《CPython Internals》阅读笔记：p118-p150

《CPython Internals》学习第 8 天，p118-p150 总结，总计 33 页。

一、技术总结

补充一些本人整理的关于 Context-Free Grammar(CFG) 的知识。

1.symbol(符号)

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object（符号是一个数字或数字的组合，用来表示一个数学对象）。

symbols也称为character(字符), letter(字母)，范围比较广，可以是 deciamal digits(十进制数，0,1,2,3,4,5,6,7,8,9), 也可以是letters(a,…,z, A,…,Z)，还可以是 >, <, =, !等。

2.alphabet(字母表)

2.1.定义

An alphabet is a finite, nonempty set of symbols. Conventionally, we use the symbol ∑(sigma) for an alphabet.

2.2.示例

{0, 1}，{a, …, z}。

3.string(串)

3.1. 定义

A string (or sometimes 01ì) is a finite sequence of symbols chosen from some alphabet.

3.2. 示例

For example, 01101 is a string from the binary alphabet Σ = {0, 1}. The string 111 is another string chosen from this alphabet.

3.3.empty string(空串)

The empty string is the string with zero occurrences of symbols. This string, denoted ϵ, is a string that may be chosen from any alphabet whatsoever.

3.4. length of string

4.language(语言)

4.1. 定义

A set of strings all of which are chosen from some alphabet, where Σ is a particular alphabet, is called a language.

注：language 是 string 的集合。

4.2. 示例

{10, 11, 101, 111, 1011,…}

5. grammar(文法)

全称为 Context-Free grammar(上下文无关文法)，简写为grammar(文法)。

G=(V, T, P, S)

注：G 是 grammar 的首字母。(V, T, P, S)称为四元组(及有四个元素的元组)。集合里面的元素是无序的，元组里面的元素是有序的——示例： {1, 2, 3, 4} 和 {4, 3, 2, 1}可以是相等的，但是 (V, T, P, S) 和 (S, P, T, V)是不相等的，因为顺序不一样。

5.1. V

V is a finite set of variables, also called sometimes nonterminals(非终结符) or syntactic categories(语法范畴).

5.2. T

T is a finite set of symbols that form the strings of the language being defined. We call this alphabet the terminals(终结符), or terminal symbols(终结符号).

5.3. P

P is a finite set of productions(产生式) or rules that represent the recursive definition of a language.

There is a finite set of productions or rules that represent the recursive definition of a language. Each production consists of:

(a) A variable that is being (partially) defined by the production. This variable is often called the head of the- production.

(b) The production symbol →.

© A string of zero or more terminals and variables. This string, called the body of the production, represents one way to form strings in the language of the variable of the head. In so doing, we leave terminals unchanged and substitute for each variable of the body any string that is known to be in the language of that variable.