception, is that I will always have my functions take the data

structure as the first argument. This isn’t something absolutely necessary,

but it fits the convention for generic functions, so it makes it easier to work

with abstract interfaces, and even when a function is not abstract—when

I need some helper functions—remembering that the first argument is

always the data structure is easier. The one exception to this rule is the

construction of linked lists, where tradition is to have a construction

function, cons, that takes an element as its first argument and a list as its

second argument and construct a new list where the element is put at the

head of the list. This construction is too much of a tradition for me to mess

with, and I won’t write a generic function of it, so it doesn’t come into

conflict with how we handle polymorphism.

Other than that, there isn’t much more language mechanics to creating

abstract data structures. All operations we define on an abstract data

structure have some intended semantics to them, but we cannot enforce

this through the language; we just have to make sure that the operations

we implement actually do what they are supposed to do.

Chapter 2 abstraCt Data struCtures

We can construct linked lists in R using R’s built-in list data structure.

That structure is not a linked list; it is a fixed-size collection of elements

that are possibly named. We exploit named elements to build pointers. We

can implement the CONS construction like this:

linked_list_cons <- function(head, tail) {

structure(list(head = head, tail = tail),

class = "linked_list_set")

}

We just construct a list with two elements, head and tail. These will

be references to other objects—head to the element we store in the list, and

tail to the rest of the list—so we are in effect using them as pointers. We

then add a class to the list to make linked lists work as an implementation

of an abstract data structure.

Using classes and generic functions to implement polymorphic

abstract data structures leads us to the second issue we need to deal with

in R.We need to be able to represent empty lists. The natural choice for

an empty list would be NULL, which represents “nothing” for the built-in

list objects, but we can’t get polymorphism to work with NULL. We can’t

give NULL a class. We could, of course, still work with NULL as the empty list

and just have classes for non-empty lists, but this clashes with our desire

to have the empty data structures being the one point where we decide

concrete data structures instead of just accessing them through an abstract

interface. If we didn’t give empty data structures a type, we would need

to use concrete update functions instead. That could make switching

between different implementations cumbersome. We really do want to

have empty data structures with classes.

The trick is to use a sentinel object to represent empty structures.

Sentinel objects have the same structure as non-empty data structure

objects—which has the added benefit of making some implementations

easier to write—but they are recognized as representing “empty.” We

construct a sentinel as we would any other object, but we remember it

Chapter 2 abstraCt Data struCtures

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