From c4ec8c3ee2c059ded49cb618815f8a5d54d76ab1 Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Tue, 5 Aug 2025 10:08:59 +0800 Subject: [PATCH 01/14] feat: ssml for course 2. --- course2/lec2.mbt.md | 108 +++++------- course2/lec2.pdf | Bin 755484 -> 774698 bytes course2/lec2_script.mbt.md | 350 ------------------------------------- course2/script.xml | 236 +++++++++++++++++++++++++ 4 files changed, 277 insertions(+), 417 deletions(-) delete mode 100644 course2/lec2_script.mbt.md create mode 100644 course2/script.xml diff --git a/course2/lec2.mbt.md b/course2/lec2.mbt.md index 74c738f..8eb3f12 100644 --- a/course2/lec2.mbt.md +++ b/course2/lec2.mbt.md @@ -30,38 +30,27 @@ backgroundImage: url('../pics/background_moonbit.png') - 开发工具 - VS Code插件:语言服务器、包级别构建等功能 - 命令行工具:项目级别构建、项目测试、依赖管理等功能 + - [语言导览](https://tour.moonbitlang.com/zh/index.html):快速学习月兔的互动教程 - 开发环境 - 浏览器环境(无命令行工具) - - 云原生开发环境 - - [腾讯云Coding](coding.net) - - [Gitpod.io](gitpod.io) - - [Github.dev](github.dev) - - ... + - 云原生开发环境(如[Github Codespaces](https://github.com/features/codespaces)) - 本地开发环境 + --- # 浏览器环境 -- 访问 [try.moonbitlang.cn](https://try.moonbitlang.cn) ,或从[官网](https://moonbitlang.cn)点击“试用” +- 访问[try.moonbitlang.cn](https://try.moonbitlang.cn),或从[官网](https://moonbitlang.cn)点击“试用” - 试用环境可以快速创建文件并运行 - 试用环境提供代码样例,方便熟悉月兔语法 - 试用环境提供分享功能 --- -# 云原生开发环境(以腾讯云为例) - -- 基于远程服务器、按需使用的开发环境 -- 需要依赖云原生开发环境供应商,如腾讯云Coding等 -- 新建/克隆仓库并启动开发环境后,安装"MoonBit Language"插件 -- 进阶开发需安装[命令行工具](https://www.moonbitlang.cn/download/),或克隆[云原生开发模板](https://github.com/peter-jerry-ye/moonbit-template)。后续参考[月兔构建系统教程](https://www.moonbitlang.cn/docs/build-system-tutorial/) - ---- - # 本地开发环境 - 安装[VS Code](https://code.visualstudio.com/)或[VS Codium](https://mirrors.cernet.edu.cn/list/VSCodium),并安装"MoonBit Language"插件 -- 进阶开发需安装[命令行工具](https://www.moonbitlang.cn/download/)(支持Windows、MacOS与Ubuntu等环境),并参考[月兔构建系统教程](https://www.moonbitlang.cn/docs/build-system-tutorial/) +- 安装[命令行工具](https://www.moonbitlang.cn/download/)(支持Windows、MacOS与Ubuntu等环境),并参考[月兔构建系统教程](https://www.moonbitlang.cn/docs/build-system-tutorial/) --- @@ -73,46 +62,40 @@ backgroundImage: url('../pics/background_moonbit.png') ```moonbit //顶层函数定义 -fn num_water_bottles(num_bottles: Int, num_exchange: Int) -> Int { - // 本地函数定义 - fn consume(num_bottles, num_drunk) { - // 条件表达式 - if num_bottles >= num_exchange { - // 数据绑定 - let num_bottles = num_bottles - num_exchange + 1 - let num_drunk = num_drunk + num_exchange - // 函数运算 - consume(num_bottles, num_drunk) +fn num_water_bottles(num_bottles : Int, num_exchange : Int) -> Int { + for num_full = num_bottles, num_empty = 0, num_total = 0 { + if num_full > 0 { + continue 0, num_empty + num_full, num_total + num_full + } else if num_empty >= num_exchange { + continue num_empty / num_exchange, num_empty % num_exchange, num_total } else { - num_bottles + num_drunk + break num_total } } - consume(num_bottles, 0) } // 程序测试 test { - // 命令 assert_eq(num_water_bottles(9, 3), 13) assert_eq(num_water_bottles(15, 4), 19) } ``` + --- # 基于表达式编程 -- 为了写出正确的程序,我们需要知道程序是如何被运算的:我们需要建立**计算模型**来理解程序的运算过程 +- 为了写出正确的程序,我们需要知道程序是如何被运算的:建立**计算模型**来理解程序的运算过程 - 月兔程序可以通过**面向值编程**来描述 - - 面向值编程:定义是什么 + - 面向值编程:定义程序**是**什么 - 我们写的月兔代码都是表达一个值的**表达式** - - 命令式编程风格:定义做什么 + - 命令式编程风格:定义程序**做**什么 - 程序由修改程序状态的**命令**组成 - `创建名为x的变量` - `令x为5` - `令y指向x` - …… - --- # 类型、值与表达式 @@ -122,7 +105,7 @@ test { |`Int`|`-1` `0` `1` `2`|`+` `-` `*` `/`|`5` `(3 + y * x)`| |`Double`|`0.12` `3.1415`|`+` `-` `*` `/`|`3.0 * (4.0 * a)`| |`String`|`"hello"` `"Moonbit"`|`+`|`"Hello, " + "MoonBit"`| -|`Bool`|`true` `false`|`&&` `\|\|` `not()`|`not(b1) \|\| b2`| +|`Bool`|`true` `false`|`&&` `\|\|` `!`|`!b1 \|\| b2`| - 每一个**类型**对应一个**值**的集合 - 每一个**表达式**由基于值的**运算**构成,并且可以简化为一个值(或已经是一个值) @@ -141,9 +124,9 @@ test { # 静态类型 - 每一个**标识符**都关联着唯一一个类型 - “冒号”用于关联一个标识符和它的类型 - - `x: Int` - - `a: Double` - - `s: String` + - `x : Int` + - `a : Double` + - `s : String` - 每一个月兔**表达式**都有一个唯一的类型,这个类型由组成它的子表达式决定 ![类型推导示范 height:200px](../pics/well-typed-expression.drawio.png) @@ -176,10 +159,10 @@ test { - `true` - `false` - 常见运算 - - 非:非真为假,非假为真  `not(true) == false` + - 非:非真为假,非假为真  `!true == false` - 与:两者皆真才为真    `true && false == false` - 或:两者皆假才为假    `true || false == true` -- 小练习:如何用或、与、非定义异或(一者为真才为真) +- 小练习:如何用或、与、非定义**异或**(一者为真才为真) --- # 整数类型 @@ -203,9 +186,9 @@ test { - 作为基础类型的浮点数只能表示有限小数,且只能近似表达 - 浮点数在计算机内部表现形式为尾数`b`与指数`e`(均为整数):$b \times 2^e$ - 例如:[`0.1 + 0.2 != 0.3`](https://try.moonbitlang.cn/#02ce0b43) -- 月兔中浮点数类型为双精度浮点数:`Double` - - `Int`与`Double`不能混合运算:`1 + 2.0` 报错 - - `Int`转换为`Double`:`(1).to_double() == 1.0` +- 月兔中浮点数类型分为单精度浮点数`Float`和双精度浮点数`Double` + - 整数和浮点数不能混合运算:`1 + 2.0` 报错 + - `Int`可以转换为`Double`:`(1).to_double() == 1.0` - `Double`转化为`Int`:`(-1.2).to_int() == -1` - 小练习:如何通过整数与浮点数的相互转换,来比较`0.1 + 0.2`与`0.3`? @@ -228,8 +211,8 @@ test { # 多元组 - 多元组允许我们将表达固定长度的、不同类型的数据组合 - - `("Bob", 3): (String, Int)` - - `(2023, 10, 24): (Int, Int, Int)` + - `("Bob", 3) : (String, Int)` + - `(2023, 10, 24) : (Int, Int, Int)` - 可以通过从0开始的下标访问数据 - `(2023, 10, 24).0 == 2023` - `(2023, 10, 24).1 == 10` @@ -240,11 +223,11 @@ test { - 月兔有丰富的类型结构 - 函数类型 - - `op_add : (Int, Int) -> Int` + - `add : (Int, Int) -> Int` - 单值类型 - - `(): Unit` + - `() : Unit` - 列表类型 - - `List::Cons(1, Nil): List[Int]` + - `List::Cons(1, Nil) : List[Int]` - …… - 我们会在后续课程中见到它们,以及自定义数据结构 @@ -258,7 +241,7 @@ test { - 我们可以将月兔的表达式看作定义**值**的一种方式 - 我们可以将月兔的运行过程看作一系列的**计算**或**简化**的求值步骤 -- 相比之下,命令式编程则可以被看作执行一系列**行为**或者**命令**,每一个命令都会修改机器的状态 +- 相比之下,命令式编程则可以被看作执行一系列**行为**或者**命令** - 创建指针`x`与`y`并分配内存,令`x`值为3,令`y`值为4 - 令`y`指向`x` - 令`x`自增 @@ -319,11 +302,10 @@ $\mapsto$ `15`                               因为 表达式块的类型即为最后的表达式的类型,表达式块的值即为最后表达式的值 ```moonbit -// 顶层(全局)即指定义在一个文件中所有表达式块外部定义的函数或标识符 -let 顶层标识符 = 10 +let 顶层标识符 = 10 // 顶层(全局)指定义在一个文件中所有表达式块外部定义的函数或标识符 + fn 顶层函数() -> Unit { - // 本地(局部)即指某个表达式块内部的函数或标识符 - fn 本地函数() { + fn 本地函数() { // 本地(局部)指某个表达式块内部的函数或标识符 let 本地标识符 = 1 // 局部数值绑定可以简化 本地标识符 // 表达式块的值 } @@ -352,14 +334,12 @@ fn 顶层函数() -> Unit { - 对剩余表达式进行化简 ```moonbit expr -let y: Int = 10 - +let y : Int = 10 let value = { let x = 1 let tmp = x * 2 let another_tmp = { let tmp = x * 3 - tmp } tmp + another_tmp + y @@ -376,14 +356,12 @@ let value = { - 对剩余表达式进行化简 ```moonbit expr -let y: Int = 10 - +let y : Int = 10 let value = { let x = 1 let tmp = 1 * 2 // 替换x let another_tmp = { let tmp = 1 * 3 // 替换x - tmp } tmp + another_tmp + 10 // 替换y @@ -401,13 +379,11 @@ let value = { ```moonbit expr // 省略y的定义 - let value = { // 省略x的定义 let tmp = 2 // 简化右侧表达式 let another_tmp = { let tmp = 3 // 简化右侧表达式 - tmp } tmp + another_tmp + 10 @@ -425,11 +401,9 @@ let value = { ```moonbit expr let value = { - let tmp = 2 let another_tmp = { let tmp = 3 - 3 // 替换表达式 } tmp + another_tmp + 10 @@ -447,7 +421,6 @@ let value = { ```moonbit expr let value = { - let tmp = 2 let another_tmp = 3 // 简化右侧表达式 tmp + another_tmp + 10 @@ -465,7 +438,6 @@ let value = { ```moonbit expr let value = { - let tmp = 2 let another_tmp = 3 // 简化右侧表达式 2 + 3 + 10 // 替换表达式 @@ -489,7 +461,7 @@ let value = 15 # 条件表达式 -`if 条件 表达式块|条件为真 else 表达式块|条件为假` +`if 条件 条件为真的表达式块 else 条件为假的表达式块` 月兔的条件表达式也是**表达式**,因此可以被用在其他表达式内 @@ -503,7 +475,9 @@ let value = 15 `if 条件 表达式块 else 表达式块` -分支的表达式块的类型需相同,且整个条件表达式的类型取决于分支的表达式块的类型;条件的类型需为逻辑值 +- 分支的表达式块的类型需相同 +- 整个条件表达式的类型取决于分支的表达式块的类型 +- 条件的类型需为逻辑值 ![](../pics/if-else-then.drawio.png) @@ -511,7 +485,7 @@ let value = 15 # 简化条件表达式 -条件式表达式的值为哪个分支的值取决于条件的简化结果为真或假 +条件式表达式的值为哪个分支的值取决于**条件的简化结果**为真或假 例如: diff --git a/course2/lec2.pdf b/course2/lec2.pdf index 454c08e7bd7c6abe1943c6ea7270423e5d277f9b..736211315a472486745c043b8b7ea25a02108927 100644 GIT binary patch delta 301334 zcmZ6yQ*>a>^935)$;6u2ww;M>+cr-)vF*vkwl%SB+nU(Po$tTy!~NZduCu$U*E#*L z*Q)B?b+Tg_$_p85dCLH9HaGzRI2TuEGb1}V&+Mw?b?bE@l%Lm6)JN?zixU@0#1M71 zq57>e67gG5?99n)R=Uuy&t@95tFd%Vun9ty65HASlhvjv!|*650%J)U1*mIPo@ml& zS)-6HA8wNG`Iv1QI9qP3&^nD)2aXZ*X03+c5)(u7#E-DbXDt31Xz0##}{}i3) 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num_bottles >= num_exchange { - // 数据绑定 - let num_bottles = num_bottles - num_exchange + 1 - let num_drunk = num_drunk + num_exchange - // 函数运算 - consume(num_bottles, num_drunk) - } else { - num_bottles + num_drunk - } - } - consume(num_bottles, 0) -} - -// 程序测试 -test { - // 命令 - assert_eq(num_water_bottles(9, 3), 13) - assert_eq(num_water_bottles(15, 4), 19) -} -``` - -我们在此定义了一个顶层函数以及程序的入口。顶层函数中,我们定义了一个本地函数并且调用该函数进行计算。本地函数的值为一个条件表达式,对应条件为真的表达式块中我们定义了数据绑定并调用函数作为表达式块的值,而在另一个分支中我们进行了简单的加法运算。在程序入口中,我们使用了两个断言命令来判断我们程序的正确性。我们在上一节课已经看到了,这个程序的运行没有任何的输出,但它具体是如何运行的呢? - -为了能够正确地理解代码所定义的程序的行为,从而写出正确的程序或是读懂他人的程序,我们需要能够理解程序的计算过程。为此,我们需要建立一个计算模型。月兔程序可以通过以值为中心的编程,或者说基于表达式的编程来描述,即将程序看作是定义一个值的表达式,而程序的运行则是对这个表达式进行简化获得我们所定义的值的过程。相比较之下,命令式编程风格则是定义做什么,通常由一系列的命令组成,例如:`创建名为x的变量`、`令x为5`、`令y指向x`、……我们将会在后续课程中更深入了解。 - -### 类型、值与表达式 - -每一个**类型**对应的是一个**值**的集合,如`Int`对应部分整数的集合;`Double`对应了部分实数的集合;`String`对应了字符串的集合等,我们稍后将详细了解月兔的基础数据类型。而每一个**表达式**由基于值的**运算**构成,并且可以简化为一个值(或已经是一个值)。在定义表达式的时候,可以通过使用括号来嵌套表达式。以下是一些例子。 - -|类型|值|运算|表达式| -|-----|------|----------|-----------| -|`Int`|`-1` `0` `1` `2`|`+` `-` `*` `/`|`5` `(3 + y * x)`| -|`Double`|`0.12` `3.1415`|`+` `-` `*` `/`|`3.0 * (4.0 * a)`| -|`String`|`"hello"` `"Moonbit"`|`+`|`"Hello, " + "MoonBit"`| -|`Bool`|`true` `false`|`&&` `\|\|` `not()`|`not(b1) \|\| b2`| - - -### 静态与动态 - -“静态”指在程序运行**之前**的事物,而“动态”指在程序运行**之时**的事物,动静描述的便是程序是否在运行状态。 - -月兔拥有静态类型系统。这意味着,在程序运行之前,编译器即会检查程序的类型是否定良好,以最大程度减少在运行时出现对数据进行错误类型的运算从而导致程序中断或给出错误的结果,如对一个逻辑值进行加减乘除。 - -月兔中每一个**标识符**(即标识某个实体的符号)都关联着唯一一个类型,一般用冒号进行关联,如: -- `x: Int` -- `a: Double` -- `s: String` - -月兔中每一个**表达式**都有唯一的一个类型,这个类型由组成它的子表达式决定: -![类型推导示范 height:200px](well-typed-expression.drawio.png) -如图中的表达式,`a`的类型为`Double`,可以与同为`Double`的0.2进行加法。之后,我们通过`to_int`函数将其转换为`Int`,此时我们可以与`x`进行整数加法,获得一个整数作为表达式的值。因此,表达式的类型为`Int`。 - -月兔使用**类型推导**来确认程序是否正确使用类型,而开发工具也会在开发时实时提示检查到的类型错误: -![类型错误示例 height:200px](not-well-typed-expression.drawio.png) -如图中的表达式,`s`的类型为`String`,因此我们期待它与另一个字符串相加,即连接两个字符串。但此时,右侧类型为`Int`,不能相加。因此,编辑器以红色下划线提示我们它的错误。 - -### 月兔的基本数据类型 - -为了进行基于表达式的编程,我们需要了解月兔中有哪些值。我们在这里先介绍最简单的月兔的基本数据类型中的一部分:逻辑值、整数、浮点数、字符与字符串、多元组。其他的数据类型将在之后的课程中一一介绍。我们在这部分的介绍中不涉及数据的底层表现,如二进制、二进制补码等,感兴趣的同学可以在推荐阅读中进行拓展学习。 - -#### 逻辑值(布尔值) - -首先我们要介绍的数据类型为逻辑值,亦称为布尔值,纪念发明布尔代数的数学家乔治·布尔而得名。它只有两种值:真和假,`true`和`false`。 - -常见的逻辑值的运算有:或、与、非。 - -非,即是对当前逻辑值取反,非真即为假,非假即为真。 - -与,当两者皆真才为真。例如,真与假,其结果为假。真与真,其结果为真。假与假,其结果为假。 - -或,当两者皆假才为假。例如,真或假,其结果为真。真或真,其结果为真。假或假,其结果为假。 - -我们这里给出月兔中定义或、与、非的代码样例: - - 非:`not(true) == false` - - 与:`true && false == false` - - 或:`true || false == true` - -代码样例中的两个等号表示比较,右侧则是我们对左侧定义的表达式的简化值的预期。换句话说,这些代码本身即是类型为逻辑值的表达式,并且我们期待它们的值均为真。 - -在这里,我们给出一个小练习:如何用或、与、非定义异或?异或,当一者为真才为真。 - -#### 整数类型 - -接下来我们介绍的数据类型为整数。整数大家都很熟悉,然而在计算机中,中央处理器一次能计算的数据大小是有限的。为了保证性能,基础数据所代表的数据范围也是有限的。在月兔中,基础类型中的整数分为两个类型,分别有不同的值域: -- 整型 `Int`:从$-2^{31}$到$2^{31}-1$(即从-2147483648到2147483647) -- 长整型 `Int64`:从$-2^{63}$到$2^{63}-1$ - -在月兔中,整数相除获得的依然是整数,其结果为整数除法中的商。若涉及负数,则按照正数进行运算后赋予正负号。例如,-4除以3结果为-1。当然,除以零依然不被允许,会在运行时产生错误中断程序。 - -既然整数有范围,那么对整数进行超出范围的运算后,获得的结果会**溢出**,即会变成范围中的某一整数而非期待的正确结果。举例来说,如果对最大的整型加一,则会变为最小的整型。 - -在月兔中,整数的四则运算只能由相同类型的整型进行,也就是整型只能与整型进行运算,长整型只能与长整型进行运算。如果想要将整型与长整型进行计算,需要将整型利用函数`to_int64`提升为长整形之后再运算,如`(100).to_int64()`。当直接定义长整型数字时,需在数字最后加上大写的L以示区别,如`2147483648L`,否则默认为整型。而将长整型转化为整型则使用`to_int`,如`100L.to_int()`。 - -需要注意的是,整数调用函数必须加括号。 - -在这里,我们给出一个小练习:如何计算两个正的`Int`的平均数(不考虑小数)而不溢出? - -#### 浮点数类型 - -接下来我们介绍实数在计算机内部的表示。如之前所说,计算机中,基础数据代表的数据长度是有限的,因此我们无法表示一切的实数,而只能表示一部分的有限小数,并且通过$b \times 2^e$(尾数`b`与指数`e`均为整数)的方式进行近似表达。[例如](https://try.moonbitlang.cn/#02ce0b43):`0.1 + 0.2 != 0.3`(感叹号与等号在月兔中代表不等号)。 - -在月兔中,浮点数有一个类型:`Double`。与整数相同,浮点数的四则运算只能是浮点数与浮点数进行并获得浮点数。若要对整数与浮点数进行运算,则须将整数提升为浮点数,如`(1).to_double()`,再进行运算。反之,也可通过舍弃小数点后的部分从浮点数近似为整数,如`(-1.2).to_int()`。 - -在这里,我们给出一个小练习:如何通过整数与浮点数之间的相互转换,比较`0.1 + 0.2`与`0.3`到小数点后一位使得结果为真? - -#### 字符与字符串 - -我们在电脑上看到的一个个汉字、英文字母、数字等,都被归类为字符。而它们的序列则是字符串。在月兔中,字符类型为`Char`,而字符串类型为`String`。字符用英文单引号标识,如`'a'`;字符串用英文双引号标识,如`"Hello!"`。 - -这些文字,是如何在计算机中表达的呢?答案是,通过编码,将一个个数字映射为一个个字母,即一个字符对应一个数字。这种映射有多种可能的方式。较为通用的是ASCII,即美国信息交换标准代码,第一版在1963年发布。它定义了英文字符与常见符号到0~127的映射。举例来说,大写字母A到Z对应了从65到90的数字。之后,为了兼容所有国家的文字以及表情符号,有了Unicode,即统一码。在兼容ASCII的基础上进行了拓展。举例来说,“月”与“兔”在统一码中分别对应26376与20820。 -统一码有不同的编码方式,如UTF-8、UTF-16等,感兴趣的同学可以搜索它们的区别。 - -月兔的字符编码采用了Unicode。基于编码,我们可以将整型转化为字符,如`Char::from_int(65)`应为`'A'`。 - -#### 多元组 - -在了解了一系列基础数据后,我们也会希望能够表达一些比较复杂的数据类型,例如日期需要由三个数字构成,而一个人的个人信息或许可以包含他/她的名字和年龄。为此,多元组允许我们将不同类型的数据结合在一起,用小括号包裹,用逗号分隔。如: -- `("Bob", 3): (String, Int)` -- `(2023, 10, 24): (Int, Int, Int)` - -我们可以通过从0开始的下标访问数据 -- `(2023, 10, 24).0 == 2023` -- `(2023, 10, 24).1 == 10` - -#### 其他数据类型 - -月兔还有着其他的类型结构,如函数类型、单值类型、列表类型、自定义结构体等。我们将会在后续的课程中见到它们,并且学习如何自定义复杂的数据结构。 - -### 计算表达式的值 - -#### 简化 vs 运行 - -我们可以将月兔的表达式看作定义**值**的一种方式;同样地,我们可以将月兔的运行过程看作一系列的**计算**或者**简化**的求值步骤。相对而言,命令式编程则可以被看作执行一系列**行为**或者**命令**,其中每一个命令都会修改机器的状态,如: -- 创建指针`x`与`y`并分配内存,令`x`值为3,令`y`值为4 -- 令`y`指向`x` -- 令`x`自增 -- …… - -![](./local-store.drawio.png) - -我们将<表达式>简化为<值>记作:<表达式> $\Rightarrow$ <值>,如: -- `3` $\Rightarrow$ 3 (此时值即为本身) -- `3 + 4` $\Rightarrow$ 7 -- `2 * (4 + 5)` $\Rightarrow$ 18 -- `num_water_bottles(9, 3)` $\Rightarrow$ 13 - -我们将分解$\Rightarrow$简化的流程为**单步**计算,记作$\mapsto$,如: - -      `(2 + 3) * (5 - 2)` -$\mapsto$ `5 * (5 - 2)`          因为`2 + 3` $\mapsto$ 5 -$\mapsto$ `5 * 3`                        因为`5 - 2` $\mapsto$ 3 -$\mapsto$ `15`                               因为`5 * 3` $\mapsto$ 15 - -故 `(2 + 3) * (5 - 2)` $\Rightarrow$ `15` - -#### 数值绑定 - -数值绑定的定义形式为:`let <标识符> : <类型> = <表达式>`。数值绑定将一个标识符与一个表达式绑定,作为计算的中间值来简化程序定义,避免出现超级复杂的表达式。数据绑定中的类型声明多数时候可以省略,月兔编译器会根据表达式类型进行推断,如: -- `let x = 10` -- `let y = "String"` - -数值绑定后,出现的标识符均可被替换为绑定的表达式。若同一标识符被绑定多次,则以最近一次绑定为准,即最新的定义遮掩了之前的定义。如超出定义生效范围,则会恢复被遮掩的定义,因此并非进行了修改。 - -#### 表达式块与作用域 - -表达式块由大括号定义,形如: -``` -{ - 数值绑定 - 数值绑定 - …… - 表达式 -} -``` - -表达式块的类型即为最后的表达式的类型,表达式块的值即为最后表达式的值。 - -如果一个函数定义或数值绑定定义在所有表达式块外,则我们称之为顶层函数或顶层定义;如果一个函数定义或数值绑定定义在某个表达式内,则我们称之为本地函数或本地定义。顶层可以被称为全局,而本地可称为局部,这是因为它们生效的范围,又称作用域。 - -作用域指的是定义或数值绑定有效的范围,分为全局和局部。全局指的是整个文件范围内生效,而局部指的是在定义开始之后到当前表达式块结束生效。在顶层定义的,在整个文件范围内生效,因此又称全局;在本地定义的,在定义之后到表达式块结束前生效,因此又称局部。 -例如: -![height:12cm](scope.drawio.png) - -图中我们定义了两个顶层标识符`value`和`y`。`value`的值由表达式块定义,其中定义了`x``tmp`和`another_tmp`。而在`another_tmp`中我们又定义了一次`tmp`。注意箭头指向,定义了`another_tmp`的值的表达式(第7行)中的`tmp`是最近定义的第5行的`tmp`,它遮掩了第3行`tmp`的定义,而定义了`value`的值的表达式(第9行)中的`tmp`则是第3行的`tmp`,因为此时已经超出了第5行的`tmp`的作用域(第5-8行)。同时我们注意到,第9行的`y`的定义出现在第12行,也就是定义出现在了使用之后。这是被允许的,因为`y`在顶层被定义,作用域为全局。 - -#### 数值绑定下的表达式简化 - -分为以下几步: -- 简化数值绑定右侧的表达式 -- 将出现的标识符**替换**为简化后的值 -- 省略数值绑定部分 -- 对剩余表达式进行化简 - -不妨分析上面看到的案例: -```rust -let value = { - let x = 1 - let tmp = x * 2 - let another_tmp = { - let tmp = x * 3 - - tmp - } - tmp + another_tmp + y -} - -let y: Int = 10 -``` - -首先,我们可以替换所有`x`出现的地方为`1`并省略`x`的定义。`y`同理。 - -```rust -let value = { - // 省略x - let tmp = 1 * 2 // 替换x - let another_tmp = { - let tmp = 1 * 3 // 替换x - - tmp - } - tmp + another_tmp + 10 // 替换y -} - -// 省略y -``` - -之后,我们可以简化两处tmp定义的右侧表达式,并对`another_tmp`中的标识符进行替换。 - -```rust -let value = { - let tmp = 2 // 简化右侧表达式 - let another_tmp = { - let tmp = 3 // 简化右侧表达式 - - 3 // 替换表达式 - } - tmp + another_tmp + 10 -} -``` - -然后,我们可以计算`another_tmp`的值。回忆一下,表达式块的值即是表达式块最后的表达式的值。 - -```rust -let value = { - - let tmp = 2 - let another_tmp = 3 - tmp + another_tmp + 10 -} -``` - -到了这一步,我们可以替换剩下的标识符为它们所绑定的值。 - -```rust -let value = { - - let tmp = 2 - let another_tmp = 3 - 2 + 3 + 10 -} -``` - -然后我们便可以得出结论: - -```rust -let value = 15 -``` - -#### 条件表达式 - -除了对值进行运算以外,月兔中还有条件表达式,用于判断,根据条件给出不同的值。 - -条件表达式的定义形式为:`if 条件 表达式块|条件为真 else 表达式块|条件为假`。在月兔中,条件表达式亦是表达式,因此可以被用在其他的表达式内,如: -- `if 1 < 100 { 1 } else { 0 } * 10` -- `if x > y { "x" } else { "y" } + " is bigger"` -- `if 0.1 + 0.2 == 0.3 { "Great!" } else { "C'est la vie :-)" }` - -条件表达式中,条件的类型需为逻辑值,而其余两个表达式块类型需相同,这个类型代表了整个表达式的类型,如: -![](if-else-then.drawio.png) -其中,条件是对两个浮点数进行相等的判定,类型为逻辑值;真假分支表达式块的值均为字符串,因此整个条件表达式类型为字符串。 - -条件表达式的简化取决于条件的简化结果为真或假。若为真,则条件表达式简化为第一个表达式块的值;若为假,则简化为第二个表达式块的值。例如: - -      `if 1 < 100 { 1 } else { 0 } * 10` -$\mapsto$ `if true { 1 } else { 0 } * 10` -$\mapsto$ `1 * 10` -$\mapsto$ `10` - -条件表达式必须有两个分支(否则如果条件为假,表达式的值该是什么呢?) - -## 课程总结 - -我们今天学习了 - -- 如何配置月兔开发环境 - - 浏览器开发环境 - - 云原生开发环境 - - 本地开发环境 -- 月兔基本数据类型 - - 逻辑值 - - 整数和浮点数 - - 字符和字符串 - - 多元组ß -- 如何以表达式和值来看待月兔程序,以简化求值来理解月兔程序的运行 \ No newline at end of file diff --git a/course2/script.xml b/course2/script.xml new file mode 100644 index 0000000..24807fd --- /dev/null +++ b/course2/script.xml @@ -0,0 +1,236 @@ + + +

+ 大家好,欢迎来到由 IDEA 研究院基础软件中心为大家带来的现代编程思想公开课。 + 今天是第二节课,主题是月兔开发与月兔中的表达式。 + 我们将会讲解如何准备月兔的开发环境,然后通过建立计算模型来逐步理解用月兔编写的程序。 +

+

+ 首先,让我们回顾一下上周提到过的内容。 + 我们这门课程使用的编程语言月兔是一门现代的、静态类型的多范式编程语言,支持函数式编程、命令式编程等多种编程范式。 + 它的语法较为容易上手。大家可以在月兔编程语言的官网看到更多的信息。 +

+

+ 月兔的开发工具主要由两部分构成:VSCode插件与命令行工具。 + 其中,VSCode插件依托VSCode这一被广泛使用的编辑器提供代码的开发环境,提供了诸如语法高亮、变量引用与定义的跳转、开发时的自动补全、程序的运行与调试等功能。 + 命令行工具提供项目级别构建、测试、依赖管理等功能。一个项目通常由多个包组成,一个包又可以包含多个月兔代码文件。 + 在一个包内,不同的文件之间可以相互引用对方的定义,方便将功能分门别类定义在不同文件中。 + 一个项目也可能引用其他项目,来借用他人实现的功能。 + 关于项目和包的组织结构与定义,我们将会在之后的课程中详细介绍。在课程中,我们将会限制于包级别的开发。 + 月兔还提供一个语言导览网站,这是一个互动式的语言教程,涵盖了月兔语言的所有方面。 + VSCode插件可以在浏览器的VSCode中使用,因此我们支持的开发环境有三类,分别是基于VSCode Web的浏览器环境、云原生开发环境和本地开发环境。 +

+

+ 访问try.moonbitlang.cn即可使用浏览器环境。 + 浏览器环境提供了诸多代码样例,方便大家熟悉月兔语法。 + 在浏览器环境中,大家可以创建新文件并运行,也可以参考包的案例。 + 浏览器环境还提供单个文件的分享功能,方便大家分享代码以及提交反馈。 + 需要注意的是,当前的浏览器环境不会自动保存修改,因此如果窗口被刷新,所有的修改都会丢失。 + 请大家使用“另存为”功能对文件进行保存。 +

+

+ 本地开发需首先安装VSCode,或兼容VSCode插件的其他开发软件,如VSCode的开源构建VSCodium。 + 国内的小伙伴可以使用后者,有各个大学提供的镜像站方便下载。 + 在开发软件的扩展中,搜索并安装"MoonBit Language"插件。 + 进阶开发需要安装命令行工具,可以在MoonBit官方网站下载命令行工具。 + 后续开发流程和浏览器环境相同。 +

+

+ 浏览器环境已经为我们准备了一个项目路径,我们只需在这个路径下新建月兔文件即可编写代码。 + 在本地环境,我们需要用命令行工具创建一个项目,然后再编写代码。 + 创建项目的命令为moon new,在交互式提示下输入项目路径、作者名字、项目名称即可,其它选项可以使用默认值。 +

+

+ 在进行了月兔的开发准备后,让我们尝试理解月兔的代码。 + 下面将为大家展示一个典型的月兔程序,亦是上一节课的案例代码。 + 我们在此定义了一个顶层函数以及测试代码块。 + 顶层函数中,我们定义了一个for循环表达式,循环体内是一个条件表达式。 + 在测试代码块,我们使用了两个断言命令来判断我们程序的正确性。 + 上节课提到,在开发环境中,测试代码上方会有个test按钮,点击它就可以运行测试用例,验证我们的代码是否正确。 + 为什么我们定义的函数可以计算出正确的结果呢?接下来我们要理解这段代码是如何运行的, +

+

+ 为了能够正确地理解代码所定义的程序的行为,从而写出正确的程序或是读懂他人的程序,我们需要能够理解程序的计算过程。 + 为此,我们需要建立一个计算模型。 + 月兔程序可以通过以值为中心的编程,或者说基于表达式的编程来描述。 + 即,将程序看作是定义一个值的表达式,而程序的运行则是对这个表达式进行简化获得我们所定义的值的过程。 + 相比较之下,命令式编程风格则是定义做什么,通常由一系列的命令组成,例如:`创建名为x的变量`、`令x为5`、`令y指向x`。 + 我们将会在后续课程中更深入了解。 +

+

+ 每一个类型对应的是一个值的集合,如Int对应部分整数的集合;Double对应了部分实数的集合;String对应了字符串的集合,等等。 + 我们稍后将详细了解月兔的基础数据类型。 + 每一个表达式由基于值的运算构成,并且可以简化为一个值(或已经是一个值)。 + 在定义表达式的时候,可以通过使用括号来嵌套表达式。以下是一些例子。 +

+

+ 另一个需要了解的概念是静态与动态。 + “静态”指在程序运行前的性质,而“动态”指在程序运行时的性质。 + 月兔拥有静态类型系统。 + 这意味着,在程序运行之前,编译器即会检查程序的类型是否定良好,以最大程度减少在运行时出现对数据进行错误类型的运算从而导致程序中断或给出错误的结果。 + 例如对一个逻辑值进行加减乘除。 + 月兔中每一个标识符(即标识某个实体的符号)都关联着唯一一个类型,标识符和类型用冒号进行关联。 + 月兔中每一个**表达式**都有唯一的一个类型,这个类型由组成它的子表达式决定。 + 如图中的表达式,a的类型为Double,可以与同为Double的0.2进行加法。 + 之后,我们通过to_int函数将其转换为Int。 + 此时我们可以与x进行整数加法,获得一个整数作为表达式的值。 + 因此,整个表达式的类型为Int。 + 月兔使用类型推导来确认程序是否正确使用类型,而开发工具也会在开发时实时提示检查到的类型错误。 + 如图中的表达式,s的类型为String,因此我们期待它与另一个字符串相加,即连接两个字符串。 + 但此时,右侧类型为Int,不能相加。因此,编辑器以红色下划线提示我们它的错误。 +

+

+ 为了进行基于表达式的编程,我们需要了解月兔中有哪些值。 + 我们在这里先介绍月兔的基本数据类型中最简单的一部分:逻辑值、整数、浮点数、字符与字符串,以及多元组。 + 其他的数据类型将在之后的课程中一一介绍。 + 我们在这部分的介绍中不涉及数据的底层表示,如二进制、二进制补码等,感兴趣的同学可以在推荐阅读中进行拓展学习。 +

+

+ 首先我们要介绍的数据类型为逻辑值,亦称为布尔值,纪念发明布尔代数的数学家乔治·布尔而得名。 + 它只有两种值:真和假,即true和false。 + 常见的逻辑值的运算有:或、与、非。 + 非,即是对当前逻辑值取反,非真即为假,非假即为真。 + 与,当两者皆真才为真。例如,真与假,其结果为假。真与真,其结果为真。假与假,其结果为假。 + 或,当两者皆假才为假。例如,真或假,其结果为真。真或真,其结果为真。假或假,其结果为假。 + 在我们给出的代码样例中,两个等号表示比较,等号右侧是我们对左侧定义的表达式的简化值的预期。 + 换句话说,这些代码本身也是类型为逻辑值的表达式,并且我们期待它们的值均为真。 + 在这里,我们给出一个小练习:如何用或、与、非定义异或? +

+

+ 接下来我们介绍的数据类型为整数。 + 整数大家都很熟悉,然而在计算机中,中央处理器一次能计算的数据大小是有限的。 + 为了保证性能,基础数据所代表的数据范围也是有限的。 + 在月兔中,基础类型中的整数分为整形和长整型,分别有不同的值域。 + 在月兔中,整数相除获得的依然是整数,其结果为整数除法中的商。 + 若涉及负数,则按照正数进行运算后赋予正负号。例如,-4除以3结果为-1。 + 当然,除以零依然不被允许,会在运行时产生错误中断程序。 + 既然整数有范围,那么对整数进行超出范围的运算后,获得的结果就会溢出。 + 溢出的结果会变成范围中的某一整数而非期待的正确结果。举例来说,如果对最大的整型加一,则会变为最小的整型。 + 在月兔中,整数的四则运算只能由相同类型的整型进行,也就是整型只能与整型进行运算,长整型只能与长整型进行运算。 + 如果想要将整型与长整型进行计算,需要将整型利用函数to_int64提升为长整形之后再运算。 + 当直接定义长整型数字时,需在数字最后加上大写的L以示区别,否则默认为整型。 + 而将长整型转化为整型则使用to_int,如100L.to_int()。 + 需要注意的是,整数调用方法必须加括号。 + 在这里,我们给出一个小练习:如何计算两个正整数的平均数而不溢出? +

+

+ 接下来我们介绍实数在计算机内部的表示。 + 如之前所说,计算机中,基础数据代表的数据长度是有限的,因此我们无法表示一切的实数,而只能表示一部分的有限小数,并且通过尾数与指数结合的方式进行近似表达。 + 例如,0.1、0.2、0.3等小数在计算机中都无法精确表示,因此0.1 + 0.2的结果并不等于0.3。 + 在月兔中,浮点数也有两个类型:Float和Double,分别对应单精度和双精度浮点数。 + 与整数相同,浮点数的四则运算只能是同精度的两个浮点数进行,并获得同精度的浮点数计算结果。 + 若要对整数与浮点数进行运算,则须将整数提升为浮点数,再进行运算。 + 反之,也可通过舍弃小数点后的部分从浮点数近似为整数。 + 在这里,我们给出一个小练习:如何通过整数与浮点数之间的相互转换,比较0.1 + 0.2与0.3到小数点后一位使得结果为真? +

+

+ 我们在电脑上看到的一个个汉字、英文字母、数字等,都被归类为字符。 + 而字符的序列则是字符串。 + 在月兔中,字符类型为Char,而字符串类型为String。 + 字符用英文单引号标识;字符串用英文双引号标识。 + 这些文字是如何在计算机中表达的呢? + 答案是,通过编码,将一个个数字映射为一个个字符,即一个字符对应一个数字。 + 这种映射有多种可能的方式。较为通用的是ASCII,即美国信息交换标准代码,第一版在1963年发布。 + 它定义了英文字符与常见符号到0~127的映射。 + 举例来说,大写字母A到Z对应了从65到90的数字。 + 之后,为了兼容所有国家的文字以及表情符号,有了Unicode,即统一码。 + 在兼容ASCII的基础上进行了拓展。 + 举例来说,“月”与“兔”在统一码中分别对应26376与20820。 + 统一码有不同的编码方式,如UTF-8、UTF-16等,感兴趣的同学可以搜索它们的区别。 + 月兔的字符编码采用了Unicode。 + 基于编码,我们可以将整型转化为字符。 +

+

+ 在了解了一系列基础数据后,我们也会希望能够表达一些比较复杂的数据类型。 + 例如日期需要由三个数字构成,而一个人的个人信息或许可以包含他/她的名字和年龄。 + 为此,多元组允许我们将不同类型的数据结合在一起,用小括号包裹,用逗号分隔。 + 我们可以通过从0开始的下标访问数据 +

+

+ 月兔还有着其他的类型结构,如函数类型、单值类型、列表类型、自定义结构体等。 + 我们将会在后续的课程中见到它们,并且学习如何自定义复杂的数据结构。 +

+

+ 下面我们学习如何计算月兔中的表达式。 +

+

+ 我们可以将月兔的表达式看作定义值的一种方式; + 进一步的,我们可以将月兔的运行过程看作一系列的计算或者简化表达式的求值步骤。 + 相对而言,命令式编程则可以被看作执行一系列行为或者命令,其中每一个命令都会修改机器的状态。 + 我们用胖箭头表示一个表达式会被化简为一个值。 +

+

+ 我们将分解化简的流程为一系列单步计算,用竖线加上箭头的符号表示。 + 例如,2+3,乘,5-2,这个表达式会被单步计算为5乘5-2,进一步计算得到5乘3,最后得到15。 + 因此,原表达式被化简为15这个值。 +

+

+ 下面我们介绍月兔的数值绑定。 + 数值绑定的定义形式为let、标识符、冒号、类型、等号、表达式。 + 数值绑定将一个标识符与一个表达式绑定,作为计算的中间值来简化程序定义,避免出现超级复杂的表达式。 + 数据绑定中的类型声明多数时候可以省略,月兔编译器会根据表达式类型进行推断。 + 数值绑定后,出现的标识符均可被替换为绑定的表达式。 + 若同一标识符被绑定多次,则以最近一次绑定为准,即最新的定义遮掩了之前的定义。 + 如超出定义生效范围,则会恢复被遮掩的定义,因此并非进行了修改。 +

+

+ 下面我们介绍月兔的表达式块。 + 表达式块由大括号定义,包含一系列表达式或数值绑定。 + 表达式块中最后的表达式的类型即为表达式块的类型;最后的表达式的值即为表达式块的值。 + 如果一个函数定义或数值绑定定义在所有表达式块外,则我们称之为顶层函数或顶层定义。 + 如果一个函数定义或数值绑定定义在某个表达式内,则我们称之为本地函数或本地定义。 + 顶层可以被称为全局,而本地可称为局部,这是因为它们生效的范围是全局或局部的。 +

+

+ 定义的生效范围又称作用域。 + 全局作用域指的是整个文件范围内生效,而局部作用域指的是在定义开始之后,直到当前表达式块结束期间生效。 + 图中我们定义了两个顶层标识符value和y。 + value的值由表达式块定义,其中定义了x、temp和another temp。 + 而在another temp中我们又定义了一次temp。 + 注意箭头指向,在第七行定义了another temp的值的表达式中的temp是最近定义的第5行的temp,它遮掩了第3行temp的定义。 + 而第九行定义了value的值的表达式中的temp则是第3行的temp,因为此时已经超出了第5行的temp的作用域(第5-8行)。 + 同时我们注意到,第9行的y的定义出现在第12行,也就是定义出现在了使用之后。这是被允许的,因为y在顶层被定义,作用域为全局。 +

+

+ 基于数值绑定,表达式的化简过程分为以下几步。 + 首先,简化数值绑定右侧的表达式。 + 然后,将出现的标识符替换为简化后的值。 + 在此过程中,省略数值绑定本身。 + 最后,重复上述步骤,对剩余表达式进行化简。 + 按此步骤对上面的案例进行化简。 + 首先,我们可以替换所有x出现的地方为1,并省略x的数值绑定。 + 同理,替换y为10,并省略y的数值绑定。 +

+

+ 之后,我们可以简化两处temp定义的右侧表达式,并对another temp中的标识符进行替换。 +

+

+ 然后,我们可以计算another temp的值。回忆一下,表达式块的值即是表达式块内最后一个表达式的值。 +

+

+ 到了这一步,我们可以替换剩下的标识符为它们所绑定的值。 +

+

+ 最后我们可以得出结论,value的值为15. +

+

+ 除了对值进行运算以外,月兔中还有条件表达式,用于判断,根据条件给出不同的值。 + 条件表达式的定义形式为if、条件、条件为真的表达式块、else、条件为假的表达式块。 + 在月兔中,条件表达式亦是表达式,因此可以被用在其他的表达式内,比如图中这些例子。 + 条件表达式中,条件的类型必须为逻辑值,而其余两个表达式块的类型必须相同,这个类型代表了整个表达式的类型。 + 比如例子中的条件表达式,条件是对两个浮点数进行相等的判定,类型为逻辑值;真假分支表达式块的值均为字符串,因此整个条件表达式类型为字符串。 + 条件表达式的简化取决于条件的简化结果为真或假。 + 若为真,则条件表达式简化为第一个表达式块的值。 + 若为假,则简化为第二个表达式块的值。 +

+

+ 总结一下今天学习的内容。 + 我们首先了解了如何配置月兔的开发环境,包括浏览器、云原生和本地开发环境。 + 然后,我们了解了月兔的基本数据类型,包括逻辑值、整数、浮点数、字符与字符串以及多元组。 + 最后,我们学习了月兔的表达式和数值绑定,以及如何通过简化表达式来理解月兔程序的运行。 +

+

+ 那么以上便是今天课程的全部内容。感谢大家的收看,我们下次再见。 +

+ + \ No newline at end of file From 565783879443205bcae8909b1e6f08c30859487f Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Tue, 5 Aug 2025 14:14:34 +0800 Subject: [PATCH 02/14] chore: adjust pronounciation for course 2 --- course2/lec2.mbt.md | 14 +++++---- course2/lec2.pdf | Bin 774698 -> 740789 bytes course2/script.xml | 75 +++++++++++++++++++++++--------------------- 3 files changed, 48 insertions(+), 41 deletions(-) diff --git a/course2/lec2.mbt.md b/course2/lec2.mbt.md index 8eb3f12..ed33d79 100644 --- a/course2/lec2.mbt.md +++ b/course2/lec2.mbt.md @@ -114,8 +114,8 @@ test { --- # 静态 vs 动态 -- “静态”指在程序运行**之前**的事物 -- “动态”指在程序运行**之时**的事物 +- “静态”指在程序运行**之前**的性质 +- “动态”指在程序运行**之时**的性质 月兔拥有静态类型系统:在程序运行之前,编译器即会检查程序的类型是否定义良好 @@ -185,9 +185,11 @@ test { - 作为基础类型的浮点数只能表示有限小数,且只能近似表达 - 浮点数在计算机内部表现形式为尾数`b`与指数`e`(均为整数):$b \times 2^e$ - - 例如:[`0.1 + 0.2 != 0.3`](https://try.moonbitlang.cn/#02ce0b43) + - 例如:[`0.1 + 0.2 != 0.3`] - 月兔中浮点数类型分为单精度浮点数`Float`和双精度浮点数`Double` - - 整数和浮点数不能混合运算:`1 + 2.0` 报错 + - 整数和浮点数不能直接混合运算:`1 + 2.0` 报错 + - 当第一个操作数是浮点数时,第二个操作数会被自动提升为浮点数: + `2.0 + 1 == 3.0` - `Int`可以转换为`Double`:`(1).to_double() == 1.0` - `Double`转化为`Int`:`(-1.2).to_int() == -1` - 小练习:如何通过整数与浮点数的相互转换,来比较`0.1 + 0.2`与`0.3`? @@ -226,8 +228,8 @@ test { - `add : (Int, Int) -> Int` - 单值类型 - `() : Unit` - - 列表类型 - - `List::Cons(1, Nil) : List[Int]` + - 数组类型 + - `[1, 2, 3] : Array[Int]` - …… - 我们会在后续课程中见到它们,以及自定义数据结构 diff --git a/course2/lec2.pdf b/course2/lec2.pdf index 736211315a472486745c043b8b7ea25a02108927..7c005844d9364a405938d6c696350d5fab37dab0 100644 GIT binary patch delta 206690 zcmZ6xV{{wEtFxJr9js?|Q}TxOCKGb#)dRYVUMU|`4!k+Bk7Kp> z-16*ZsC+$gyOl?l2w{&@YUdi4`@-zH;rKHa-ol(Y-ya8 zo2S0fMG}5gB72NEl2gtA;V!7^tAK~hM~dgLl=E7ONNtS_prqTu0$xx^Us4~y8KJ7` za`}ejrT}6tMrr3nWo`fb%}>bLDJ9k_!9jg z2lY9h-jV3|vAnJ^;8I_$O0Xnm;ba0==-58r$?dS8ucd!-sb-Nh8)^j;qR30h+i`(f zUXCGi4}uNQ(sUzAEt9`MJLJ=^gTWtFh`13!_%E*SRZl3473n zuwr3V9_F_P>(e!H@u*j%=Y{cr0HC_ShpfCa@&N&qefg 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大家好,欢迎来到由 IDEA 研究院基础软件中心为大家带来的现代编程思想公开课。 今天是第二节课,主题是月兔开发与月兔中的表达式。 @@ -11,9 +11,12 @@ 它的语法较为容易上手。大家可以在月兔编程语言的官网看到更多的信息。

- 月兔的开发工具主要由两部分构成:VSCode插件与命令行工具。 + 关于月兔的开发环境。 +

+

+ 月兔的开发工具主要由两部分构成:VSCode插件与命令工具。 其中,VSCode插件依托VSCode这一被广泛使用的编辑器提供代码的开发环境,提供了诸如语法高亮、变量引用与定义的跳转、开发时的自动补全、程序的运行与调试等功能。 - 命令行工具提供项目级别构建、测试、依赖管理等功能。一个项目通常由多个包组成,一个包又可以包含多个月兔代码文件。 + 命令工具提供项目级别构建、测试、依赖管理等功能。一个项目通常由多个包组成,一个包又可以包含多个月兔代码文件。 在一个包内,不同的文件之间可以相互引用对方的定义,方便将功能分门别类定义在不同文件中。 一个项目也可能引用其他项目,来借用他人实现的功能。 关于项目和包的组织结构与定义,我们将会在之后的课程中详细介绍。在课程中,我们将会限制于包级别的开发。 @@ -32,12 +35,13 @@ 本地开发需首先安装VSCode,或兼容VSCode插件的其他开发软件,如VSCode的开源构建VSCodium。 国内的小伙伴可以使用后者,有各个大学提供的镜像站方便下载。 在开发软件的扩展中,搜索并安装"MoonBit Language"插件。 - 进阶开发需要安装命令行工具,可以在MoonBit官方网站下载命令行工具。 + 安装完成后会提示安装命令工具,点击确认即可安装。 + 也可以在MoonBit官方网站手动下载命令工具。 后续开发流程和浏览器环境相同。

浏览器环境已经为我们准备了一个项目路径,我们只需在这个路径下新建月兔文件即可编写代码。 - 在本地环境,我们需要用命令行工具创建一个项目,然后再编写代码。 + 在本地环境,我们需要用命令工具创建一个项目,然后再编写代码。 创建项目的命令为moon new,在交互式提示下输入项目路径、作者名字、项目名称即可,其它选项可以使用默认值。

@@ -52,7 +56,7 @@

为了能够正确地理解代码所定义的程序的行为,从而写出正确的程序或是读懂他人的程序,我们需要能够理解程序的计算过程。 为此,我们需要建立一个计算模型。 - 月兔程序可以通过以值为中心的编程,或者说基于表达式的编程来描述。 + 月兔程序可以通过面向值的编程,或者说基于表达式的编程来描述。 即,将程序看作是定义一个值的表达式,而程序的运行则是对这个表达式进行简化获得我们所定义的值的过程。 相比较之下,命令式编程风格则是定义做什么,通常由一系列的命令组成,例如:`创建名为x的变量`、`令x为5`、`令y指向x`。 我们将会在后续课程中更深入了解。 @@ -61,21 +65,21 @@ 每一个类型对应的是一个值的集合,如Int对应部分整数的集合;Double对应了部分实数的集合;String对应了字符串的集合,等等。 我们稍后将详细了解月兔的基础数据类型。 每一个表达式由基于值的运算构成,并且可以简化为一个值(或已经是一个值)。 - 在定义表达式的时候,可以通过使用括号来嵌套表达式。以下是一些例子。 + 在定义表达式的时候,可以通过使用括号来嵌套表达式。

另一个需要了解的概念是静态与动态。 “静态”指在程序运行前的性质,而“动态”指在程序运行时的性质。 月兔拥有静态类型系统。 - 这意味着,在程序运行之前,编译器即会检查程序的类型是否定良好,以最大程度减少在运行时出现对数据进行错误类型的运算从而导致程序中断或给出错误的结果。 + 这意味着,在程序运行之前,编译器即会检查程序的类型是否定义良好,以最大程度减少在运行时出现对数据进行错误类型的运算从而导致程序中断或给出错误的结果。 例如对一个逻辑值进行加减乘除。 月兔中每一个标识符(即标识某个实体的符号)都关联着唯一一个类型,标识符和类型用冒号进行关联。 - 月兔中每一个**表达式**都有唯一的一个类型,这个类型由组成它的子表达式决定。 + 月兔中每一个表达式都有唯一的一个类型,这个类型由组成它的子表达式决定。 如图中的表达式,a的类型为Double,可以与同为Double的0.2进行加法。 - 之后,我们通过to_int函数将其转换为Int。 + 之后,我们通过to int函数将其转换为Int。 此时我们可以与x进行整数加法,获得一个整数作为表达式的值。 因此,整个表达式的类型为Int。 - 月兔使用类型推导来确认程序是否正确使用类型,而开发工具也会在开发时实时提示检查到的类型错误。 + 月兔使用类型推导来确认程序是否正确使用类型,而开发工具也会在开发时,实时提示检查到的类型错误。 如图中的表达式,s的类型为String,因此我们期待它与另一个字符串相加,即连接两个字符串。 但此时,右侧类型为Int,不能相加。因此,编辑器以红色下划线提示我们它的错误。

@@ -86,17 +90,17 @@ 我们在这部分的介绍中不涉及数据的底层表示,如二进制、二进制补码等,感兴趣的同学可以在推荐阅读中进行拓展学习。

- 首先我们要介绍的数据类型为逻辑值,亦称为布尔值,纪念发明布尔代数的数学家乔治·布尔而得名。 + 首先我们要介绍的数据类型为逻辑值,亦称为布尔值,纪念发明布尔代数的数学家乔治布尔而得名。 它只有两种值:真和假,即true和false。 常见的逻辑值的运算有:或、与、非。 - 非,即是对当前逻辑值取反,非真即为假,非假即为真。 + 非,对当前逻辑值取反,非真即为假,非假即为真。 与,当两者皆真才为真。例如,真与假,其结果为假。真与真,其结果为真。假与假,其结果为假。 或,当两者皆假才为假。例如,真或假,其结果为真。真或真,其结果为真。假或假,其结果为假。 在我们给出的代码样例中,两个等号表示比较,等号右侧是我们对左侧定义的表达式的简化值的预期。 换句话说,这些代码本身也是类型为逻辑值的表达式,并且我们期待它们的值均为真。 - 在这里,我们给出一个小练习:如何用或、与、非定义异或? + 在这里,我们给出一个小练习:如何用或、与、非,定义异或?

-

+

接下来我们介绍的数据类型为整数。 整数大家都很熟悉,然而在计算机中,中央处理器一次能计算的数据大小是有限的。 为了保证性能,基础数据所代表的数据范围也是有限的。 @@ -107,9 +111,9 @@ 既然整数有范围,那么对整数进行超出范围的运算后,获得的结果就会溢出。 溢出的结果会变成范围中的某一整数而非期待的正确结果。举例来说,如果对最大的整型加一,则会变为最小的整型。 在月兔中,整数的四则运算只能由相同类型的整型进行,也就是整型只能与整型进行运算,长整型只能与长整型进行运算。 - 如果想要将整型与长整型进行计算,需要将整型利用函数to_int64提升为长整形之后再运算。 + 如果想要将整型与长整型进行计算,需要将整型利用函数to int六四提升为长整形之后再运算。 当直接定义长整型数字时,需在数字最后加上大写的L以示区别,否则默认为整型。 - 而将长整型转化为整型则使用to_int,如100L.to_int()。 + 而将长整型转化为整型则使用to int,如100L.to int()。 需要注意的是,整数调用方法必须加括号。 在这里,我们给出一个小练习:如何计算两个正整数的平均数而不溢出?

@@ -120,8 +124,9 @@ 在月兔中,浮点数也有两个类型:Float和Double,分别对应单精度和双精度浮点数。 与整数相同,浮点数的四则运算只能是同精度的两个浮点数进行,并获得同精度的浮点数计算结果。 若要对整数与浮点数进行运算,则须将整数提升为浮点数,再进行运算。 + 当四则运算的第一个操作数是浮点数时,第二个操作数会被自动提升为浮点数类型。 反之,也可通过舍弃小数点后的部分从浮点数近似为整数。 - 在这里,我们给出一个小练习:如何通过整数与浮点数之间的相互转换,比较0.1 + 0.2与0.3到小数点后一位使得结果为真? + 在这里,我们给出一个小练习:如何通过整数与浮点数之间的相互转换,比较0.1 + 0.2与0.3到小数点后一位,使得结果为真?

我们在电脑上看到的一个个汉字、英文字母、数字等,都被归类为字符。 @@ -136,18 +141,18 @@ 之后,为了兼容所有国家的文字以及表情符号,有了Unicode,即统一码。 在兼容ASCII的基础上进行了拓展。 举例来说,“月”与“兔”在统一码中分别对应26376与20820。 - 统一码有不同的编码方式,如UTF-8、UTF-16等,感兴趣的同学可以搜索它们的区别。 + 统一码有不同的编码方式,如UTF8、UTF16等,感兴趣的同学可以搜索它们的区别。 月兔的字符编码采用了Unicode。 基于编码,我们可以将整型转化为字符。

在了解了一系列基础数据后,我们也会希望能够表达一些比较复杂的数据类型。 - 例如日期需要由三个数字构成,而一个人的个人信息或许可以包含他/她的名字和年龄。 + 例如日期需要由三个数字构成,而一个人的个人信息或许可以包含他的名字和年龄。 为此,多元组允许我们将不同类型的数据结合在一起,用小括号包裹,用逗号分隔。 - 我们可以通过从0开始的下标访问数据 + 我们可以通过从0开始的下标访问数据。

- 月兔还有着其他的类型结构,如函数类型、单值类型、列表类型、自定义结构体等。 + 月兔还有着其他的类型结构,如函数类型、单值类型、数组类型、自定义结构体等。 我们将会在后续的课程中见到它们,并且学习如何自定义复杂的数据结构。

@@ -167,37 +172,37 @@

下面我们介绍月兔的数值绑定。 数值绑定的定义形式为let、标识符、冒号、类型、等号、表达式。 - 数值绑定将一个标识符与一个表达式绑定,作为计算的中间值来简化程序定义,避免出现超级复杂的表达式。 - 数据绑定中的类型声明多数时候可以省略,月兔编译器会根据表达式类型进行推断。 - 数值绑定后,出现的标识符均可被替换为绑定的表达式。 + 数值绑定将一个标识符与一个表达式绑定,作为计算的中间值,来简化程序定义,避免出现超级复杂的表达式。 + 数据绑定中的类型声明多数时候可以省略,“月兔编译器”会根据表达式类型进行推断。 + 数值绑定后,出现的标识符“均可”被替换为绑定的表达式。 若同一标识符被绑定多次,则以最近一次绑定为准,即最新的定义遮掩了之前的定义。 如超出定义生效范围,则会恢复被遮掩的定义,因此并非进行了修改。

下面我们介绍月兔的表达式块。 表达式块由大括号定义,包含一系列表达式或数值绑定。 - 表达式块中最后的表达式的类型即为表达式块的类型;最后的表达式的值即为表达式块的值。 + 表达式块中最后的表达式的类型,即为表达式块的类型;最后的表达式的值,即为表达式块的值。 如果一个函数定义或数值绑定定义在所有表达式块外,则我们称之为顶层函数或顶层定义。 如果一个函数定义或数值绑定定义在某个表达式内,则我们称之为本地函数或本地定义。 顶层可以被称为全局,而本地可称为局部,这是因为它们生效的范围是全局或局部的。

定义的生效范围又称作用域。 - 全局作用域指的是整个文件范围内生效,而局部作用域指的是在定义开始之后,直到当前表达式块结束期间生效。 + “全局作用域”指的是整个文件范围内生效,而“局部作用域”指的是在定义开始之后,直到当前表达式块结束期间生效。 图中我们定义了两个顶层标识符value和y。 value的值由表达式块定义,其中定义了x、temp和another temp。 而在another temp中我们又定义了一次temp。 注意箭头指向,在第七行定义了another temp的值的表达式中的temp是最近定义的第5行的temp,它遮掩了第3行temp的定义。 - 而第九行定义了value的值的表达式中的temp则是第3行的temp,因为此时已经超出了第5行的temp的作用域(第5-8行)。 - 同时我们注意到,第9行的y的定义出现在第12行,也就是定义出现在了使用之后。这是被允许的,因为y在顶层被定义,作用域为全局。 + 而第九行定义了value的值的表达式中的temp则是第3行的temp,因为此时已经超出了第5行的temp的作用域。 + 同时我们注意到,第9行的y的定义出现在第12行,也就是定义“出现”在了使用之后。这是被允许的,因为y在顶层被定义,作用域为全局。

基于数值绑定,表达式的化简过程分为以下几步。 首先,简化数值绑定右侧的表达式。 - 然后,将出现的标识符替换为简化后的值。 + 然后,将出现的“标识符”替换为简化后的值。 在此过程中,省略数值绑定本身。 最后,重复上述步骤,对剩余表达式进行化简。 - 按此步骤对上面的案例进行化简。 + 我们尝试按此步骤对上面的案例进行化简。 首先,我们可以替换所有x出现的地方为1,并省略x的数值绑定。 同理,替换y为10,并省略y的数值绑定。

@@ -205,20 +210,20 @@ 之后,我们可以简化两处temp定义的右侧表达式,并对another temp中的标识符进行替换。

- 然后,我们可以计算another temp的值。回忆一下,表达式块的值即是表达式块内最后一个表达式的值。 + 然后,我们可以计算another temp的值。回忆一下,表达式块的值,是表达式块内最后一个表达式的值。

- 到了这一步,我们可以替换剩下的标识符为它们所绑定的值。 + 到了这一步,我们可以替换剩下的标识符,它们所绑定的值。

最后我们可以得出结论,value的值为15.

除了对值进行运算以外,月兔中还有条件表达式,用于判断,根据条件给出不同的值。 - 条件表达式的定义形式为if、条件、条件为真的表达式块、else、条件为假的表达式块。 + 条件表达式的定义形式为if、条件、“条件为真的表达式块”、else、“条件为假的表达式块”。 在月兔中,条件表达式亦是表达式,因此可以被用在其他的表达式内,比如图中这些例子。 条件表达式中,条件的类型必须为逻辑值,而其余两个表达式块的类型必须相同,这个类型代表了整个表达式的类型。 - 比如例子中的条件表达式,条件是对两个浮点数进行相等的判定,类型为逻辑值;真假分支表达式块的值均为字符串,因此整个条件表达式类型为字符串。 + 比如例子中的条件表达式,条件是对两个浮点数进行相等的判定,类型为逻辑值;真假分支表达式块的值,均为字符串,因此整个条件表达式类型为字符串。 条件表达式的简化取决于条件的简化结果为真或假。 若为真,则条件表达式简化为第一个表达式块的值。 若为假,则简化为第二个表达式块的值。 From c83202e3468035c109a9d06187e787afebebfa54 Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Fri, 8 Aug 2025 11:13:03 +0800 Subject: [PATCH 03/14] chore: add spaces between Chinese and English characters. --- course2/lec2.mbt.md | 2 +- course2/script.xml | 94 ++++++++++++++++++++++----------------------- 2 files changed, 48 insertions(+), 48 deletions(-) diff --git a/course2/lec2.mbt.md b/course2/lec2.mbt.md index ed33d79..acc6e0e 100644 --- a/course2/lec2.mbt.md +++ b/course2/lec2.mbt.md @@ -301,7 +301,7 @@ $\mapsto$ `15`                               因为 } ``` -表达式块的类型即为最后的表达式的类型,表达式块的值即为最后表达式的值 +最后的表达式的类型即为表达式块的类型,最后表达式的值即为表达式块的值 ```moonbit let 顶层标识符 = 10 // 顶层(全局)指定义在一个文件中所有表达式块外部定义的函数或标识符 diff --git a/course2/script.xml b/course2/script.xml index 2e89f07..06f699b 100644 --- a/course2/script.xml +++ b/course2/script.xml @@ -14,17 +14,17 @@ 关于月兔的开发环境。

- 月兔的开发工具主要由两部分构成:VSCode插件与命令工具。 - 其中,VSCode插件依托VSCode这一被广泛使用的编辑器提供代码的开发环境,提供了诸如语法高亮、变量引用与定义的跳转、开发时的自动补全、程序的运行与调试等功能。 + 月兔的开发工具主要由两部分构成:VSCode 插件与命令工具。 + 其中,VSCode 插件依托 VSCode 这一被广泛使用的编辑器提供代码的开发环境,提供了诸如语法高亮、变量引用与定义的跳转、开发时的自动补全、程序的运行与调试等功能。 命令工具提供项目级别构建、测试、依赖管理等功能。一个项目通常由多个包组成,一个包又可以包含多个月兔代码文件。 在一个包内,不同的文件之间可以相互引用对方的定义,方便将功能分门别类定义在不同文件中。 一个项目也可能引用其他项目,来借用他人实现的功能。 关于项目和包的组织结构与定义,我们将会在之后的课程中详细介绍。在课程中,我们将会限制于包级别的开发。 月兔还提供一个语言导览网站,这是一个互动式的语言教程,涵盖了月兔语言的所有方面。 - VSCode插件可以在浏览器的VSCode中使用,因此我们支持的开发环境有三类,分别是基于VSCode Web的浏览器环境、云原生开发环境和本地开发环境。 + VSCode 插件可以在浏览器的 VSCode 中使用,因此我们支持的开发环境有三类,分别是基于 VSCode Web 的浏览器环境、云原生开发环境和本地开发环境。

- 访问try.moonbitlang.cn即可使用浏览器环境。 + 访问 try.moonbitlang.cn 即可使用浏览器环境。 浏览器环境提供了诸多代码样例,方便大家熟悉月兔语法。 在浏览器环境中,大家可以创建新文件并运行,也可以参考包的案例。 浏览器环境还提供单个文件的分享功能,方便大家分享代码以及提交反馈。 @@ -32,25 +32,25 @@ 请大家使用“另存为”功能对文件进行保存。

- 本地开发需首先安装VSCode,或兼容VSCode插件的其他开发软件,如VSCode的开源构建VSCodium。 + 本地开发需首先安装 VSCode,或兼容 VSCode 插件的其他开发软件,如 VSCode 的开源构建 VSCodium。 国内的小伙伴可以使用后者,有各个大学提供的镜像站方便下载。 - 在开发软件的扩展中,搜索并安装"MoonBit Language"插件。 + 在开发软件的扩展中,搜索并安装 "MoonBit Language" 插件。 安装完成后会提示安装命令工具,点击确认即可安装。 - 也可以在MoonBit官方网站手动下载命令工具。 + 也可以在 MoonBit 官方网站手动下载命令工具。 后续开发流程和浏览器环境相同。

浏览器环境已经为我们准备了一个项目路径,我们只需在这个路径下新建月兔文件即可编写代码。 在本地环境,我们需要用命令工具创建一个项目,然后再编写代码。 - 创建项目的命令为moon new,在交互式提示下输入项目路径、作者名字、项目名称即可,其它选项可以使用默认值。 + 创建项目的命令为 moon new,在交互式提示下输入项目路径、作者名字、项目名称即可,其它选项可以使用默认值。

在进行了月兔的开发准备后,让我们尝试理解月兔的代码。 下面将为大家展示一个典型的月兔程序,亦是上一节课的案例代码。 我们在此定义了一个顶层函数以及测试代码块。 - 顶层函数中,我们定义了一个for循环表达式,循环体内是一个条件表达式。 + 顶层函数中,我们定义了一个 for 循环表达式,循环体内是一个条件表达式。 在测试代码块,我们使用了两个断言命令来判断我们程序的正确性。 - 上节课提到,在开发环境中,测试代码上方会有个test按钮,点击它就可以运行测试用例,验证我们的代码是否正确。 + 上节课提到,在开发环境中,测试代码上方会有个 test 按钮,点击它就可以运行测试用例,验证我们的代码是否正确。 为什么我们定义的函数可以计算出正确的结果呢?接下来我们要理解这段代码是如何运行的,

@@ -58,11 +58,11 @@ 为此,我们需要建立一个计算模型。 月兔程序可以通过面向值的编程,或者说基于表达式的编程来描述。 即,将程序看作是定义一个值的表达式,而程序的运行则是对这个表达式进行简化获得我们所定义的值的过程。 - 相比较之下,命令式编程风格则是定义做什么,通常由一系列的命令组成,例如:`创建名为x的变量`、`令x为5`、`令y指向x`。 + 相比较之下,命令式编程风格则是定义做什么,通常由一系列的命令组成,例如:`创建名为 x 的变量`、`令 x 为5`、`令 y 指向 x`。 我们将会在后续课程中更深入了解。

- 每一个类型对应的是一个值的集合,如Int对应部分整数的集合;Double对应了部分实数的集合;String对应了字符串的集合,等等。 + 每一个类型对应的是一个值的集合,如 Int 对应部分整数的集合;Double 对应了部分实数的集合;String 对应了字符串的集合,等等。 我们稍后将详细了解月兔的基础数据类型。 每一个表达式由基于值的运算构成,并且可以简化为一个值(或已经是一个值)。 在定义表达式的时候,可以通过使用括号来嵌套表达式。 @@ -75,13 +75,13 @@ 例如对一个逻辑值进行加减乘除。 月兔中每一个标识符(即标识某个实体的符号)都关联着唯一一个类型,标识符和类型用冒号进行关联。 月兔中每一个表达式都有唯一的一个类型,这个类型由组成它的子表达式决定。 - 如图中的表达式,a的类型为Double,可以与同为Double的0.2进行加法。 - 之后,我们通过to int函数将其转换为Int。 - 此时我们可以与x进行整数加法,获得一个整数作为表达式的值。 - 因此,整个表达式的类型为Int。 + 如图中的表达式,a 的类型为 Double,可以与同为 Double 的0.2进行加法。 + 之后,我们通过 to int 函数将其转换为 Int。 + 此时我们可以与 x 进行整数加法,获得一个整数作为表达式的值。 + 因此,整个表达式的类型为 Int。 月兔使用类型推导来确认程序是否正确使用类型,而开发工具也会在开发时,实时提示检查到的类型错误。 - 如图中的表达式,s的类型为String,因此我们期待它与另一个字符串相加,即连接两个字符串。 - 但此时,右侧类型为Int,不能相加。因此,编辑器以红色下划线提示我们它的错误。 + 如图中的表达式,s 的类型为 String,因此我们期待它与另一个字符串相加,即连接两个字符串。 + 但此时,右侧类型为 Int,不能相加。因此,编辑器以红色下划线提示我们它的错误。

为了进行基于表达式的编程,我们需要了解月兔中有哪些值。 @@ -91,7 +91,7 @@

首先我们要介绍的数据类型为逻辑值,亦称为布尔值,纪念发明布尔代数的数学家乔治布尔而得名。 - 它只有两种值:真和假,即true和false。 + 它只有两种值:真和假,即 true 和 false。 常见的逻辑值的运算有:或、与、非。 非,对当前逻辑值取反,非真即为假,非假即为真。 与,当两者皆真才为真。例如,真与假,其结果为假。真与真,其结果为真。假与假,其结果为假。 @@ -111,9 +111,9 @@ 既然整数有范围,那么对整数进行超出范围的运算后,获得的结果就会溢出。 溢出的结果会变成范围中的某一整数而非期待的正确结果。举例来说,如果对最大的整型加一,则会变为最小的整型。 在月兔中,整数的四则运算只能由相同类型的整型进行,也就是整型只能与整型进行运算,长整型只能与长整型进行运算。 - 如果想要将整型与长整型进行计算,需要将整型利用函数to int六四提升为长整形之后再运算。 - 当直接定义长整型数字时,需在数字最后加上大写的L以示区别,否则默认为整型。 - 而将长整型转化为整型则使用to int,如100L.to int()。 + 如果想要将整型与长整型进行计算,需要将整型利用函数 to int 六四提升为长整形之后再运算。 + 当直接定义长整型数字时,需在数字最后加上大写的 L 以示区别,否则默认为整型。 + 而将长整型转化为整型则使用 to int,如100L.to int()。 需要注意的是,整数调用方法必须加括号。 在这里,我们给出一个小练习:如何计算两个正整数的平均数而不溢出?

@@ -121,7 +121,7 @@ 接下来我们介绍实数在计算机内部的表示。 如之前所说,计算机中,基础数据代表的数据长度是有限的,因此我们无法表示一切的实数,而只能表示一部分的有限小数,并且通过尾数与指数结合的方式进行近似表达。 例如,0.1、0.2、0.3等小数在计算机中都无法精确表示,因此0.1 + 0.2的结果并不等于0.3。 - 在月兔中,浮点数也有两个类型:Float和Double,分别对应单精度和双精度浮点数。 + 在月兔中,浮点数也有两个类型:Float 和 Double,分别对应单精度和双精度浮点数。 与整数相同,浮点数的四则运算只能是同精度的两个浮点数进行,并获得同精度的浮点数计算结果。 若要对整数与浮点数进行运算,则须将整数提升为浮点数,再进行运算。 当四则运算的第一个操作数是浮点数时,第二个操作数会被自动提升为浮点数类型。 @@ -131,18 +131,18 @@

我们在电脑上看到的一个个汉字、英文字母、数字等,都被归类为字符。 而字符的序列则是字符串。 - 在月兔中,字符类型为Char,而字符串类型为String。 + 在月兔中,字符类型为 Char,而字符串类型为 String。 字符用英文单引号标识;字符串用英文双引号标识。 这些文字是如何在计算机中表达的呢? 答案是,通过编码,将一个个数字映射为一个个字符,即一个字符对应一个数字。 - 这种映射有多种可能的方式。较为通用的是ASCII,即美国信息交换标准代码,第一版在1963年发布。 + 这种映射有多种可能的方式。较为通用的是 ASCII,即美国信息交换标准代码,第一版在1963年发布。 它定义了英文字符与常见符号到0~127的映射。 - 举例来说,大写字母A到Z对应了从65到90的数字。 - 之后,为了兼容所有国家的文字以及表情符号,有了Unicode,即统一码。 - 在兼容ASCII的基础上进行了拓展。 + 举例来说,大写字母 A 到 Z 对应了从65到90的数字。 + 之后,为了兼容所有国家的文字以及表情符号,有了 Unicode,即统一码。 + 在兼容 ASCII 的基础上进行了拓展。 举例来说,“月”与“兔”在统一码中分别对应26376与20820。 - 统一码有不同的编码方式,如UTF8、UTF16等,感兴趣的同学可以搜索它们的区别。 - 月兔的字符编码采用了Unicode。 + 统一码有不同的编码方式,如 UTF8、UTF16等,感兴趣的同学可以搜索它们的区别。 + 月兔的字符编码采用了 Unicode。 基于编码,我们可以将整型转化为字符。

@@ -166,15 +166,15 @@

我们将分解化简的流程为一系列单步计算,用竖线加上箭头的符号表示。 - 例如,2+3,乘,5-2,这个表达式会被单步计算为5乘5-2,进一步计算得到5乘3,最后得到15。 + 例如,2+3,乘,5减2,这个表达式会被单步计算为5乘5减2,进一步计算得到5乘3,最后得到15。 因此,原表达式被化简为15这个值。

下面我们介绍月兔的数值绑定。 - 数值绑定的定义形式为let、标识符、冒号、类型、等号、表达式。 + 数值绑定的定义形式为 let、标识符、冒号、类型、等号、表达式。 数值绑定将一个标识符与一个表达式绑定,作为计算的中间值,来简化程序定义,避免出现超级复杂的表达式。 数据绑定中的类型声明多数时候可以省略,“月兔编译器”会根据表达式类型进行推断。 - 数值绑定后,出现的标识符“均可”被替换为绑定的表达式。 + 数值绑定后,出现的标识符均可被替换为绑定的表达式。 若同一标识符被绑定多次,则以最近一次绑定为准,即最新的定义遮掩了之前的定义。 如超出定义生效范围,则会恢复被遮掩的定义,因此并非进行了修改。

@@ -187,14 +187,14 @@ 顶层可以被称为全局,而本地可称为局部,这是因为它们生效的范围是全局或局部的。

- 定义的生效范围又称作用域。 + 定义的生效范围又称“作用域”。 “全局作用域”指的是整个文件范围内生效,而“局部作用域”指的是在定义开始之后,直到当前表达式块结束期间生效。 - 图中我们定义了两个顶层标识符value和y。 - value的值由表达式块定义,其中定义了x、temp和another temp。 - 而在another temp中我们又定义了一次temp。 - 注意箭头指向,在第七行定义了another temp的值的表达式中的temp是最近定义的第5行的temp,它遮掩了第3行temp的定义。 - 而第九行定义了value的值的表达式中的temp则是第3行的temp,因为此时已经超出了第5行的temp的作用域。 - 同时我们注意到,第9行的y的定义出现在第12行,也就是定义“出现”在了使用之后。这是被允许的,因为y在顶层被定义,作用域为全局。 + 图中我们定义了两个顶层标识符 value 和 y。 + value 的值由表达式块定义,其中定义了 x、temp 和 another temp。 + 而在 another temp 中我们又定义了一次 temp。 + 注意箭头指向,在第七行定义了 another temp 的值的表达式中的 temp 是最近定义的第5行的 temp,它遮掩了第3行 temp 的定义。 + 而第九行定义了 value 的值的表达式中的 temp 则是第3行的 temp,因为此时已经超出了第5行的 temp 的作用域。 + 同时我们注意到,第9行的 y 的定义出现在第12行,也就是定义“出现”在了使用之后。这是被允许的,因为 y 在顶层被定义,作用域为全局。

基于数值绑定,表达式的化简过程分为以下几步。 @@ -203,24 +203,24 @@ 在此过程中,省略数值绑定本身。 最后,重复上述步骤,对剩余表达式进行化简。 我们尝试按此步骤对上面的案例进行化简。 - 首先,我们可以替换所有x出现的地方为1,并省略x的数值绑定。 - 同理,替换y为10,并省略y的数值绑定。 + 首先,我们可以替换所有 x 出现的地方为1,并省略 x 的数值绑定。 + 同理,替换 y 为10,并省略 y 的数值绑定。

- 之后,我们可以简化两处temp定义的右侧表达式,并对another temp中的标识符进行替换。 + 之后,我们可以简化两处 temp 定义的右侧表达式,并对 another temp 中的标识符进行替换。

- 然后,我们可以计算another temp的值。回忆一下,表达式块的值,是表达式块内最后一个表达式的值。 + 然后,我们可以计算 another temp 的值。回忆一下,表达式块的值,是表达式块内最后一个表达式的值。

到了这一步,我们可以替换剩下的标识符,它们所绑定的值。

- 最后我们可以得出结论,value的值为15. + 最后我们可以得出结论,value 的值为15.

除了对值进行运算以外,月兔中还有条件表达式,用于判断,根据条件给出不同的值。 - 条件表达式的定义形式为if、条件、“条件为真的表达式块”、else、“条件为假的表达式块”。 + 条件表达式的定义形式为 if、条件、“条件为真的表达式块”、else、“条件为假的表达式块”。 在月兔中,条件表达式亦是表达式,因此可以被用在其他的表达式内,比如图中这些例子。 条件表达式中,条件的类型必须为逻辑值,而其余两个表达式块的类型必须相同,这个类型代表了整个表达式的类型。 比如例子中的条件表达式,条件是对两个浮点数进行相等的判定,类型为逻辑值;真假分支表达式块的值,均为字符串,因此整个条件表达式类型为字符串。 @@ -232,7 +232,7 @@ 总结一下今天学习的内容。 我们首先了解了如何配置月兔的开发环境,包括浏览器、云原生和本地开发环境。 然后,我们了解了月兔的基本数据类型,包括逻辑值、整数、浮点数、字符与字符串以及多元组。 - 最后,我们学习了月兔的表达式和数值绑定,以及如何通过简化表达式来理解月兔程序的运行。 + 最后,我们学习了月兔的表达式和数值绑定,以及如何通过简化“表达式”来理解月兔程序的运行。

那么以上便是今天课程的全部内容。感谢大家的收看,我们下次再见。 From c61ac287991d5289d41a9be1b034b0bd6da27718 Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Tue, 19 Aug 2025 15:26:55 +0800 Subject: [PATCH 04/14] feat: ssml and slide update for course2. Main changes: number upcast and demo. --- course2/lec2.mbt.md | 63 ++++++++++++++++++++++++++------------------ course2/lec2.pdf | Bin 740789 -> 786014 bytes course2/script.xml | 61 ++++++++++++++++++++++++++++-------------- 3 files changed, 79 insertions(+), 45 deletions(-) diff --git a/course2/lec2.mbt.md b/course2/lec2.mbt.md index acc6e0e..3014ca5 100644 --- a/course2/lec2.mbt.md +++ b/course2/lec2.mbt.md @@ -28,29 +28,28 @@ backgroundImage: url('../pics/background_moonbit.png') # 月兔开发环境 - 开发工具 - - VS Code插件:语言服务器、包级别构建等功能 - - 命令行工具:项目级别构建、项目测试、依赖管理等功能 + - [VS Code 插件](https://marketplace.visualstudio.com/items?itemName=moonbit.moonbit-lang):语言服务器功能 + - [命令行工具](https://www.moonbitlang.com/download/#moonbit-cli-tools):项目构建、测试、依赖管理等功能 - [语言导览](https://tour.moonbitlang.com/zh/index.html):快速学习月兔的互动教程 - 开发环境 - - 浏览器环境(无命令行工具) - - 云原生开发环境(如[Github Codespaces](https://github.com/features/codespaces)) + - [浏览器环境](https://try.moonbitlang.cn)(无命令行工具) + - 云原生开发环境(如 [Github Codespaces](https://github.com/features/codespaces)) - 本地开发环境 --- # 浏览器环境 -- 访问[try.moonbitlang.cn](https://try.moonbitlang.cn),或从[官网](https://moonbitlang.cn)点击“试用” +- 访问 [try.moonbitlang.cn](https://try.moonbitlang.cn),或从[官网](https://moonbitlang.cn)点击“试用” - 试用环境可以快速创建文件并运行 - 试用环境提供代码样例,方便熟悉月兔语法 -- 试用环境提供分享功能 --- # 本地开发环境 -- 安装[VS Code](https://code.visualstudio.com/)或[VS Codium](https://mirrors.cernet.edu.cn/list/VSCodium),并安装"MoonBit Language"插件 -- 安装[命令行工具](https://www.moonbitlang.cn/download/)(支持Windows、MacOS与Ubuntu等环境),并参考[月兔构建系统教程](https://www.moonbitlang.cn/docs/build-system-tutorial/) +- 安装 [VS Code](https://code.visualstudio.com/) 或 [VS Codium](https://mirrors.cernet.edu.cn/list/VSCodium),并安装["MoonBit Language"插件](https://marketplace.visualstudio.com/items?itemName=moonbit.moonbit-lang) +- 安装[命令行工具](https://www.moonbitlang.cn/download/)(支持 Windows、MacOS 与 Ubuntu 等环境),并参考[月兔构建系统教程](https://www.moonbitlang.cn/docs/build-system-tutorial/) --- @@ -102,18 +101,19 @@ test { |类型|值|运算|表达式| |-----|------|----------|-----------| -|`Int`|`-1` `0` `1` `2`|`+` `-` `*` `/`|`5` `(3 + y * x)`| -|`Double`|`0.12` `3.1415`|`+` `-` `*` `/`|`3.0 * (4.0 * a)`| +|`Int`|`-1` `0` `1` `2`|`+` `-` `*` `/`|`5` `3 + (y * x)`| |`String`|`"hello"` `"Moonbit"`|`+`|`"Hello, " + "MoonBit"`| |`Bool`|`true` `false`|`&&` `\|\|` `!`|`!b1 \|\| b2`| - 每一个**类型**对应一个**值**的集合 - 每一个**表达式**由基于值的**运算**构成,并且可以简化为一个值(或已经是一个值) +- 直接写出来,而不是通过变量、表达式、计算或函数调用得到的值叫做**字面量** - 可以使用括号来嵌套表达式 --- # 静态 vs 动态 + - “静态”指在程序运行**之前**的性质 - “动态”指在程序运行**之时**的性质 @@ -144,12 +144,14 @@ test { # 月兔的基本数据类型 - 逻辑值(布尔值) -- 整数(整型、长整形) +- 整数(整型、长整型) - 浮点数(单精度浮点数、双精度浮点数) - 字符与字符串 - 多元组 - …… + + --- # 逻辑值(布尔值) @@ -163,21 +165,21 @@ test { - 与:两者皆真才为真    `true && false == false` - 或:两者皆假才为假    `true || false == true` - 小练习:如何用或、与、非定义**异或**(一者为真才为真) + --- # 整数类型 -- 作为基础类型的整数分为两个类型,分别有不同的范围: - - 整型 `Int`:从$-2^{31}$到$2^{31}-1$(即从-2147483648到2147483647) - - 长整型 `Int64`:从$-2^{63}$到$2^{63}-1$ +|类型|范围|字面量|转换到该类型| +|-----|------|----------|---| +| 整型 `Int` | $-2^{31} \sim 2^{31}-1$ | `123` | `123L.to_int()` | +| 长整型 `Int64` | $-2^{63} \sim 2^{63}-1$ | `123L` | `(123).to_int64()` | +| 无符号整型 `UInt` | $0 \sim 2^{32}-1$ | `123U` | `123UL.to_uint()` | +| 无符号长整型 `UInt64` | $0 \sim 2^{64}-1$ | `123UL` | `123U.to_uint64()` | + - 在月兔中,整数相除依然获得整数,其结果为商 - - 被除数÷除数=**商**······余数 -- 对整数进行超出范围的运算后会**溢出** - - 2147483647 + 1结果为-2147483648 -- 整型只能与整型进行四则运算,长整型只能与长整型进行四则运算 - - 长整型数值后需加`L`进行标记:如`2147483648L` `-2147483649L` - - `Int`与`Int64`互相转换:`(100).to_int64()` `100L.to_int()` -- 小练习:如何计算两个正的`Int`的平均数?小心溢出! +- 对整数进行超出范围的运算后会**溢出**:`2147483647 + 1` 结果为 `-2147483648` +- 小练习:如何计算两个正的 `Int` 的平均数?小心溢出! --- @@ -186,14 +188,25 @@ test { - 作为基础类型的浮点数只能表示有限小数,且只能近似表达 - 浮点数在计算机内部表现形式为尾数`b`与指数`e`(均为整数):$b \times 2^e$ - 例如:[`0.1 + 0.2 != 0.3`] -- 月兔中浮点数类型分为单精度浮点数`Float`和双精度浮点数`Double` +- 月兔中浮点数类型分为单精度浮点数 `Float` 和双精度浮点数 `Double` - 整数和浮点数不能直接混合运算:`1 + 2.0` 报错 - - 当第一个操作数是浮点数时,第二个操作数会被自动提升为浮点数: - `2.0 + 1 == 3.0` - `Int`可以转换为`Double`:`(1).to_double() == 1.0` - `Double`转化为`Int`:`(-1.2).to_int() == -1` - 小练习:如何通过整数与浮点数的相互转换,来比较`0.1 + 0.2`与`0.3`? +--- + +# 数字自动类型提升 + +- 不同数据类型之间不能直接混合运算:`1 + 2.0` 报错 +- 在值的类型已知的情况下,字面量会进行自动类型提升 + - 整数字面量会提升为特定整数或特定精度的浮点数类型: + `1U + 1 == 2` + `1.0 + 2 == 3.0` + - 浮点数字面量会提升为特定精度的浮点数类型: + `Float::to_int(1.0) == Double::to_int(1.0)` + (例子中:`1.0` 既可以作为 `Float`,也可以作为 `Double`) + --- # 字符与字符串 @@ -206,7 +219,7 @@ test { - 例如:A~Z对应65~90 - Unicode(统一码):支持中文等多国字符及表情符号(emoji),兼容ASCII,有UTF-8、UTF-16等编码方式 - 例如:“月”“兔”分别对应26376与20820 - - `Int`转化为`Char`:`Char::from_int(65) == 'A'` + - `Int`转化为`Char`:`(65).unsafe_to_char() == 'A'` --- diff --git a/course2/lec2.pdf b/course2/lec2.pdf index 7c005844d9364a405938d6c696350d5fab37dab0..3f5d78a5486ced28b9e0998330d4b4786ef86f42 100644 GIT binary patch delta 252875 zcmY&;V{~T0vUW7FCzE6{v2EM7ZQD-vWP*up+qP}nn2Bw^(KqMb`{O%5x~jUmdau1! z_pa{R&(oAaxBbRY%Toq$vBLB7!@IaTn;F@`duCQ8Zdh*!qJ~^OQ609=E=`^*5kl43 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- 首先,让我们回顾一下上周提到过的内容。 + 首先,让我们回顾第一节课提到过的内容。 我们这门课程使用的编程语言月兔是一门现代的、静态类型的多范式编程语言,支持函数式编程、命令式编程等多种编程范式。 它的语法较为容易上手。大家可以在月兔编程语言的官网看到更多的信息。

@@ -16,10 +16,10 @@

月兔的开发工具主要由两部分构成:VSCode 插件与命令工具。 其中,VSCode 插件依托 VSCode 这一被广泛使用的编辑器提供代码的开发环境,提供了诸如语法高亮、变量引用与定义的跳转、开发时的自动补全、程序的运行与调试等功能。 - 命令工具提供项目级别构建、测试、依赖管理等功能。一个项目通常由多个包组成,一个包又可以包含多个月兔代码文件。 + 命令工具提供项目构建、测试、依赖管理等功能。一个项目通常由多个包组成,一个包又可以包含多个月兔代码文件。 在一个包内,不同的文件之间可以相互引用对方的定义,方便将功能分门别类定义在不同文件中。 一个项目也可能引用其他项目,来借用他人实现的功能。 - 关于项目和包的组织结构与定义,我们将会在之后的课程中详细介绍。在课程中,我们将会限制于包级别的开发。 + 关于项目和包的组织结构与定义,我们将会在之后的课程中详细介绍。 月兔还提供一个语言导览网站,这是一个互动式的语言教程,涵盖了月兔语言的所有方面。 VSCode 插件可以在浏览器的 VSCode 中使用,因此我们支持的开发环境有三类,分别是基于 VSCode Web 的浏览器环境、云原生开发环境和本地开发环境。

@@ -27,7 +27,6 @@ 访问 try.moonbitlang.cn 即可使用浏览器环境。 浏览器环境提供了诸多代码样例,方便大家熟悉月兔语法。 在浏览器环境中,大家可以创建新文件并运行,也可以参考包的案例。 - 浏览器环境还提供单个文件的分享功能,方便大家分享代码以及提交反馈。 需要注意的是,当前的浏览器环境不会自动保存修改,因此如果窗口被刷新,所有的修改都会丢失。 请大家使用“另存为”功能对文件进行保存。

@@ -43,15 +42,28 @@ 浏览器环境已经为我们准备了一个项目路径,我们只需在这个路径下新建月兔文件即可编写代码。 在本地环境,我们需要用命令工具创建一个项目,然后再编写代码。 创建项目的命令为 moon new,在交互式提示下输入项目路径、作者名字、项目名称即可,其它选项可以使用默认值。 + 创建完成后,我们可以看到 src 目录下有两个子目录,分别是 lib 和 main。 + 我们打开 main 文件,点击 main 函数上方的 run 按钮,即可运行程序。 + 可以看到,我们成功打印出了 Hello World。 + 文件目录中有一个测试案例,以下划线 test 结尾。 + 在 hello test 文件中,我们可以看到测试代码块。 + 点击测试代码块上的 test 按钮,或者执行 moon test,可以运行测试。 + 我们会发现测试成功通过。 + 我们可以修改 hello 文件中的 hello 函数。 + 再运行测试,会发现测试失败了。 + 以上便是本节课的全部内容,感谢大家的观看。 +

+

+ 大家好,欢迎来到由 IDEA 研究院基础软件中心为大家带来的现代编程思想公开课。 + 在上一个视频,我们介绍了月兔的开发环境。这节课让我们尝试理解月兔的表达式。

- 在进行了月兔的开发准备后,让我们尝试理解月兔的代码。 下面将为大家展示一个典型的月兔程序,亦是上一节课的案例代码。 我们在此定义了一个顶层函数以及测试代码块。 顶层函数中,我们定义了一个 for 循环表达式,循环体内是一个条件表达式。 在测试代码块,我们使用了两个断言命令来判断我们程序的正确性。 上节课提到,在开发环境中,测试代码上方会有个 test 按钮,点击它就可以运行测试用例,验证我们的代码是否正确。 - 为什么我们定义的函数可以计算出正确的结果呢?接下来我们要理解这段代码是如何运行的, + 为什么我们定义的函数可以计算出正确的结果呢?接下来我们要理解这段代码是如何运行的。

为了能够正确地理解代码所定义的程序的行为,从而写出正确的程序或是读懂他人的程序,我们需要能够理解程序的计算过程。 @@ -62,9 +74,11 @@ 我们将会在后续课程中更深入了解。

- 每一个类型对应的是一个值的集合,如 Int 对应部分整数的集合;Double 对应了部分实数的集合;String 对应了字符串的集合,等等。 + 每一个类型对应的是一个值的集合,如 Int 对应部分整数的集合;String 对应了字符串的集合;Bool 对应了逻辑值的集合;等等。 我们稍后将详细了解月兔的基础数据类型。 每一个表达式由基于值的运算构成,并且可以简化为一个值(或已经是一个值)。 + 直接写出来,而不是通过变量、表达式、计算或函数调用得到的值叫做字面量。 + 比如表格中的值都是字面量,而通过运算和后面将要介绍的“数值绑定”得到的值则不是字面量。 在定义表达式的时候,可以通过使用括号来嵌套表达式。

@@ -100,34 +114,39 @@ 换句话说,这些代码本身也是类型为逻辑值的表达式,并且我们期待它们的值均为真。 在这里,我们给出一个小练习:如何用或、与、非,定义异或?

-

+

接下来我们介绍的数据类型为整数。 整数大家都很熟悉,然而在计算机中,中央处理器一次能计算的数据大小是有限的。 为了保证性能,基础数据所代表的数据范围也是有限的。 - 在月兔中,基础类型中的整数分为整形和长整型,分别有不同的值域。 + 在月兔中,基础类型中的整数分为有符号和无符号的32位和64位整型,分别有不同的值域。 在月兔中,整数相除获得的依然是整数,其结果为整数除法中的商。 - 若涉及负数,则按照正数进行运算后赋予正负号。例如,-4除以3结果为-1。 - 当然,除以零依然不被允许,会在运行时产生错误中断程序。 + + 既然整数有范围,那么对整数进行超出范围的运算后,获得的结果就会溢出。 溢出的结果会变成范围中的某一整数而非期待的正确结果。举例来说,如果对最大的整型加一,则会变为最小的整型。 - 在月兔中,整数的四则运算只能由相同类型的整型进行,也就是整型只能与整型进行运算,长整型只能与长整型进行运算。 - 如果想要将整型与长整型进行计算,需要将整型利用函数 to int 六四提升为长整形之后再运算。 - 当直接定义长整型数字时,需在数字最后加上大写的 L 以示区别,否则默认为整型。 - 而将长整型转化为整型则使用 to int,如100L.to int()。 - 需要注意的是,整数调用方法必须加括号。 + 当直接定义64位整型字面量时,需在数字最后加上大写的 L 以示区别,否则默认为整型。 + 同样的,无符号整形和无符号长整型的字面量需要分别加上大写U和UL。 + 在月兔中,整数的四则运算只能由相同类型的整型进行。 + 如果想要将不同整型进行计算,需要利用函数to int, to int六四, to u int, to u int六四转换之后再运算。 + 需要注意的是,整数字面量调用方法必须加括号。 在这里,我们给出一个小练习:如何计算两个正整数的平均数而不溢出?

- 接下来我们介绍实数在计算机内部的表示。 + 接下来我们介绍实数在月兔的表示。 如之前所说,计算机中,基础数据代表的数据长度是有限的,因此我们无法表示一切的实数,而只能表示一部分的有限小数,并且通过尾数与指数结合的方式进行近似表达。 例如,0.1、0.2、0.3等小数在计算机中都无法精确表示,因此0.1 + 0.2的结果并不等于0.3。 在月兔中,浮点数也有两个类型:Float 和 Double,分别对应单精度和双精度浮点数。 与整数相同,浮点数的四则运算只能是同精度的两个浮点数进行,并获得同精度的浮点数计算结果。 - 若要对整数与浮点数进行运算,则须将整数提升为浮点数,再进行运算。 - 当四则运算的第一个操作数是浮点数时,第二个操作数会被自动提升为浮点数类型。 + 若要对整数与浮点数进行运算,则须将整数转换为浮点数,再进行运算。 反之,也可通过舍弃小数点后的部分从浮点数近似为整数。 在这里,我们给出一个小练习:如何通过整数与浮点数之间的相互转换,比较0.1 + 0.2与0.3到小数点后一位,使得结果为真?

+

+ 在月兔中,如果值的类型已知,整数和浮点数字面量会自动提升到对应的类型。 + 比如,当加法操作的第一个操作数是无符号整数时,第二个字面量会自动提升为无符号整数。 + 当第一个操作数是浮点数时,第二个字面量也会自动提升为浮点数。 + 同样的,浮点数字面量也会自动提升到对应的Float或者Double类型。 +

我们在电脑上看到的一个个汉字、英文字母、数字等,都被归类为字符。 而字符的序列则是字符串。 @@ -154,9 +173,11 @@

月兔还有着其他的类型结构,如函数类型、单值类型、数组类型、自定义结构体等。 我们将会在后续的课程中见到它们,并且学习如何自定义复杂的数据结构。 + 以上便是本节课的全部内容,感谢大家的观看。

- 下面我们学习如何计算月兔中的表达式。 + 大家好,欢迎来到由 IDEA 研究院基础软件中心为大家带来的现代编程思想公开课。 + 在上一节课,我们介绍了月兔的表达式,下面我们学习如何计算月兔中的表达式。

我们可以将月兔的表达式看作定义值的一种方式; From 7d6d303c56f1efe076e5879ad8586ea6132621eb Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Mon, 25 Aug 2025 12:41:12 +0800 Subject: [PATCH 05/14] feat: ssml for course 3. --- course3/script.xml | 364 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 364 insertions(+) create mode 100644 course3/script.xml diff --git a/course3/script.xml b/course3/script.xml new file mode 100644 index 0000000..d552336 --- /dev/null +++ b/course3/script.xml @@ -0,0 +1,364 @@ + + +

+ 大家好,欢迎来到由 IDEA 研究院基础软件中心为大家带来的现代编程思想公开课。 + 今天是第三节课,主题是函数、列表与递归。 +

+

+ 让我们先从作为基本数据类型的函数开始。 + 在数学上,函数是描述对应关系的一种特殊集合。 + 例如大家可能都知道的一元二次函数、对数函数、三角函数等。 + 函数的一大特点是,对于特定的输入,总是有特定的输出。 + 请大家记住这一特点,我们之后还会再回顾。 +

+

在计算机中,我们使用函数来对相同的运算进行抽象,避免大量重复定义。 例如,我想要计算半径为1的圆的面积, 可以写作: + 三点一四一五 乘 1 乘 1。 + 同样的,如果要求半径为2的圆的面积,可以写作:三点一四一五 乘 2 乘 2。 + 那么半径为3呢?半径为4呢?每一次都要重复写:三点一四一五 乘 半径 乘 半径吗? + 大家在写程序的时候,如果一个任务或者模式重复出现了三次以上,就可以开始考虑对它进行抽象了。 +

+

+ 大家可以对比一下使用与未使用函数的情况。 + 我们定义了面积函数,对重复的运算过程进行了抽象:给定半径,计算代表面积的值。 + 在未使用函数时,我们有大量重复代码。 + 而使用函数后,我们的代码变得精简易读。 +

+

+ 我们首先来看顶层函数的定义,也就是在文件结构最外层的函数的定义。 + 顶层函数的定义为 fn、函数名,用括号包裹、逗号分割的参数列表。每一个参数都是参数名,冒号,类型。 + 然后用箭头加上类型表示返回值类型,最后用表达式块表示函数体。 + 其中,参数可以有零或多个。 + 这样的类型声明可以让我们关注于函数的接口,而不是函数的具体实现。 + 例如,我们这里定义了两个函数,第一个函数 one 没有参数,返回一个整数1。 + 第二个函数 add char 接收两个参数,一个 Char 和一个 String,然后返回一个 String。 + 显然,参数名不能重复定义。 +

+

+ 当函数定义后,可以通过函数名加上用括号包裹、逗号分割的一连串表达式的方式来应用函数。 + 比如 one 加上空括号,或者 add char 加上括号中包含字符 m 和字符串 oonbit 。 + 当应用函数时,表达式与函数定义时的参数数量应当相同,且类型一一对应。 + 一一对应的意思就是说,顺序不能打乱。比如 add char 函数的第一个参数类型是 Char,那么传入一个字符串就是错误的。

+

+ 在计算应用函数的表达式时,我们首先要从左到右计算参数表达式的值, 然后用这些值,替换函数内部出现的参数,并最终简化表达式。让我们来看一个例子。 + 以刚才定义的 add char 函数为例。我们将其应用到 Int unsafe to char 109 和字符串 oonbit 。 + 首先我们从左向右计算参数表达式,我们将 Int unsafe to char 109 简化为字符 m。 在参数全部化简后,我们用参数替换表达式块中的标识符,得到 m to + string 加字符串 oonbit 。 m to string 会把字符 m + 转换为字符串 m,所以我们得到了字符串 m 加上字符串 oonbit 。 + 因为这两个字符串相加会简化为字符串 MoonBit,所以我们得到了最终结果 MoonBit。 +

+

+ 函数定义域有的时候是输入类型的子集,因此可能会有对于输入未定义输出的情况。 + 例如,整数转换为字符时输入负数,就是不合理的输入,因为统一码没有定义负数对应的字符。 + 又例如,整数除法的除数为零时,尽管类型正确,操作也是不被允许的,会在运行时出错。 + 对于这种函数,我们称为部分函数;相对的, + 函数对类型的每个值都定义了输出的,我们称为完全函数。 + 为了避免程序运行时因不被允许的操作中止,也为了区分对应合理与不合理输入的输出,我们使用 `Option[T]` 这一数据结构 +

+

+ Option T 代表类型T的可选值,分为两种情况,一种是没有值 None,一种是有值 Some,Some 中包含一个 value,其类型为 T。 + 在除法函数的第二行,我们使用 if 判断除数是否为0,如果为0,我们返回 None,否则返回 Some,Some 中存放正常的除法结果。 + Option 后的 T 表示 Option 是一个泛型类型,包含的数值类型为类型参数 T。 + 例如 Option Int 代表可能有的值类型为整数,我们将在稍后看到如何获得 Some 中的值。 +

+

+ 回到函数。说完了顶层函数,让我们再来看看局部函数。 + 局部函数的定义要求简化了不少,因为很多时候,月兔可以通过函数的定义以及应用时的类型来推断出函数的类型。 + 有时甚至可以省略函数的名称,此时可称为匿名函数。 + 例如在下面的例子中,我们定义了一个局部匿名函数,并将它绑定到 answer 上。 + 这个匿名函数省略了返回值类型,我们可以根据它的定义来推断。 + 它的定义调用了另一个局部函数 real answer。可以看到,这个函数也没有声明返回值类型,但我们可以通过42来推断它输出一个数字。 + 它的输出并不取决于输入,且输入亦未声明具体的类型。 + 但当我们传入字符串“终极问题”后,我们可以看到月兔将函数的类型推断 String to Int。 + 大家可以试试将传递的字符串改为其他东西,例如数字、字符、元组等。但是需要注意的是,仍然需要有且仅有一个参数。 + 函数在月兔中是一等公民:可以将函数作为参数、返回值,亦可以绑定或存储函数。我们将在后续课程中深入学习。 +

+

+ 函数类型的定义为,一连串用括号包裹、逗号分隔的参数类型,后接一个箭头和返回值类型。 + 例如,前面定义的 one,它的类型是一对空括号,返回一个 Int; + 第二行的函数类型代表接受一个 Int、一个 String 和一个 Char,返回一个 Int; + 注意,这里的括号并不代表元组。当使用元组作为参数时,需要再加一层括号,例如第三行的函数类型。 + 第四行的例子则是一个接受整数,返回一个函数的函数,其返回类型是一个接受整数并返回整数的函数类型。 + 另外,箭头是右结合的,因此最后一个情况中,箭头右侧的外层括号可以省略。 +

+

+ 接下来让我们进入列表的学习。 + 在生活中,我们会遇到很多数据,其中一些数据有如下的特征: + 第一,数据是有序的; + 第二,数据是可以重复的; + 第三,数据的数量是不定的。 + 举例来说,我们说的话中的文字,有序、可以重复、数量不定。 + 又比如DNA序列片段,有序、四个碱基重复出现,片段长短不一。 + 为了在计算机中表示这些数据,我们定义了列表这一数据结构。 +

+

+ 我们在这里定义一个单向不可变列表。 + 也就是说,添加内容时,列表只能往一个方向增长,我们称之为头。同时,列表中包含的内容不能被修改。 + 回想我们第一课所介绍的流程,让我们来定义它的接口,即它所允许的操作: + 我们以整数列表 Int List 为例,它应该被定义如下操作: + 首先,对于构造列表,它应该有一个 nil 操作,用于返回一个空列表; + 以及一个 cons 操作,用于将一个整数添加到列表头部,得到一个新列表。 + 而解构也有两个操作,首先是 head option,用于获得列表的头部元素。 + 因为头部元素不一定存在,所以返回类型是 Option Int。当头部元素不存在时,就返回 None。 + 另一个是 tail,返回除头部元素以外的列表。若本身是空列表,则依然返回空列表。 +

+

+ 我们来看看例子。 + 第二行,我们对空列表执行 head option 操作,期望获得头部元素。 + 由于空列表没有头部元素,因此返回 None。 + 第三行,我们对空列表执行 tail 操作,此时获得的依然是空列表,因此应该获得它本身。 + 接下来我们将整数1添加到空列表,获得了一个包含整数1的列表。 + 接着我们对它执行 head option 操作,因为列表中有元素1,所以我们获得的是 Some 1. + 我们对这个列表执行 tail 操作,获得的依然是空列表。 + 同样的,我们再添加第二项,整数2,获得了一个包含整数2和1的列表。 + 我们获得的头部是 Some 2,尾部则是原来的 list1. +

+

+ 在月兔中,列表可以被定义为,一个 Nil,代表空列表,以及 Cons,包含一个类型为 T 的值,以及一个类型为 List T 的子列表。 + 和前面介绍的 Option 一样,List 同样是泛型类型。 + 我们可以看到,列表的定义是归纳的。 + 需要注意的是,这里的“归纳”是数学归纳法的归纳,而不是从经验中归纳总结规律的归纳。 + 它属于严谨的演绎推理法。 + 让我们回想一下,数学归纳法首先证明在一个起点值命题成立,之后证明从一个值到下一个值的过程有效。 + 类比到列表,我们定义了列表为空的数据结构 Nil。 + 之后,我们定义了当列表添加了一个值的时候的数据结构 Cons。 + 下图展现了列表的结构。 +

+

+ 我们再来看几个列表的例子。最上面的两个是列表。 + Cons 1 Cons 2 Cons 3 Nil 是整数列表,而 Cons 一,Cons 句,Cons 话,Nil,是字符列表。 + 而以下几个不是列表。 + 第一个 Cons 1 Cons true Cons 3 Nil 不是列表,因为它混杂了不同的数据。这是不允许的。 + 而 Cons 1 2 不是列表,因为 Cons 应该包含一个值和一个子列表,而不是两个值。 + 最后一个 Cons 1,Cons Nil Nil 也不是列表,因为它混杂了一个整数和另一个列表。 +

+

+ 列表的类型写法与 Option 类似,是 List 中括号、类型。 + 以下分别是整数、字符串和浮点数列表类型的例子。 + +

+

+ 我们在这里已经看到了如何在月兔中构建列表。为了能够对列表进行运算,我们也需要能够分解列表。 + 因为有两种情况,所以我们需要通过模式匹配来分情况查看列表的内部结构。 + 模式匹配的定义为,match,表达式,大括号中每一都是一个模式、胖箭头、表达式。 + 模式可以用数据的构造方式定义。模式中定义了标识符,其作用域为右侧表达式。让我们看一个例子。 + 在这个例子中,我们希望访问一个数字列表的第一项。 + 我们使用模式匹配分情况进行讨论,分为空列表和非空列表。 + 我们分别使用了 Nil 和 Cons 这两个列表的构造器来匹配。 + 如果列表为空,则给出我们的默认值 None。 + 如果列表有一个值,则我们返回这个值。 + 其中,head 这个标识符,匹配了非空列表的值,而 tail 这个标识符,匹配了非空列表的子列表。 +

+

+ 模式匹配的化简可以分为几步。 + 首先,简化待匹配的表达式; + 然后,从上到下,依次进行匹配; + 接下来匹配成功后,根据模式定义,替换表达式中的标识符, + 最后,简化表达式。 +

+

+ 我们以 head option 为例,将它应用到 Cons 1 Cons 2 Nil 这个列表上。 +

+

+ 第一步,我们替换函数内的标识符,于是我们有了 match Cons 1 Cons 2 Nil。 + 然后我们从上到下进行匹配。 + 显然,不匹配 Nil。 + 但它匹配 Cons。 + 于是 head 和 tail 这两个标识符就分别绑定 1 和 Cons 2 Nil。 + 因此我们可以根据匹配的内容来替换表达式中的标识符。 + 得到 Some 1。 +

+

+ 同样地,我们也可以用模式匹配查看 Option 的结构来获得值。 + 例如,在 get or else 函数中,我们获取 option int 参数中的值,如果值不存在,我们提供了一个默认值。 + 我们在第二行使用了一个 match 来分情况处理。 + 如果 option int 是 None,则返回默认值 default。 + 如果 option int 是 Some,则返回其中的 value。 + 在模式匹配中,如果确认值存在,我们也可以省去匹配 None 的情况,来构造部分函数。 + 此时编译器会警告我们有模式尚未被匹配。 + 我们需要对这种情况负责,如果此时 option int 真的为 None,那么程序会出错中止。 + +

+

+ 以上便是本节课的内容,我们学习了函数和列表。下节课我们继续学习递归。 +

+

+ 大家好,欢迎来到由 IDEA 研究院基础软件中心为大家带来的现代编程思想公开课。 + 接下来,我们继续学习递归。 +

+

+ 递归有很多例子: + 比如大家听说过的 GNU 操作系统,GNUGNU is Not Unix 的递归缩写。 + 其中 GNU 代表的还是 GNU is Not Unix. + 另一个例子是在 Linux 上运行 Windows 程序的软件 Wine,它是 Wine Is Not an Emulator 的递归缩写。 + 其中,Wine 代表的还是 Wine Is Not an Emulator。 + 还有个例子是经典的斐波那契数列的计算,第一项和第二项是1,之后每一项都是前两项的和。 + 还有个大家耳熟能详的故事: + 山里有个庙,庙里有个老和尚和小和尚,一天,老和尚给小和尚讲故事。 + 山里有个庙,庙里有个老和尚和小和尚,一天,老和尚给小和尚讲故事。 + 山里有个庙,庙里有个老和尚和小和尚,一天,老和尚给小和尚讲故事。 +

+

+ 什么是递归呢? + 递归是将问题分解为与原问题相似的、规模更小的问题来求解。 + 递归应当有边界条件,否则便会像老和尚和小和尚讲故事一样喋喋不休无穷尽。 + 而对于一个函数而言,递归意味着在函数的定义中,直接或间接地使用函数自身。 + 请看下面两个例子。 + 第一个例子计算斐波那契数列的第 n 项。如果 n 等于 1 或者 2,就返回1,否则返回前两项之和。 + 怎么计算前两项呢?可以看到,我们递归地使用了 fib 函数本身来计算前两项的值。 + 第二个例子中,我们判断某个数是否为奇数或者偶数。 + 一个数是否为偶数,取决于它是否为0或1,或者比它小一的数是否为奇数。 + 同样的,一个数是否为奇数,取决于它是否为0或1,或者比它小一的数是否为偶数。 + 在这个例子中,even 调用 odd,odd 调用 even,因此都是递归函数。 +

+

+ 列表的数据结构是递归定义的。 + 让我们回忆一下它的定义:列表要么是一个空列表,要么是一个值和一个列表。 + 这里的列表便递归了。 + 因此,在列表上的操作十分适合用递归函数进行定义。 + 例如这里的求列表长度的函数,便同时运用了模式匹配和递归。 + 我们用模式匹配判断,若列表为空,则长度为0;若列表非空,则长度为1加上尾部列表的长度。 +

+

+ 递归的运算与函数的运算相同。只不过,除了替换参数所定义的表达式以外,还需要将内部出现的自身再一次用自身的定义替代。 + 以刚才定义的求列表长度的 length 函数为例: + 我们在它应用到列表 Cons 1 Cons 2 Nil 上。 + 第一步,我们替换函数定义,得到 match Cons 1 Cons 2 Nil。 + 第二步,进行模式匹配,获得 1 加 length t l,其中 t l 是 Cons 2 Nil。 + 此时又出现了 length,于是我们再次替换 length 的定义,得到 1 + length Cons 2 Nil。 + 再次进行模式匹配,并替换标识符,于是我们有了 1 + 1 + length Nil。 + 此时,再对 length Nil 进行模式匹配,得到 1 + 1 + 0,可以简化为2. + +

+

+ 我们再看一个更复杂的递归的例子。 + concat 是一个将两个列表连接起来的函数。 + 它的定义为,如果第一个列表为空,则返回第二个列表;否则, + 返回第一个列表的头部元素和第二个列表连接起来的结果。 + 让我们来看一个例子。 + 我们将它应用到两个列表上,Cons 1 Cons 2 Nil 和 Cons 3 Nil。 + 首先,我们替换函数定义,得到 Cons 1 concat Cons 2 Nil Cons 3 Nil。 + 接下来,我们替换 concat 的定义,Cons 的第二项变成了 Cons 2 concat Nil Cons 3 Nil. + 再次替换 concat 的定义,发现第一个列表非空,因此这一项变成了 Cons 3 Nil + 我们便得到了计算结果,原来的两个列表连接起来就是 Cons 1 Cons 2 Cons 3 Nil。 +

+

+ 像这种定义在递归的数据结构上的递归,我们称之为结构化递归。 + 我们需要定义基础数据结构的计算,对应着终结递归的情形,例如空列表的情况。 + 之后,我们需要定义对于中间数据结构的计算,对应着递归的情形,例如非空列表的情况。 + 在定义递归情形时,我们可以假设该定义在递归的子结构上已经存在。 + 例如,定义 Cons head tail 的 length 时, + 我们可以假设 tail 的 length 已经被定义好了。这种假设称为归纳假设。 + 通常,我们可以用数学归纳法来证明结构化递归定义的函数是正确的。 +

+

+ 让我们看一个数学归纳法证明命题的例子。假设我们要证明,对于任意列表 l1 和 l2, + 它们拼接后得到的列表 concat l1 l2 的长度,等于 l1 的长度加上 l2 的长度。 + 首先,我们证明基础情形: + 若 l1 为空,则拼接后的列表就是 concat Nil l2。 + 我们替换 concat 的定义,得到 length Cons Nil l2. + 根据 length 的定义,上式化简为 length l2. + 而 length l2 刚好等于 length l1 加上 length l2,因为 length l1 可以化简为 0。 +

+

+ 数学归纳法的第二步,是证明归纳情形。该步骤有些繁琐。 + 我们要计算的式子是 length concat l1 l2。 + 若 l1 非空,也就是说,它是一个 Cons head tail。 + 使用模式匹配,原式化简为 length concat Cons head tail l2。 + 这个式子中,concat 函数应用是可以继续化简的,我们替换 concat 函数的定义, + 式子化简为 length Cons head concat tail l2 + 此时可以替换 length 函数的定义,将式子进一步,化简为, 1 加 length concat tail l2 + 然后,根据归纳假设,l1 的子列表 tail 和 l2 拼接后的长度等于 tail 的长度加上 l2 的长度。 + 所以我们可以把这一部分替换为 length tail 加 length l2. + 而根据整数加法的结合律,我们可以先计算左边两个数的和。 + 再次回顾 length 的定义和 l1 的结构,1 加 length tail 刚好就等于 length l1。 + 所以,原式化简为 length l1 加上 length l2,这就是我们需要的结果。 + 证明了基础情形和归纳情形后,我们就成功证明了原命题: + 对于任意列表 l1 和 l2,concat l1 l2 的长度等于 length l1 加上 length l2。 +

+

+ 当我们定义出正确的程序后,我们依然有其他的追求,那就是,我们的程序运行得够快吗? + 以斐波那契数列为例。我们为大家提供了两个实现。求第44项的时候,在我的电脑上已经可以观察到性能的差别了: + 第一种方法需要2.08秒,而第二种方法几乎瞬间完成。 + 我们分析一下简单的计算方法,看一下它为什么这么慢。 + 如图所示,求解`f(5)`需要计算`f(3)`,而求解`f(4)`的时候,还要再一次求解`f(3)`。 + 因此,每一次求值时,我们都需要计算前两项的值,而同样地,它们也会计算更前面的项的值。 + 这就导致了一个问题,我们观察到了大量重复计算。 + 大家可以大致数一下,求`f(3)`需要应用几次函数,而`f(4)`需要应用几次函数,`f(5)`需要应用几次函数。 + 大家会发现,每增加一项,函数的应用次数几乎要翻倍。 + 这个性能显然是不能被接受的。我们可以采用动态规划这一技巧来避免上述问题。 + 动态规划,即是将问题分解为与原问题相似的、规模更小的问题来求解。 + 这听起来像是递归的定义,但动态规划是对递归的一种优化。 + 动态规划有两个适用条件。一个条件是,有重叠的子问题。 + 动态规划对每一个子问题求解一次,将其保存,避免重复运算。 + 另一个条件是,有最优子结构。因为我们只计算一次子问题,因此子问题的最优解应当也是最优解的一部分。 + 动态规划实现方式分为两种:自顶向下和自底向上。 + 自顶向下方式,针对每个子问题,如果已求解,直接使用缓存结果;否则求解并缓存。 + 自底向上方式先解决子问题,再从子问题的解,构建更大的子问题的解。 +

+

+ 以斐波那契数列为例。求解斐波那契数列符合使用动态规划的条件,因为它有重叠的子问题和最优子结构。 + 可以从图中看到,如果我们重复使用了之前的计算结果, + 那么我们总的函数应用次数,只是我们所要计算的项数,增长速度相比最简单的实现方式变慢了。 + 我们用两种方式来实现:自顶向下和自底向上。 + 我们先看自顶向下的例子: + 为了缓存我们之前的计算结果,我们需要一个数据结构 cache。 + 考虑到我们缓存的结果数量会随着问题的规模增长而增长,因此一个理想的数据结构的平均存取速度,应当与当前存储数据量大小无关。 + + 按照第一节课所说的,我们先定义这个数据结构所应当有的接口。 + 首先,我们应该能够构造一个空的数据结构。也就是 empty 函数。 + 之后,以斐波那契数列为例,我们需要能够针对每个项数存储一个结果, + 因此我们需要一个 put 函数向数据结构中存储一个整型以及对应的一个长整型。 + 这个存储操作我们只期待它执行一次。 + 之后,我们也应当有个 get 函数让我们读取存储的结果。 + 但此时对应的子问题可能尚未求解完毕,因此我们用 Option 类型来承载这个结果。 + 事实上,符合条件的数据结构有很多种。 + 我们的样例代码采用 immutable HashMap Int Int64,因为这是一个相对简单的数据结构。 + 但模块化编程的好处就在于,我们只需要关心接口而无需关心具体实现。 + 事实上,我们完全可以把它替换成其他的数据结构,例如 Array Option Int64 等。 + 定义完了数据结构,让我们来看具体实现。 + 自顶向下的解法为,每次计算时看当前数据结构中,是否存有我们所求的项数所对应的结果。 + 如果有,我们直接使用。如果没有,我们需要计算求解,并且将结果添加至数据结构中方便下次计算。 + 如代码所示。我们定义了一个辅助的递归函数帮助计算。 + 我们在第三行根据传入的缓存和项数判断当前是否已经有了结果。 + 如果有,那么结果就是缓存的结果,并且对于缓存我们没有进行修改。 + 如果没有,那么我们便要进行求解。 + 需要注意的是,在求解所需的一个项的同时,我们也需要更新缓存,以确保缓存中存有此次求解的结果。 + 因此,我们的辅助递归函数把缓存结构作为参数,并将其返回。 + 在求解第二项的时候,我们需要把更新后的缓存传进去,并再次获得更新后的缓存。 + 最后,我们在求解当前项成功之后,还是要把当前项,也加入缓存,并且作为结果返回。 + 可以注意到,我们这里的 let 定义同样也使用了模式匹配,匹配了我们的元组结构。 + 这样将缓存不断地传递,在书写时会有些麻烦,因此月兔也提供了可变变量,方便大家的书写。 + 可变变量绑定的数据可以被改变。 + 例如代码样例中,我们将缓存结构通过 let mut 进行了定义,并赋予了最初的值。 + 之后,我们通过变量、等于、值,的方式对它进行了修改。 + 在此之后再使用 map 这个值,便是获得修改后的值。 + 如此,我们便可以将我们的定义稍稍化简。 + 关于可变变量,我们之后还会再遇到。 + +

+

+ 接下来让我们看看自底向上的例子。 + 自底向上,意味着先计算子问题,再从子问题构建更大的子问题,直到子问题等于原问题。 + 这里,我们从最初的第一项开始,不断向后进行求解。 + 我们首先从前两项构建当前子问题的解。之后,我们判断,当前的子问题是不是就是原问题? + 如果是,那我们已经获得了解;如果没有,那我们继续进行更大的子问题的计算,在这里也就是计算斐波那契数列的后一项。 + 当然,我们在这里会发现,我们每次构建更大的子问题的时候,只需要保留前两项便足够,更早的数据其实可以被遗忘。 + 因此,我们可以简化我们的结构,舍弃缓存,直接通过递归参数传递。 + 我们可以从图中看到,具体的计算流程。 + + 一个斐波那契数列,就有那么多种解法。你能想到别的思路吗? + +

+

+ 总结一下,我们今天学习了 + 函数的定义与运算 + 列表的定义与模式匹配 + 递归的含义与运算,我们还对时间复杂度有了感性的认识。 + 我们在此对于涉及的一些概念的解释都还不够深入。 + 为此我们推荐大家进行拓展学习。在这里给大家推荐几本好书: + 想要了解如何用数学归纳法证明结构化递归的正确性,可以参阅:Software Foundations 前三章 + 或 Programming Language Foundations in Agda 前三章,后者有中文版 + 想要更深入地了解算法的定义以及时间复杂度的定义等,可以参阅:《算法第四版》第一章或《算法导论》第三章 +

+ + \ No newline at end of file From 2999a6452b12fca002637a8988826830f5b681fa Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Mon, 25 Aug 2025 12:41:45 +0800 Subject: [PATCH 06/14] chore: update slides for course 3. --- course3/lec3.mbt.md | 179 +++++++++++++++++++++++++++----------------- course3/lec3.pdf | Bin 655078 -> 724176 bytes 2 files changed, 111 insertions(+), 68 deletions(-) diff --git a/course3/lec3.mbt.md b/course3/lec3.mbt.md index e87243b..148b600 100644 --- a/course3/lec3.mbt.md +++ b/course3/lec3.mbt.md @@ -7,7 +7,7 @@ backgroundImage: url('../pics/background_moonbit.png') # 现代编程思想 -## 函数, 列表与递归 +## 函数,列表与递归 ### 月兔公开课课程组 @@ -26,7 +26,7 @@ backgroundImage: url('../pics/background_moonbit.png') - 计算半径为2的圆的面积:`3.1415 * 2 * 2` - 计算半径为3的圆的面积:`3.1415 * 3 * 3` - …… - - `fn 面积(半径: Double) -> Double { 3.1415 * 半径 * 半径 }` + - `fn 面积(半径 : Double) -> Double { 3.1415 * 半径 * 半径 }` --- @@ -57,7 +57,7 @@ let result : (Double, Double, Double) = (area(1.0), area(2.0), area(3.0)) # 顶层函数的定义 ``` -fn <函数名> (<参数名>: <类型>, <参数名>: <类型>, ...) -> <类型> <表达式块> +fn <函数名> (<参数名> : <类型>, <参数名> : <类型>, ...) -> <类型> <表达式块> ``` 定义的函数接口让其他使用者无需关注内部实现 @@ -82,7 +82,7 @@ fn add_char(ch : Char, str : String) -> String { - 应用函数时,表达式与函数定义时的参数数量应当相同,且类型一一对应 这是错误的:`add_char("oonbit", 'm')` - 计算应用函数的表达式时 - - **从左到右**计算定义了参数的表达式的值 + - **从左到右**计算参数表达式的值 - 替换函数内部参数 - 简化表达式 @@ -91,11 +91,11 @@ fn add_char(ch : Char, str : String) -> String { # 函数的应用与计算 ```moonbit skip -fn add_char(ch: Char, str: String) -> String { - ch.to_string() + str +fn add_char(ch : Char, str : String) -> String { + ch.to_string() + str } -let moonbit: String = add_char(Int::unsafe_to_char(109), "oonbit") +let moonbit : String = add_char(Int::unsafe_to_char(109), "oonbit") ```       `add_char(Int::unsafe_to_char(109), "oonbit")` @@ -111,32 +111,33 @@ $\mapsto$ `"moonbit"`                               函数定义域有的时候是输入类型的子集,因此可能会有对于输入未定义输出的情况 ```moonbit -let ch: Char = Int::unsafe_to_char(-1) // 不合理输入:-1在统一码中不对应任何字符 -let nan: Int = 1 / 0 // 不被允许的操作:运行时出错并终止 +let ch : Char = Int::unsafe_to_char(-1) // 不合理输入:-1在统一码中不对应任何字符 + +let nan : Int = 1 / 0 // 不被允许的操作:运行时出错并终止 ``` 对于这种函数,我们称为**部分函数**(Partial Function);相对的,函数对类型的每个值定义了输出的,我们称为**完全函数**(Total Function) -为了避免程序运行时因不被允许的操作中止,也为了区分对应合理与不合理输入的输出,我们使用`Option[T]`这一数据结构 +为了避免程序运行时因不被允许的操作中止,也为了区分对应合理与不合理输入的输出,我们使用 `Option[T]` 这一数据结构 --- # Option的定义 -`Option[T]`分为两种情况: +`Option[T]` 分为两种情况: - 无值:`None` -- 有值:`Some(value: T)` +- 有值:`Some(value : T)` -例如,我们可以用`Option`定义一个整数除法的完全函数 +例如,我们可以用 `Option` 定义一个整数除法的完全函数 ```moonbit -fn div(a: Int, b: Int) -> Option[Int] { +fn div(a : Int, b : Int) -> Option[Int] { if b == 0 { None } else { Some(a / b) } } ``` -`[T]`代表`Option`是一个泛型类型,包含的数值类型为类型参数`T`,如 +`[T]` 代表 `Option` 是一个泛型类型,包含的数值类型为类型参数 `T`,如 - `Option[Int]`:可能有的值类型为整数 -我们将在稍后看到如何获得`Some`中的值 +我们将在稍后看到如何获得 `Some` 中的值 --- @@ -145,14 +146,13 @@ fn div(a: Int, b: Int) -> Option[Int] { 局部函数定义大多数时候可以省略参数类型和返回类型,亦可以省略名称(匿名函数) ```moonbit -let answer: () -> Int = fn () { +let answer : () -> Int = fn() { fn real_answer(i) { 42 } real_answer("Ultimate Question") } - -let x: Int = answer() // 42 +let x : Int = answer() // 42 ``` ![height:70px](../pics/func_without_parameter_type.png) @@ -169,6 +169,8 @@ let x: Int = answer() // 42 - `() -> Int` - `(Int, String, Char) -> Int` - `((Int, Int, Int)) -> (Int, Int, Int)` 接受一个元组并返回一个元组 +- `(Int) -> ((Int) -> Int)` 接受一个整数并返回一个函数,该函数接受一个整数并返回一个整数 + 可省略箭头:`(Int) -> (Int) -> Int` --- @@ -193,7 +195,7 @@ let x: Int = answer() // 42 我们定义一个单向不可变列表 -以整数的列表为例(暂名之`IntList`),它应当定义如下操作: +以整数的列表为例(暂名之 `IntList`),它应当定义如下操作: - 构造 - `nil : () -> IntList`                                    返回一个空列表 - `cons : (Int, IntList) -> IntList`  向列表添加一项 @@ -244,8 +246,8 @@ enum List[T] { # 列表样例 - 以下是列表 - - `let int_list: List[Int] = Cons(1, Cons(2, Cons(3, Nil)))` - - `let char_list: List[Char] = Cons('一', Cons('句', Cons('话', Nil)))` + - `let int_list : List[Int] = Cons(1, Cons(2, Cons(3, Nil)))` + - `let char_list : List[Char] = Cons('一', Cons('句', Cons('话', Nil)))` - 以下不是列表 - `Cons(1, Cons(true, Cons(3, Nil)))` 因为混杂不同类型的数据 @@ -337,7 +339,7 @@ Option::Some(head) 同样地,我们也可以用模式匹配查看`Option`的结构来获得值 ```moonbit -fn get_or_else(option_int: Option[Int64], default: Int64) -> Int64 { +fn get_or_else(option_int : Option[Int64], default : Int64) -> Int64 { match option_int { None => default Some(value) => value @@ -347,7 +349,7 @@ fn get_or_else(option_int: Option[Int64], default: Int64) -> Int64 { 模式匹配中,亦可以省略部分情况(如确认存在值),来构造部分函数 ```moonbit -fn get(option_int: Option[Int64]) -> Int64 { +fn get(option_int : Option[Int64]) -> Int64 { match option_int { // 编辑器会警告我们有模式尚未被匹配 Some(value) => value // 若option_int为None则会程序出错中止 @@ -405,7 +407,7 @@ fn odd(n: Int) -> Bool { > - `List::Cons(head, tail)`:一个值`head`以及一个**列表`tail`** ```moonbit -fn length(list: List[Int]) -> Int { +fn length(list : List[Int]) -> Int { match list { Nil => 0 Cons(_, tl) => 1 + length(tl) @@ -468,6 +470,26 @@ $\mapsto$ `1 + 1 + 0` $\mapsto$ `2` --- +# 列表拼接 + +```moonbit +fn concat(l1 : List[Int], l2 : List[Int]) -> List[Int] { + match l1 { + Nil => l2 + Cons(hd, tl) => Cons(hd, concat(tl, l2)) + } +} +``` + +计算例子: + +`concat(Cons(1, Cons(2, Nil)), Cons(3, Nil))` +$\mapsto$ `Cons(1, concat(Cons(2, Nil), Cons(3, Nil)))` +$\mapsto$ `Cons(1, Cons(2, concat(Nil, Cons(3, Nil))))` +$\mapsto$ `Cons(1, Cons(2, Cons(3, Nil)))` + +--- + # 结构化递归 对基于递归定义的数据结构 @@ -489,22 +511,31 @@ fn length(list: List[Int]) -> Int { --- -# 数学归纳法:以子列表长度为例 +# 数学归纳法:以拼接列表长度为例 -- 命题:对于任意列表`a`,令列表`a`长度为$l_1$,子列表`tail(a)`长度为$l_2$,则总有$l_1 \geq l_2$ +- 命题:对于任意列表 `l1` 和 `l2`,拼接后的列表 `concat(l1, l2)` 的长度为 `l1` 的长度与 `l2` 的长度之和。 -```moonbit -fn tail(list: List[Int]) -> List[Int] { - match list { - Nil => Nil - Cons(_, tail) => tail - } -} -``` -- 证明:对`a`分类讨论 - - 若`a`为空(`Nil`),则子列表`tail(a) == a`,两者长度均为0,命题成立 - - 若`a`为非空(`Cons(head, tail)`),则子列表`tail(Cons(head, tail)) == tail`,可知$l_1 = l_2 + 1 > l_2$,命题成立 - - 由数学归纳法,原命题成立 +- 证明:对 `l1` 分类讨论: + - 若 `l1` 为空(`Nil`),则拼接后的列表的长度为 + `length(concat(Nil, l2))` + $\mapsto$ `length(Cons(Nil, l2))`(替换 `concat` 的定义) + $\mapsto$ `length(l2)`(替换 `length` 的定义) + 该结果等于 `length(l1) + length(l2)`,因为 `length(l1)` 为 `0` + +--- + +# 数学归纳法:以拼接列表长度为例(续) + +- 证明: + - 若 `l1` 非空(`Cons(hd, tl)`),则拼接后列表长度为 + `length(concat(l1, l2))` + $\mapsto$ `length(concat(Cons(hd, tl), l2))`(模式匹配) + $\mapsto$ `length(Cons(hd, concat(tl, l2)))`(由 `concat` 的定义) + $\mapsto$ `1 + length(concat(tl, l2))`(由 `length` 的定义) + $\mapsto$ `1 + (length(tl) + length(l2))`(归纳假设) + $\mapsto$ `(1 + length(tl)) + length(l2)`(加法结合律) + $\mapsto$ `length(l1) + length(l2)`(在 `length(l1)` 替换 `length` 的定义) + - 根据数学归纳法,命题成立 --- @@ -516,13 +547,12 @@ fn tail(list: List[Int]) -> List[Int] { 1, 1, 2, 3, 5, 8, 13, 21, …… -不同的斐波那契数列的计算方式带来的不同性能差别(`num` > 40) +不同的斐波那契数列的计算方式带来的性能差别(`num` > 40) -```moonbit -fn fib(num: Int) -> Int { - if num == 1 || num == 2 { 1 } else { fib(num - 1) + fib(num - 2) } +```moonbit skip +fn fib1(num : Int) -> Int { + if num == 1 || num == 2 { 1 } else { fib1(num - 1) + fib1(num - 2) } } - fn fib2(num : Int) -> Int { fn aux(n, acc1, acc2) { match n { @@ -535,13 +565,22 @@ fn fib2(num : Int) -> Int { } ``` + + --- # 简单的斐波那契数列的计算方式 -```moonbit -fn fib(num: Int) -> Int64 { - if num == 1 || num == 2 { 1L } else { fib(num - 1) + fib(num - 2) } +```moonbit skip +fn fib1(num : Int) -> Int64 { + if num == 1 || num == 2 { 1L } + else { fib1(num - 1) + fib1(num - 2) } } ``` ![](../pics/fib_simple.drawio.png) @@ -576,15 +615,15 @@ fn fib(num: Int) -> Int64 { # 自顶向下:以斐波那契数列为例 - 我们需要一个数据结构,平均存取速度应当与当前存储数据量大小无关 -- 以求解斐波那契数列为例,我们假设的`IntMap`应有如下接口: +- 以求解斐波那契数列为例,我们假设的 `Cache` 应有如下接口: ```moonbit no-check -fn empty() -> IntMap // 创建数据结构 -fn insert(map: IntMap, num: Int, value: Int64) -> IntMap // 存储数据,只执行一次 -fn lookup(map: IntMap, num: Int) -> Option[Int64] // 提取数据 +fn empty() -> Cache // 创建数据结构 +fn put(cache : Cache, num : Int, value : Int64) -> Cache // 存储数据,只执行一次 +fn get(cache : Cache, num : Int) -> Option[Int64] // 提取数据 ``` -- 符合条件的数据结构有很多,我们的样例代码以`Map[Int, Int64]`为例 +- 符合条件的数据结构有很多,我们的样例代码以 `@immut/hashmap.T[Int, Int64]` 为例(后文记作 `Map[Int, Int64]`) --- @@ -595,8 +634,8 @@ fn lookup(map: IntMap, num: Int) -> Option[Int64] // 提取数据 - 若无,并将结果添加至数据结构中 ```moonbit -fn fib1(num: Int) -> Int64 { - fn aux(num: Int, map: Map[Int, Int64]) -> (Int64, Map[Int, Int64]) { +fn fib1(num : Int) -> Int64 { + fn aux(num : Int, map : Map[Int, Int64]) -> (Int64, Map[Int, Int64]) { match get(map, num) { Some(result) => (result, map) None => { @@ -606,27 +645,28 @@ fn fib1(num: Int) -> Int64 { } } } - let map = put(put(make(), 1, 1L), 2, 1L) + let map = put(put(empty(), 1, 1L), 2, 1L) aux(num, map).0 } ``` + --- # 可变变量 -注意到`map: Map[Int, Int64]`被不断传递。为了简化写法,月兔提供可变变量 +注意到`map : Map[Int, Int64]`被不断传递。为了简化写法,月兔提供可变变量 ```moonbit -fn fib1_mut(num: Int) -> Int64 { - let mut map = put(put(make(), 1, 1L), 2, 1L) // 通过let mut声明可变变量 - fn aux(num: Int) -> Int64 { +fn fib1_mut(num : Int) -> Int64 { + let mut map = put(put(empty(), 1, 1L), 2, 1L) // 通过let mut声明可变变量 + fn aux(num : Int) -> Int64 { match get(map, num) { Some(result) => result None => { let result_1 = aux(num - 1) let result_2 = aux(num - 2) // 通过 <变量> = <值> 修改绑定的值 - map = put(map, num, result_1 + result_2) + map = put(map, num, result_1 + result_2) result_1 + result_2 } } @@ -642,14 +682,17 @@ fn fib1_mut(num: Int) -> Int64 { - 我们从第一项出发,逐个计算之后的值,并将当前项的计算结果存入数据结构 ```moonbit -fn fib2(num: Int) -> Int64 { - fn aux(n: Int, map: Map[Int, Int64]) -> Int64 { - let result = get_or_else(get(map, n - 1), 1L) + +fn fib2(num : Int) -> Int64 { + fn aux(n : Int, map : Map[Int, Int64]) -> Int64 { + let result = get_or_else(get(map, n - 1), 1L) + get_or_else(get(map, n - 2), 1L) - if n == num { result } - else { aux(n + 1, put(map, n, result)) } + if n == num { + result + } else { + aux(n + 1, put(map, n, result)) + } } - let map = put(put(make(), 0, 0L), 1, 1L) + let map = put(put(empty(), 0, 0L), 1, 1L) aux(1, map) } ``` @@ -658,11 +701,11 @@ fn fib2(num: Int) -> 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zwxF=FXfcZx-T+m(QBJ9dc0>cap#?Vw8mSliuK5`2AzBWZ7SY^tnA71TVbl`V@iF3E zh^*<53?+;HFElKdNa8HB9wS3OQxJe#ncW*u=suFLM!E#AQWqI)93^ItmC8KW+feS3 z6S!VekU1mqG4I|ur?WEEE2Od3rG;<#QNG(o;CSknK_=0ve3*Nv#iu$`BLvcqRYPu_ zPYl&Ya@RU6A-{K*y4FH>R|MbMH&&28>$Rr6_2Q?JXsUG%c<&(9@zeXlI-b zQ>;$leDk;8Ry7)CA`4eo_zX~}Vf65nMteNHBRpL7qYg~f^s4q7(sa27*gc=PMp%Kp zq%&N7@nT{CCK4to!;PEf4jz;BQYlosyVJ*CYS27ZRqRKd8{$W zes`5{)6Ax!`J9ru^}GA Date: Mon, 25 Aug 2025 16:34:49 +0800 Subject: [PATCH 07/14] fix: pronounciation `mut`; illustration for `concat`. --- course3/script.xml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/course3/script.xml b/course3/script.xml index d552336..a69c265 100644 --- a/course3/script.xml +++ b/course3/script.xml @@ -233,7 +233,7 @@ 我们再看一个更复杂的递归的例子。 concat 是一个将两个列表连接起来的函数。 它的定义为,如果第一个列表为空,则返回第二个列表;否则, - 返回第一个列表的头部元素和第二个列表连接起来的结果。 + 计算第一个列表的 tail 与第二个列表拼接起来的列表,再添加第一个列表的 head 作为结果。 让我们来看一个例子。 我们将它应用到两个列表上,Cons 1 Cons 2 Nil 和 Cons 3 Nil。 首先,我们替换函数定义,得到 Cons 1 concat Cons 2 Nil Cons 3 Nil。 @@ -329,7 +329,7 @@ 可以注意到,我们这里的 let 定义同样也使用了模式匹配,匹配了我们的元组结构。 这样将缓存不断地传递,在书写时会有些麻烦,因此月兔也提供了可变变量,方便大家的书写。 可变变量绑定的数据可以被改变。 - 例如代码样例中,我们将缓存结构通过 let mut 进行了定义,并赋予了最初的值。 + 例如代码样例中,我们将缓存结构通过 let mut 进行了定义,并赋予了最初的值。 之后,我们通过变量、等于、值,的方式对它进行了修改。 在此之后再使用 map 这个值,便是获得修改后的值。 如此,我们便可以将我们的定义稍稍化简。 From f260782df0aa07bd99a2a3dfca2d06cdcfa5b772 Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Mon, 25 Aug 2025 16:35:47 +0800 Subject: [PATCH 08/14] feat: links for moonbitlang.cn and tour. --- course2/lec2.mbt.md | 11 ++++++----- course2/lec2.pdf | Bin 786014 -> 787160 bytes 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/course2/lec2.mbt.md b/course2/lec2.mbt.md index 3014ca5..7b31757 100644 --- a/course2/lec2.mbt.md +++ b/course2/lec2.mbt.md @@ -17,7 +17,9 @@ backgroundImage: url('../pics/background_moonbit.png') - 现代静态类型**多范式**编程语言 - 语法轻量,易上手 -- 参考资料: [moonbitlang.cn](https://moonbitlang.cn) +- 参考资料: + - [官网 moonbitlang.cn](https://moonbitlang.cn) + - [语言导览 tour.moonbitlang.com/zh](https://tour.moonbitlang.com/zh/index.html):快速学习月兔的互动教程 --- @@ -28,11 +30,10 @@ backgroundImage: url('../pics/background_moonbit.png') # 月兔开发环境 - 开发工具 - - [VS Code 插件](https://marketplace.visualstudio.com/items?itemName=moonbit.moonbit-lang):语言服务器功能 - - [命令行工具](https://www.moonbitlang.com/download/#moonbit-cli-tools):项目构建、测试、依赖管理等功能 - - [语言导览](https://tour.moonbitlang.com/zh/index.html):快速学习月兔的互动教程 + - VS Code 插件:语言服务器功能 + - 命令行工具:项目构建、测试、依赖管理等功能 - 开发环境 - - [浏览器环境](https://try.moonbitlang.cn)(无命令行工具) + - [浏览器环境 try.moonbitlang.cn](https://try.moonbitlang.cn)(无命令行工具) - 云原生开发环境(如 [Github Codespaces](https://github.com/features/codespaces)) - 本地开发环境 diff --git a/course2/lec2.pdf b/course2/lec2.pdf index 3f5d78a5486ced28b9e0998330d4b4786ef86f42..0301a8f3dcc2e5ca49b778a1b21364f9fea86ff4 100644 GIT binary patch delta 207762 zcmY(qbyOI!(g%vWyHniV-QC@-xE6Oo5iXzm4^rj+Nvq^e8%+~49-jh$*HJSuG0?iv34i$uFaSYYO+q0hUI`C+46p|++&441@{DgqGVCU@AEIu 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+ 大家好,欢迎来到由IDEA研究院基础软件中心为大家带来的现代编程思想公开课。 + 今天是第四节课,主题是多元组,结构体与枚举类型。 + 一言以蔽之,今天介绍如何在月兔中自定义数据结构。 + +

+

+ 首先让我们来回顾第二节课已经介绍过的月兔基础数据类型:多元组。 + +

+

+ 多元组是固定长度的不同类型数据的组合。 + 相比较之下,列表则是任意长度的相同类型的数据的集合。 + 例如,下方字符的列表长度不定,但是存储的值必须都是字符类型。 + 第三课没有提到 Cons 为什么要叫 Cons Cons 是 Construct 的缩写,在这里补充一下。 + 多元组的定义通过括号包裹,逗号分隔的表达式组成, + 类型也是类似的,通过括号包裹,逗号分隔的类型组成, + 例如我们这里看到的身份信息的定义,Bob、2023、10、24 这个多元组的类型为 String、Int、Int、Int 四元组。 + 多元组的成员的访问可以通过索引访问,从左到右索引从0开始,例如图中这个元组的第0项,就是 2023。 + +

+

+ 大家或许了解笛卡尔积。 + 两个集合的笛卡尔积,便是一个集合,其中所有的元素便是原来两个集合元素构成的有序对。 + 例如这里扑克牌的花色的集合与1到52的数字构成的笛卡尔积,便构成了所有花色与数字的有序对。 + 而多元组,不仅仅是两个集合的笛卡尔积,是多个集合的笛卡尔积,因此更确切的说法是构成的有序元素组。 + 也因此,多元组又被称为积类型。那么大家可能会好奇,有积类型,那么有禾类型吗? + 有积类型和禾类型,那有零有一吗?我们会在稍后的课程中为大家介绍。 + +

+

+ 元组的问题在于,难以理解其所代表的数据。 + 举例来说,String Int,究竟代表一个人的姓名和年龄?还是代表一个人的姓名和手机号?亦或是地址和邮编? + 结构体允许我们赋予名称,即是赋予名称给整个类型,也是赋予名称给每个字段,例如: + PersonalInfo 结构体代表个人信息, name 代表姓名,age 代表年龄。 + ContactInfo 结构体代表联系方式,telephone 字段代表电话号码。 + AddressInfo 结构体代表地址信息,postal 字段代表邮编。 + 通过名称,我们能明确数据的信息以及对应字段的含义。 + +

+

+ 结构体的定义为 struct、结构体名称,大括号,字段列表;每个字段都有名称禾类型。 + 字段之间用分号分隔,在换行的情况下可以省略。 + 定义结构体的值时候,是用大括号包裹,用字段名、冒号、值,的语法,给每一个字段赋值。 + 例如这里的 info,就给 name age 分别赋值为 MoonBit 和 1. + 每个值后都有逗号。如果最后一个逗号后面直接跟着大括号未有换行,则最后一个逗号可以省略。这里的定义不在意顺序。 + 例如,先赋值 age,再赋值 name ,依然是 PersonalInfo 结构体的值。 + 如果两个结构体碰巧字段名称禾类型完全相同,只定义了值是无法区分的; + 此时我们可以在结构体的值的后面加上类型声明,例如冒号 A 来进行区分。 + +

+

+ 结构体的访问可以通过类似多元组的方法访问,通过字段名获取对应数据。 + 例如,点 age 来获得 age 所对应的数据。 + 在根据已有结构体创建新的结构体的时候,如果我们有个非常大型的结构体,那么重新声明每个字段显然是非常费时费力的。 + 为了方便起见,月兔也提供了仅更新部分字段的功能。只需要在结构体值的定义前,用点点加上原结构体的方式,标明基于哪个结构体, + 之后便只需要声明重新修改过的值对应的字段即可。如下方的例子。 + new info 和 other info 在 old info 的基础上分别对 name age 字段进行了更新。 + +

+

+ 大家可能会发现,多元组和结构体似乎非常相像。 + 事实上,一个结构体与相同类型集合构成的多元组是同构的关系。 + 同构,也就是两个集合之间存在着一一映射的关系。 + 如果在集合 A 和 B 之间存在一对映射关系 f从 A 到 B,和 g 从 B 到 A, + 并且对于任意的集合 A 中的 a 或集合 B 中的 b,有 g f a 等于 a,f g b 等于 b。就是如下图所示,那么这两个集合就是同构的。 + 举例来说,PersonalInfo 与二元组 String Int 就是同构的,因为我们可以构筑如下的一对映射: + 函数 f 从 PersonalInfo 映射到 String Int 二元组,函数 g 从 String Int 二元组映射到 PersonalInfo. + 两个函数在映射过程中都没有丢失任何的信息。大家可以自行验证上面的性质。 + 同理,PersonalInfo 与 Int String 二元组也是同构的,大家可以自己尝试验证。 + +

+

+ 多元组和结构体的区别则在于,多元组是 structural,也就是只要结构相同,即字段类型一一对应,那么类型就是兼容的。 + 例如此处,函数成功接受了一个多元组。 + 而结构体不同。结构体是 nominal,也就是只有类型名相同,类型才是兼容的(而内部定义的顺序可以打乱)。 + 例如第一个例子中,即使结构是完全一致的,但两者的类型名称不相同,函数无法接受这个结构体。 + 而第二个例子中,虽然结构的顺序是不同的,但是因为类型相同,函数可以顺利接受。 + +

+

+ 让我们接下来梳理一下模式匹配,来看看多元组和结构体除了通过下标和字段名访问以外的另一种方式。 + 我们回顾一下,之前我们用模式匹配查看了列表和 Option 的结构。 + 例如,Nil 和 Cons 来匹配列表,None 和 Some 来匹配 Option。 + 事实上,模式匹配可以匹配值(逻辑值、数字、字符、字符串)以及构造器。 + 上面的例子中,我们便是匹配了数字。注意到,如果是匹配值,我们还可以用竖线来分割模式,同时匹配多种可能的值。 + 最后我们则用下划线这一“通配符”,匹配所有的剩余的情况。 + 在构造器中,我们也可以嵌套模式进行匹配,或者用标识符绑定对应结构。 + 例如,第一个 Cons 便是用数字0来匹配所有以0开头的列表,而第二个 Cons 则是用“通配符”和标识符,来匹配剩下的任何列表, + 同时将列表的子列表绑定到 tail 这个标识符上,以便进行进一步处理;而当前列表的头部元素,则是因为使用了“通配符”而被抛弃。 + +

+

+ 对于多元组和结构体而言,模式匹配与构造的形式颇为类似。 + 多元组的模式便是小括号包裹,逗号分隔。 + 匹配时需数量一一对应。结构体匹配则是大括号包裹,逗号分隔。 + 如果需要匹配其他模式或者自定义其他的标识符,则需要用字段名加冒号,例如 age,冒号,0, + 否则可以直接使用字段名作为标识符。匹配的时候,可以忽略部分字段,在最后用点点即可。 + +

+

+ 现在让我们来看一个用到了多元组模式匹配的例子。 + 在这里,我们尝试缝合两个列表,像拉链一样,将它们组合在一起, + 构成的是列表中元素两两组合构成的元素对的列表,以更短的列表长度为准。 + 例如例子中,两个列表分别为:1、2、3 和 a b c d。 + 那么缝合后的列表则是 1a,2b,3c。 + 于是我们便可以定义我们的函数,接受两个列表,返回一个列表。 + 在这里,我们通过构造二元组再匹配二元组嵌套模式的方式,利用模式匹配,同时匹配两个列表。 + 只有当两个列表都为非空列表,我们构建一个非空列表,首项即为两个值构成的有序对,后续则是两个列表的子列表的缝合结果。 + 如果是其他情况,那么至少有一个列表为空,结果为空,因此我们用“通配符”一起匹配了。 + 需要注意的是,正如上节课所说,模式匹配的顺序是从上到下,因此如果“通配符”在上面, + 则之后的模式永远不会被匹配到,代码也永远不能被运行。 + 好消息是,月兔可以检查出这种情况,并且提示我们。 + 这种提示仅仅是警告,而不会阻止编译,因此要注意 IDE 问题面板的内容。 + +

+

+ 最后,模式匹配不仅可以用在 match 中,还可以用在数据绑定中。 + 在本地定义中,我们可以利用模式匹配表达式,并且将对应的子结构绑定到标识符上。 + 需要注意的是,如果在这个时候进行值的比较,那么如果匹配失败,程序一样会出现运行时错误,从而导致程序中止。 + +

+

+ 接下来让我们进入枚举类型的学习。 + 一个问题是,我们应该如何表示不同情况的并集? + 例如,如何定义一个类型表示周一到周日的集合? + 如何定义一个类型定义硬币落下结果的集合,也就是正反面? + 如何定义一个类型表示整数四则运算的结果的集合,例如成功获得结果,计算溢出,除数为零等? + 答案是,枚举类型。 + 我们使用枚举类型,来定义表示不同情况的数据结构。 + 例如,我们在这里定义了一周七天的集合。下方则定义了硬币的正反面。 + +

+

+ 枚举类型的构造如下:enum、类型名称、之后用大括号包裹、分号分隔定义不同情形。 + 在换行处可以省略分号,例如下方的例子。 + 每一种可能的情形即是数据的构造器。 + 例如,这里的 Monday 就定义了星期一这个值。 + 不同的枚举类型之间可能产生冲突,因为它们可能用了相同的方式命名了一些情况。 + 例如,Repeat1 和 Repeat2 都使用了 A 和 B 来命名情形。 + 此时我们可以在构造器前方加上类型、两个冒号,加以区分。 + +

+

+ 那看到一周七天的枚举类型,有的人可能问,为什么我们要定义枚举类型呢? + 为什么我们不能直接用数字一到七来分别对应周一到周日呢? + 我们可以来对比一下以下两个函数。 + 最显著的区别在于,用枚举类型定义的函数是完全函数,而用整型定义的函数是不完全函数,这就增加了用户传入错误输入的可能性: + 用户可能传入-1,传入8,而我们没有办法通过编译器阻止这一点。 + 另外一点就在于,星期几加一有什么含义?星期几乘以几有什么含义? + 星期一乘以二为什么是星期二呢?星期二除以二为什么是星期一呢? + 枚举类型可以与现有的类型区分开,更好地实现抽象。 + +

+

+ 同时,枚举类型也可以禁止不合理数据的表示。 + 例如,我们在使用各种服务的时候,通常需要用邮箱注册或是手机注册。 + 那么用户身份的标识符即可以是手机,也可以是邮箱,这两个都是可选项,但是必须有且仅有一个。 + 如果我们用一个结构体,两个可空来表示,那么很可能出现两个字段都为空,或者两个字段都有数据这两种情况,而这不是我们想要的。 + 因此,我们可以使用枚举类型更好地限定合理数据的范畴。 + +

+

+ 枚举类型的每一种情况也可以承载数据,例如我们看到过的 Option 便是一个枚举类型。 + 此时只需在情况后用小括号包裹、逗号分隔,定义参数的类型即可。 + 例如第二个例子中,我们定义了整数运算成功的情况,此时值为整数。 + 枚举类型对应的是可区分的并集。 + 什么意思呢?首先它是一个不同情况对应的并集,例如 Some 对应的类型 T 所代表的集合,以及 None 这个单个值定义的集合; + 其次,这个集合是可以区分的,因为每个情况被情况的名称所区分。 + 即便有两种情况,每个情况所包含的数据类型相同,它们也完全不相同。 + 故此,枚举类型又被称为禾类型。 + +

+

+ 即然提到了积类型、禾类型,让我来简单介绍一下代数数据类型。 + 需要声明的是,这里的代数数据类型的介绍十分粗浅,欢迎大家参考课后的拓展阅读资料。 + +

+

+ 我们刚才提到的多元组、结构体和枚举类型被统称为代数数据类型,因为它们通过代数运算,也就是“禾”与“积”构造类型,也因为它们具有代数结构。 + 回想一下普通的数,我们有相等的判断,相乘相加的运算,以及任何数乘1都等于本身,任何数加0都等于本身等等性质。 + 类似的,在代数数据类型中也有:类型相等即意味着类型对应的集合是同构的;类型相乘即构成积类型,如多元组或结构体; + 类型相加即为禾类型,如枚举类型。零在这里是一个类型,它对应着空的类型。 + 我们可以通过一个没有定义任何情况的枚举类型,这样的类型没有任何的构造器,没有人可以构造出任何一个属于这个类型的值,因此它是空的。 + 而一在这里是一个对应只有一个元素的类型,我们称之为单值类型 Unit,它的值即是一个零元组。 + +

+

+ 我们可以来验证一下之前提到的性质:任何数乘1都等于本身,任何数加0都等于本身。 + 任何数乘1都等于本身在这里便意味着,对于任意类型 T,二元组 T、Unit 与 T 同构。 + 我们构造一组映射:从 T 到二元组 T、Unit 非常简单,只需添加零元组即可。 + 反之亦然,只需忽略零元组即可。大家可以直观地感受到它们是同构的。 + 而任何数加零都等于本身在这里则意味着,对于任意类型,我们定义一个枚举类型 PlusZero, + 其中一种情况包含类型为 T 的值,而另一种情况则包含类型为 Nothing 的值; + 这个类型与 T 同构。我们同样可以构造一组映射。 + 从 PlusZero 开始,我们用模式匹配分情况讨论。 + 如果其中包含的值类型为 T,则直接映射为 T。 + 如果类型为 Nothing,那么事实上这种情况根本不会发生, + 因为没有任何的值的类型是 Nothing,因此我们采用 abort 来定义这种情况,也就是程序会中断; + 而反之,我们则只需要将 T 用 CaseT 包裹即可。 + 还是要强调,这里的介绍非常粗浅,只是给大家一个直观的感受。有兴趣的同学可以进行拓展学习。 + +

+

+ 这里还有几个例子。我们定义的硬币的数据类型,可以看作是1+1, + 因为每一个情况:Head 和 Tail,事实上都是只有一个值的集合,因此它们每一个都和单值类型同构; + 用禾类型结合起来的 Coin 类型就是1 + 1 = 2,是一个有两个值的集合,它也与其他任何有两个值的类型同构。 + 同样的,DaysOfWeek 就是有七个值的集合,与任何有七个值的类型同构。 + 而比较有趣的是 List,我们这里以 List Int 为例。 + List[Int] 的定义是,空列表或者一个整数和一个子列表,而空列表同样与单值类型同构,因此可以写作 1 + Int 乘 List。 + 而这里的 List 是递归的,因此可以被替换为 1 + Int 乘 List。 + 之后,我们可以使用乘法结合律,获得 1 + Int 乘 1 + Int 乘 Int 乘 List。 + 继续进行替换与化简,于是我们便可以发现,整数的列表的集合, + 是一个单值集合、一个整数集合、两个整数集合的笛卡尔积乃至无数整数集合的笛卡尔积的可区分并集。而这也符合事实。 + +

+

+ 总结一下,今天的课程中,我们学习了月兔中的诸多自定义数据类型, + 包括多元组、结构体、枚举类型,同时介绍了代数数据类型的概念。 + 我们推荐大家阅读 Category Theory for Programmers 第六章。 + 我们下节课再见。 +

+ + \ No newline at end of file From 309afcb670c4df6c9a748a0360dc7c77f085f8cd Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Tue, 26 Aug 2025 18:26:03 +0800 Subject: [PATCH 11/14] feat: ssml for course4 (wip) --- course4/lec4.mbt.md | 347 +++++++++++++++++++++++--------------------- course4/script.xml | 6 +- 2 files changed, 187 insertions(+), 166 deletions(-) diff --git a/course4/lec4.mbt.md b/course4/lec4.mbt.md index 22c4f58..b62be79 100644 --- a/course4/lec4.mbt.md +++ b/course4/lec4.mbt.md @@ -10,7 +10,7 @@ headingDivider: 1 ## 多元组,结构体与枚举类型 -### Hongbo Zhang +### 月兔公开课课程组 # 基础数据类型:多元组与结构体 @@ -21,6 +21,7 @@ headingDivider: 1 - 类型:`(<表达式类型>, <表达式类型>, ...)` - 例如: - 身份信息:`("Bob", 2023, 10, 24): (String, Int, Int, Int)` + - 零元组:`() : Unit` - 成员访问: - `<多元组>.<索引>`:`(2023, 10, 24).0 == 2023` - 列表:**任意**长度的**相同**类型数据的集合 @@ -34,7 +35,7 @@ headingDivider: 1 - 集合的笛卡尔积,又称积类型 - 例:扑克牌的所有花色:{ ♥️ ♦️ ♠️ ♣️ } $\times \{ n \in \mathbb{N} | 1 \leq n \leq 52 \}$ -![](../pics/product.drawio.png) + ![](../pics/product.drawio.png) # 结构体 @@ -61,120 +62,132 @@ headingDivider: 1 # 结构体的访问与更新 - 访问结构体时,我们通过`<结构体>.<字段名>` -```moonbit -let old_info : PersonalInfo = { name : "Moonbit", age : 1, } -let a : Int = old_info.age // 1 -``` + ```moonbit + let old_info : PersonalInfo = { name : "Moonbit", age : 1, } + let a : Int = old_info.age // 1 + ``` - 更新原有的结构体时,我们可以复用原有的部分,如 -```moonbit -let new_info = { .. old_info, age : 2, } -let other_info = { .. old_info, name : "Hello", } -``` - -# 多元组与结构体的关系 - -- 结构体与相同类型集合构成的多元组**同构** - - 集合`A`与`B`之间存在一一映射的关系 - - 存在一对映射`f : (A) -> B`与`g : (B) -> A`使得 - - `g(f(a)) == a` - - `f(g(b)) == b` -- 例:`struct PersonalInfo { name: String; age: Int }`与`(String, Int)`同构 - -```moonbit -fn f(info : PersonalInfo) -> (String, Int) { (info.name, info.age) } -fn g(pair : (String, Int)) -> PersonalInfo { { name: pair.0, age: pair.1, }} -``` - -![](../pics/isomorphism.drawio.png) + ```moonbit + let new_info = { .. old_info, age : 2, } + let other_info = { .. old_info, name : "Hello", } + ``` # 多元组与结构体的关系 - 多元组是 structural:只要结构相同(字段类型一一对应)就类型兼容 -```moonbit -fn accept_tuple(tuple : (Int, String)) -> Bool { - true -} -let accepted : Bool = accept_tuple((1, "Yes")) -``` + + ```moonbit + fn accept_tuple(tuple : (Int, String)) -> Bool { + true + } + let accepted : Bool = accept_tuple((1, "Yes")) + ``` - 结构体是 nominal:只有类型名相同(字段顺序可以打乱)才类型兼容 -```moonbit -struct A { val : Int ; other : Int } -struct B { val : Int ; other : Int } -fn accept_a(a : A) -> Bool { - true -} -let not_accepted : Bool = accept_a(({ val : 1, other : 2 } : B)) // DO NOT COMPILE -let accepted : Bool = accept_a(({other : 2, val : 1} : A)) -``` + ```moonbit + struct A { val : Int ; other : Int } + struct B { val : Int ; other : Int } + fn accept_a(a : A) -> Bool { + true + } + let not_accepted : Bool = accept_a(({ val : 1, other : 2 } : B)) // DO NOT COMPILE + let accepted : Bool = accept_a(({other : 2, val : 1} : A)) + ``` + +# 元组结构体 + +- 元组结构体: + - 命名的元组 + - 字段不命名的结构体 +- 元组结构体的定义:`struct <结构体名称>(<类型>, ...)` +- 通过索引访问:`<元组结构体>.<索引>` +- 例子: + ``` + struct IntPair(Int, Int) + let info : IntPair = IntPair(0, 1) + inspect(info.0, content="0") + ``` +- 元组结构体是 nominal:类型名相同,且字段类型一一对应则类型兼容 # 模式匹配 - 回顾:我们可以通过模式匹配查看列表和Option的结构 -```moonbit -fn head_opt(list : List[Int]) -> Option[Int] { - match list { - Nil => None - Cons(head, _tail) => Some(head) + ```moonbit + fn head_opt(list : List[Int]) -> Option[Int] { + match list { + Nil => None + Cons(head, _tail) => Some(head) + } } -} -``` + ``` -```moonbit -fn get_or_else(option_int : Option[Int], default : Int) -> Int { - match option_int { - None => default - Some(value) => value + ```moonbit + fn get_or_else(option_int : Option[Int], default : Int) -> Int { + match option_int { + None => default + Some(value) => value + } } -} -``` + ``` # 模式匹配 - 模式匹配可以匹配值(逻辑值、数字、字符、字符串)或者构造器 -```moonbit -fn is_zero(i : Int) -> Bool { - match i { - 0 => true - 1 | 2 | 3 => false - _ => false + ```moonbit + fn is_zero(i : Int) -> Bool { + match i { + 0 => true + 1 | 2 | 3 => false + _ => false + } } -} -``` + ``` - 构造器中可以嵌套模式进行匹配,或定义标识符绑定对应结构 -```moonbit -fn contains_zero(l : List[Int]) -> Bool { - match l { - Nil => false - Cons(0, _) => true - Cons(_, tl) => contains_zero(tl) + ```moonbit + fn contains_zero(l : List[Int]) -> Bool { + match l { + Nil => false + Cons(0, _) => true + Cons(_, tl) => contains_zero(tl) + } } -} -``` + ``` -# 多元组和结构体的模式匹配 +# 多元组、结构体、元组结构体的模式匹配 - 多元组模式匹配需数量一一对应 -```moonbit -fn first(pair : (Int, Int)) -> Int { - match pair { - (first, second) => first + ```moonbit + fn first(pair : (Int, Int)) -> Int { + match pair { + (first, second) => first + } } -} -``` + ``` + +- 元组结构体模式匹配和元组类似 + ```moonbit + fn second(pair : Pair) -> Int { + match pair { + Pair(first, second) => second + } + } + ``` + +# 多元组、结构体、元组结构体的模式匹配 - 结构体模式匹配可以匹配部分字段;可以不用另外命名标识符 -```moonbit -fn baby_name(info : PersonalInfo) -> String? { - match info { - { age: 0, .. } => None - { name, age } => Some(name) + + ```moonbit + fn baby_name(info : PersonalInfo) -> String? { + match info { + { age: 0, .. } => None + { name, age } => Some(name) + } } -} -``` + ``` # 缝合列表 @@ -214,6 +227,7 @@ fn zip(l1 : List[Int], l2 : List[Char]) -> List[(Int, Char)] { 此时会根据模式将表达式的值的子结构绑定到定义的标识符上,如: - `let (first, second) = (1, 2) // first == 1, second == 2` +- `let Pair(first, second) = Pair(1, 2) // first == 1, second == 2` - `let Cons(1, x) = List::Cons(1, Nil) // x == Nil` - `let Cons(2, x) = List::Cons(1, Nil) // 运行时错误,程序中止` @@ -252,106 +266,113 @@ enum DaysOfWeek { ``` - 每一种可能的情况即是构造器 -```moonbit -let monday : DaysOfWeek = Monday -let tuesday : DaysOfWeek = Tuesday -``` + ```moonbit + let monday : DaysOfWeek = Monday + let tuesday : DaysOfWeek = Tuesday + ``` - 枚举类型定义可能重复,需要加上`<类型>::`加以区分 -```moonbit -enum Repeat1 { A; B } -enum Repeat2 { A; B } -let x : Repeat1 = Repeat1::A -``` + ```moonbit + enum Repeat1 { A; B } + enum Repeat2 { A; B } + let x : Repeat1 = Repeat1::A + ``` # 枚举类型的意义 - 对比一下两个函数,枚举类型可以与现有类型区分开,更好地实现抽象 -```moonbit -fn tomorrow(today : Int) -> Int -fn tomorrow(today : DaysOfWeek) -> DaysOfWeek -let tuesday = 1 * 2 // 这是周二吗? -``` + ```moonbit + fn tomorrow(today : Int) -> Int + fn tomorrow(today : DaysOfWeek) -> DaysOfWeek + let tuesday = 1 * 2 // 这是周二吗? + ``` - 禁止不合理数据的表示 -```moonbit -struct UserId { email : Option[String]; telephone : Option[Int] } -enum UserId { - Email(String) - Telephone(Int) -} -``` + ```moonbit + struct UserId { email : Option[String]; telephone : Option[Int] } + enum UserId { + Email(String) + Telephone(Int) + } + ``` # 枚举类型 - 枚举类型的每一种情况也可以承载数据,如 -```moonbit -enum Option[T] { + ```moonbit + enum Option[T] { Some(T) None -} -``` + } + ``` -```moonbit -enum ComputeResult { + ```moonbit + enum ComputeResult { Success(Int) Overflow DivideByZero -} -``` + } + ``` + +# is 表达式 -- 此时枚举类型对应可区分的并集,又称和类型 - - $\textit{Option}(T) = \textit{Some}(T) \sqcup \{ \textit{None} \}$ - -# 代数数据类型 - -# 代数数据类型 - -我们将多元组、结构体、枚举类型等称为代数数据类型,它们具有代数结构 -- 类型相等:同构 -- 类型相乘:积类型 -- 类型相加:和类型 -- 加法的单位元:`enum Nothing {}` -- 乘法的单位元:`(): Unit` - -# 代数数据类型 - -- $1 \times n = n$ - - 对于任意类型`T`,`(T, Unit)`与`T`同构 - ```moonbit - fn[T] f1(t : T) -> (T, Unit) { (t, ()) } - fn[T] g1(pair : (T, Unit)) -> T { pair.0 } - ``` -- $0 + n = n$ - - 对于任意类型 `T`,`enum PlusZero[T] { CaseT(T); CaseZero(Nothing) }` 与 `T` 同构 - ```moonbit - fn[T] f2(t : PlusZero) -> T { - match t { - CaseT(t) => t - CaseZero(_) => abort("对应集合为空,即不存在这样的值") - } +- is 表达式用于测试某个值是否符合某个模式 + ```moonbit expr + let opt : Option[Int] = Some(10) + inspect(opt is None, content="false") + ``` +- 同时,is 表达式也会对模式进行匹配 + + ```moonbit expr + fn get_or_else2(option_int : Option[Int], default : Int) -> Int { + if option_int is Some(value) { + value + } else { + default } + } + ``` + +# 错误处理 + +# 错误类型 + +- 月兔中的错误有一个统一的类型 `Error` +- `Error` 类型无法直接构造,必须使用 `suberror` 定义 `Error` 的子类型 +- 定义错误类型: + - 无负载数据的错误类型:`suberror <错误类型1>` + - 有单一负载的错误类型:`suberror <错误类型2> <负载类型>` + - 类似枚举的错误类型:`suberror <错误类型3> { <情形1>; <情形2>; ... }` +- 所有的错误类型都可以被自动提升为 `Error` 类型 + +# 错误的构造 + +- 每一种定义错误的方式 +- 定义错误类型: + - `suberror <错误类型1>`,例如 `suberror E1` + - `suberror <错误类型2> <负载类型>`,例如 `suberror E2 Int` + - `suberror <错误类型3> { <情形1>; <情形2>; ... }` + 例如 `suberror E3 { Case1; Case2(Int); }` +- 定义错误的值: + - `<错误类型1>`,例如 `E1 : E1` + - `<错误类型2>(<负载类型的值>)`,例如 `E2(10) : E2` + - `<情形>`,例如 `Case1 : E3` 或 `Case2(10) : E3` +- 所有的错误同时也是 `Error` 类型的值:`E1 : Error` + +# 函数中抛出错误 + +- 错误类型和错误的值可以当作普通的类型和值使用 +- 关键字 `raise` 用于抛出错误:`raise <错误表达式>` +- 函数 + + ```moonbit + + ``` + +# 处理错误 - fn[T] g2(t : T) -> PlusZero { CaseT(t) } - ``` - -# 代数数据类型 - -- `enum Coins { Head; Tail }` - - $\texttt{Coins} = 1 + 1 = 2$ -- `enum DaysOfWeek { Monday; Tuesday; ...; }` - - $\texttt{DaysOfWeek} = 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7$ -- `List` 的定义(以 `List[Int]` 为例): -$$ -\begin{array}{r@{}l} -\texttt{enum} \;\; \texttt{List} & = \texttt{Nil} + \texttt{Int} \times \texttt{List} \\ -& = \texttt{1} + \texttt{Int} \times \texttt{List} \\ -& = \texttt{1} + \texttt{Int} \times (\texttt{1} + \texttt{Int} \times \texttt{List} ) \\ -& = \texttt{1} + \texttt{Int} \times \texttt{1} + \texttt{Int} \times \texttt{Int} \times \texttt{List} \\ -& = \texttt{1} + \texttt{Int} + \texttt{Int} \times \texttt{Int} + \texttt{Int} \times \texttt{Int} \times \texttt{Int} + ... -\end{array} -$$ +# 错误多态 # 总结 diff --git a/course4/script.xml b/course4/script.xml index b00531f..02530ac 100644 --- a/course4/script.xml +++ b/course4/script.xml @@ -41,13 +41,13 @@

- 结构体的定义为 struct、结构体名称,大括号,字段列表;每个字段都有名称禾类型。 + 结构体的定义为 struct、结构体名称,大括号,字段列表;每个字段都有名称和类型。 字段之间用分号分隔,在换行的情况下可以省略。 定义结构体的值时候,是用大括号包裹,用字段名、冒号、值,的语法,给每一个字段赋值。 例如这里的 info,就给 name age 分别赋值为 MoonBit 和 1. - 每个值后都有逗号。如果最后一个逗号后面直接跟着大括号未有换行,则最后一个逗号可以省略。这里的定义不在意顺序。 + 每个值后都有逗号。最后一个逗号可以省略。这里的定义不在意顺序。 例如,先赋值 age,再赋值 name ,依然是 PersonalInfo 结构体的值。 - 如果两个结构体碰巧字段名称禾类型完全相同,只定义了值是无法区分的; + 如果两个结构体碰巧字段名称和类型完全相同,只定义了值是无法区分的; 此时我们可以在结构体的值的后面加上类型声明,例如冒号 A 来进行区分。

From 0ecf573efdab893ef0d04eec20ac4b6846e7c69d Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Fri, 12 Sep 2025 13:19:59 +0800 Subject: [PATCH 12/14] feat: ssml update for course 4. --- course4/script.xml | 219 ++++++++++++++++++++++++++++++++------------- 1 file changed, 156 insertions(+), 63 deletions(-) diff --git a/course4/script.xml b/course4/script.xml index 02530ac..ac896d0 100644 --- a/course4/script.xml +++ b/course4/script.xml @@ -2,7 +2,7 @@

大家好,欢迎来到由IDEA研究院基础软件中心为大家带来的现代编程思想公开课。 - 今天是第四节课,主题是多元组,结构体与枚举类型。 + 今天是第四节课,主题是多元组、结构体、枚举与错误类型。 一言以蔽之,今天介绍如何在月兔中自定义数据结构。

@@ -14,7 +14,6 @@ 多元组是固定长度的不同类型数据的组合。 相比较之下,列表则是任意长度的相同类型的数据的集合。 例如,下方字符的列表长度不定,但是存储的值必须都是字符类型。 - 第三课没有提到 Cons 为什么要叫 Cons Cons 是 Construct 的缩写,在这里补充一下。 多元组的定义通过括号包裹,逗号分隔的表达式组成, 类型也是类似的,通过括号包裹,逗号分隔的类型组成, 例如我们这里看到的身份信息的定义,Bob、2023、10、24 这个多元组的类型为 String、Int、Int、Int 四元组。 @@ -26,17 +25,17 @@ 两个集合的笛卡尔积,便是一个集合,其中所有的元素便是原来两个集合元素构成的有序对。 例如这里扑克牌的花色的集合与1到52的数字构成的笛卡尔积,便构成了所有花色与数字的有序对。 而多元组,不仅仅是两个集合的笛卡尔积,是多个集合的笛卡尔积,因此更确切的说法是构成的有序元素组。 - 也因此,多元组又被称为积类型。那么大家可能会好奇,有积类型,那么有禾类型吗? - 有积类型和禾类型,那有零有一吗?我们会在稍后的课程中为大家介绍。

元组的问题在于,难以理解其所代表的数据。 - 举例来说,String Int,究竟代表一个人的姓名和年龄?还是代表一个人的姓名和手机号?亦或是地址和邮编? + 举例来说,String Int,究竟代表一个人的姓名和年龄?还是地址和邮编? + 三个 Double 组成的三元组,代表的是三维空间中一个点的三个坐标?还是一个三维向量的三个分量? 结构体允许我们赋予名称,即是赋予名称给整个类型,也是赋予名称给每个字段,例如: PersonalInfo 结构体代表个人信息, name 代表姓名,age 代表年龄。 - ContactInfo 结构体代表联系方式,telephone 字段代表电话号码。 AddressInfo 结构体代表地址信息,postal 字段代表邮编。 + 即便字段的名称和类型完全相同,我们也能通过结构体类型的名称来区分不同的结构体。 + 例如 Vector 3 类型和 Point 3 类型,它们都拥有 x、y、z 三个类型为 Double 的字段,但仍然是不同的类型。 通过名称,我们能明确数据的信息以及对应字段的含义。

@@ -44,7 +43,7 @@ 结构体的定义为 struct、结构体名称,大括号,字段列表;每个字段都有名称和类型。 字段之间用分号分隔,在换行的情况下可以省略。 定义结构体的值时候,是用大括号包裹,用字段名、冒号、值,的语法,给每一个字段赋值。 - 例如这里的 info,就给 name age 分别赋值为 MoonBit 和 1. + 例如这里的 info,就给 name age 分别赋值为 MoonBit 和 3. 每个值后都有逗号。最后一个逗号可以省略。这里的定义不在意顺序。 例如,先赋值 age,再赋值 name ,依然是 PersonalInfo 结构体的值。 如果两个结构体碰巧字段名称和类型完全相同,只定义了值是无法区分的; @@ -62,17 +61,7 @@

大家可能会发现,多元组和结构体似乎非常相像。 - 事实上,一个结构体与相同类型集合构成的多元组是同构的关系。 - 同构,也就是两个集合之间存在着一一映射的关系。 - 如果在集合 A 和 B 之间存在一对映射关系 f从 A 到 B,和 g 从 B 到 A, - 并且对于任意的集合 A 中的 a 或集合 B 中的 b,有 g f a 等于 a,f g b 等于 b。就是如下图所示,那么这两个集合就是同构的。 - 举例来说,PersonalInfo 与二元组 String Int 就是同构的,因为我们可以构筑如下的一对映射: - 函数 f 从 PersonalInfo 映射到 String Int 二元组,函数 g 从 String Int 二元组映射到 PersonalInfo. - 两个函数在映射过程中都没有丢失任何的信息。大家可以自行验证上面的性质。 - 同理,PersonalInfo 与 Int String 二元组也是同构的,大家可以自己尝试验证。 - -

-

+ 它们都可以存储不同类型的数据。 多元组和结构体的区别则在于,多元组是 structural,也就是只要结构相同,即字段类型一一对应,那么类型就是兼容的。 例如此处,函数成功接受了一个多元组。 而结构体不同。结构体是 nominal,也就是只有类型名相同,类型才是兼容的(而内部定义的顺序可以打乱)。 @@ -80,12 +69,34 @@ 而第二个例子中,虽然结构的顺序是不同的,但是因为类型相同,函数可以顺利接受。

+

+ 我们已经知道了,多元组的类型没有名称,字段也没有名称;而结构体的类型有名称,字段也有名称。 + 那么,有没有字段完全相同的类型呢? + 比如,对于先前提到的 Vector 3 和 Point 3 类型,它们包含相同的字段,同时,它们是不同的类型。 + 或者,有没有类型名称和字段的顺序,比字段名称更有代表性的类型呢? + 比如,一个整数对,它的两个字段分别为 first 和 second,这两个名称显然是冗余的。 + 一个区间的两个字段分别为 start 和 end,这也是不言自明的。 + +

+

+ 在月兔中,有一种特殊的结构体,称为元组结构体。刚好用来定义上述类型。 + 元组结构体结合了元组和结构体的特点,它的定义和结构体一样,会引入一个新的类型名称;而字段和元组一样,没有名称且顺序固定。 + 元组结构体的定义方式也兼具元组和结构体的特点,定义为:struct、元组结构体名称、用括号包裹、逗号分隔的类型。 + 元组结构体的值通过元组结构体的名称加上括号包裹、逗号分隔的表达式来定义。 + 这个形式和函数应用表达式、以及我们即将学习到的枚举类型的构造形式是类似的。 + 和元组一样,元组结构体通过索引来访问字段。 + 例如,我们可以定义一个元组结构体来表示一个 Int 对: + 然后通过 pair 点 0 和 pair 点 1 来分别访问两个整数字段。 + 元组结构体和结构体一样,也是 nominal。也就是说,只有类型名相同、且字段类型一一对应时,两个元组结构体才是类型兼容的。 + +

让我们接下来梳理一下模式匹配,来看看多元组和结构体除了通过下标和字段名访问以外的另一种方式。 我们回顾一下,之前我们用模式匹配查看了列表和 Option 的结构。 例如,Nil 和 Cons 来匹配列表,None 和 Some 来匹配 Option。 - 事实上,模式匹配可以匹配值(逻辑值、数字、字符、字符串)以及构造器。 - 上面的例子中,我们便是匹配了数字。注意到,如果是匹配值,我们还可以用竖线来分割模式,同时匹配多种可能的值。 + 模式匹配可以匹配值和构造器,值包括逻辑值、数字、字符、字符串等。构造器包括各种自定义类型的构造器,例如 Cons 和 Nil。 + 上面的例子中,我们便是匹配了数字。 + 我们还可以用竖线来分割模式,同时匹配多种可能的值。 最后我们则用下划线这一“通配符”,匹配所有的剩余的情况。 在构造器中,我们也可以嵌套模式进行匹配,或者用标识符绑定对应结构。 例如,第一个 Cons 便是用数字0来匹配所有以0开头的列表,而第二个 Cons 则是用“通配符”和标识符,来匹配剩下的任何列表, @@ -93,9 +104,13 @@

- 对于多元组和结构体而言,模式匹配与构造的形式颇为类似。 - 多元组的模式便是小括号包裹,逗号分隔。 - 匹配时需数量一一对应。结构体匹配则是大括号包裹,逗号分隔。 + 对于多元组、结构体和元组结构体而言,模式匹配与构造的形式颇为类似。 + 多元组的模式便是小括号包裹,逗号分隔。匹配时需数量一一对应。 + 元组结构体的模式匹配还需要带上其类型名称。同样的,字段的数量需要和类型的定义相对应。 + +

+

+ 结构体匹配则是大括号包裹,逗号分隔。 如果需要匹配其他模式或者自定义其他的标识符,则需要用字段名加冒号,例如 age,冒号,0, 否则可以直接使用字段名作为标识符。匹配的时候,可以忽略部分字段,在最后用点点即可。 @@ -116,12 +131,6 @@ 这种提示仅仅是警告,而不会阻止编译,因此要注意 IDE 问题面板的内容。

-

- 最后,模式匹配不仅可以用在 match 中,还可以用在数据绑定中。 - 在本地定义中,我们可以利用模式匹配表达式,并且将对应的子结构绑定到标识符上。 - 需要注意的是,如果在这个时候进行值的比较,那么如果匹配失败,程序一样会出现运行时错误,从而导致程序中止。 - -

接下来让我们进入枚举类型的学习。 一个问题是,我们应该如何表示不同情况的并集? @@ -170,56 +179,140 @@ 什么意思呢?首先它是一个不同情况对应的并集,例如 Some 对应的类型 T 所代表的集合,以及 None 这个单个值定义的集合; 其次,这个集合是可以区分的,因为每个情况被情况的名称所区分。 即便有两种情况,每个情况所包含的数据类型相同,它们也完全不相同。 - 故此,枚举类型又被称为禾类型。

- 即然提到了积类型、禾类型,让我来简单介绍一下代数数据类型。 - 需要声明的是,这里的代数数据类型的介绍十分粗浅,欢迎大家参考课后的拓展阅读资料。 + 在使用枚举类型时,除了模式匹配,也可以用 is 表达式来判断某个值是否是某个枚举类型的某个情形。 + 例如例子中的 opt 是一个 Some,因此 opt is None 会被求值为 false。 + 事实上,is 表达式可以判断任意的值是否符合某种模式。 + 前面提到,整数字面量作为一个值,同时也是一个模式,因此可以用在 is 表达式中。 + 而 Pair 是一个 元组结构体,也能用作模式匹配,所以也可以用在 is 表达式中。 + 同时,is 表达式也兼具模式匹配的标识符绑定功能。 + 在下面的例子中,我们对 option int 这个变量使用 is Some 进行判断。如果判断为真,则 option int 的值会被绑定到 value 上。 + +

+

+ 当我们确定某个表达式一定就是某个模式时,也可以使用本地定义中的模式匹配来取出承载数据。 + 在本地定义中,我们可以利用模式匹配表达式,并且将对应的子结构绑定到标识符上。 + 需要注意的是,如果此时匹配失败,程序会出现运行时错误,从而导致程序中止。 + 最后一个例子定义了 unsafe get 函数,利用本地定义的模式匹配,从 Option Int 中直接取出其承载的整数,如果参数是 none 程序就直接中止。 + +

+

+ 接下来让我们来学习最后一个自定义数据类型:错误类型。 + +

+

+ 理想的情况下,程序总是能正确地运行,而程序的输入也都是符合要求的。 + 但是,现实世界充满了有问题的代码和不合规的程序输入。 + 例如,当用户的输入不符合预期时,当试图访问的文件不存在时,当传输数据过程中网络突然中断时,程序都可能出现问题。 + 程序阻止不了错误的存在,但是当错误发生时,要尽可能减小错误所带来的损失。 + 那么,这些错误应当怎么在程序中表示、以及如何应对呢? + +

+

+ 月兔使用错误类型和错误处理机制来应对上述情况。 + 月兔中的错误有一个统一的类型 Error。所有错误都是 Error 类型的值。 + 但是,Error 类型是不能直接构造的,必须使用 sub error 定义特定的错误类型。 + 定义错误类型的方式有三种: + 第一种,也是最简单的错误类型:无负载数据的错误类型。 + 这种错误类型只需使用 sub error 加上类型名称即可。 + 第二种,有单一负载的错误类型。 + 这种错误类型需要使用 sub error 加上类型名称和负载类型。 + 第三种是类似枚举的错误类型。 + 这种错误类型的定义方法与枚举类型类似,用大括号包裹,分号分隔不同情形,每一种情形都可以带上负载类型。 + 由于使用 sub error 定义的错误类型都是 Error 的子类型,因此所有的错误类型都可以被自动提升为 Error 类型。 + +

+

+ 如何构造错误类型的值呢? + 对于上述三种错误类型,错误值的构造方法各不相同: + 对于无负载数据的错误类型,我们只需使用错误类型的名称即可构造。例如对于 E1 这个错误类型,直接使用 E1 就能构造出一个该类型的值。 + 对于有单一负载的错误类型,我们需要使用错误类型的名称和用括号包裹的负载值来构造。例如对于 E2 这个负载为整数类型的错误类型,构造一个值的方式是 E2 加上括号包裹的负载值,在例子中是整数 10。 + 对于类似枚举的错误类型,构造方法也和枚举类型类似,使用某个情形的构造器即可构造对应错误类型的错误值,当该情形包含了负载值时,需要加上用括号包裹、逗号分隔的负载值表达式。 + 例如此处,case 1 和 case2 10 都是错误类型 E3 的值。 + 由于所有错误类型都是 Error 类型的子类型,所有上述值同时也是 Error 类型的值。 + +

+

+ 错误类型和错误的值可以当作普通的类型和值来使用。 + 不同之处在于,错误可以在表达式化简过程中被抛出。 + 抛出错误的表达式为:raise 加上错误值的表达式。 + 在函数的化简过程中,如果抛出了错误,那么整个函数的化简过程将会中止,并且错误会被传递到调用该函数的地方。 + 在函数签名中,需要使用 raise 关键字来指明该函数可能抛出的错误类型。 + 我们再次使用除法函数作为例子,但这次的除法函数和之前略有不同。 + 在例子中,函数 div 可能会抛出 Div Error 类型的错误,因此需要在函数的签名中使用 raise Div Error 来指明。 + 当调用函数的参数 y 为 0 时,抛出错误,错误类型是有单一字符串负载值的 Div Error 类型,因此错误需要包含一个字符串作为负载。 + +

+

+ 由于所有错误类型都是 Error 类型的子类型,所以在不关心错误的具体类型时,也可以使用 Error 来表示抛出错误的类型。 + 当 Error 直接出现在函数签名中,可以直接省略 Error,只标注 raise 关键字即可。 + 对于一定不会抛出错误的函数,可以在函数签名中使用 no raise 关键字来指明。 + +

+

+ 定义了错误类型和抛出错误之后,更关键的步骤,是处理错误。 + +

+

+ 最常见的错误处理方式是捕获错误。 + 当计算中出现一个可能抛出错误的表达式时,可以使用 try-catch 来捕获并进行处理。 + try-catch 表达式的形式为:try,可能抛出错误的表达式0,catch,大括号包裹的处理各种错误的 catch 部分;no raise;大括号包裹的正常处理的 no raise 部分。 + 其中 catch 部分和 no raise 部分都类似于模式匹配。 + 当表达式0 抛出错误时,catch 部分可以匹配不同类型的错误模式;当表达式0 没有抛出错误,化简得到了正常的值,则 no raise 部分会将该值匹配到普通模式。 + 无论是进入哪个分支,都会有一个最终的表达式,作为整个 try catch 表达式的结果。 + 另外,当 no raise 部分没有任何处理过程时,也就是,表达式3 与模式3 相同时,no raise 关键字和 no raise 部分可以省略。 + +

+

+ 要对 try-catch 表达式进行化简,分为下面几个步骤: + 首先,化简 可能抛出错误的表达式。 + 如果这个表达式抛出了错误,那么会进入 catch 部分进行处理。 + 如果没有,则进入 no raise 部分进行处理。 + catch 部分会使用模式匹配来处理错误信息; + no raise 部分也会使用模式匹配来处理正常结果。 + 最终得到的表达式,即为整个 try-catch 表达式的化简结果。 + +

+

+ 让我们来看一个例子。 + 对于例子中的 try-catch 表达式,首先化简 div 1 0 这个表达式。 + 这是一个函数应用,它的化简过程是将参数 1 和 0 传递给函数 div。替换 div 定义中的 x 和 y。 + 得到了 raise Div Error "division by zero" 这个被抛出的错误。 + 接下来,由于抛出了错误,进入 catch 部分进行处理。Div Error 这个错误类型只有一种情况,匹配到这个情况后,胖箭头右侧的表达式 0 已经是一个值,不需要化简。因此整个 try-catch 表达式的化简结果就是 0。

- 我们刚才提到的多元组、结构体和枚举类型被统称为代数数据类型,因为它们通过代数运算,也就是“禾”与“积”构造类型,也因为它们具有代数结构。 - 回想一下普通的数,我们有相等的判断,相乘相加的运算,以及任何数乘1都等于本身,任何数加0都等于本身等等性质。 - 类似的,在代数数据类型中也有:类型相等即意味着类型对应的集合是同构的;类型相乘即构成积类型,如多元组或结构体; - 类型相加即为禾类型,如枚举类型。零在这里是一个类型,它对应着空的类型。 - 我们可以通过一个没有定义任何情况的枚举类型,这样的类型没有任何的构造器,没有人可以构造出任何一个属于这个类型的值,因此它是空的。 - 而一在这里是一个对应只有一个元素的类型,我们称之为单值类型 Unit,它的值即是一个零元组。 + 另外,try-catch 表达式也可以捕获多个错误类型。 + 在例子中,函数 f1 和 f2 分别会抛出 E1 和 E2 两种类型的错误。 + 相应的,try-catch 表达式的 catch 部分也匹配了这两种错误类型。 + 要注意的是,当 try-catch 捕获多个错误类型时,实际上是在处理 Error 类型的错误。 + 所以,需要使用通配符下划线或者一定能捕获所有可能错误的标识符来匹配剩余的错误,以避免遗漏。

- 我们可以来验证一下之前提到的性质:任何数乘1都等于本身,任何数加0都等于本身。 - 任何数乘1都等于本身在这里便意味着,对于任意类型 T,二元组 T、Unit 与 T 同构。 - 我们构造一组映射:从 T 到二元组 T、Unit 非常简单,只需添加零元组即可。 - 反之亦然,只需忽略零元组即可。大家可以直观地感受到它们是同构的。 - 而任何数加零都等于本身在这里则意味着,对于任意类型,我们定义一个枚举类型 PlusZero, - 其中一种情况包含类型为 T 的值,而另一种情况则包含类型为 Nothing 的值; - 这个类型与 T 同构。我们同样可以构造一组映射。 - 从 PlusZero 开始,我们用模式匹配分情况讨论。 - 如果其中包含的值类型为 T,则直接映射为 T。 - 如果类型为 Nothing,那么事实上这种情况根本不会发生, - 因为没有任何的值的类型是 Nothing,因此我们采用 abort 来定义这种情况,也就是程序会中断; - 而反之,我们则只需要将 T 用 CaseT 包裹即可。 - 还是要强调,这里的介绍非常粗浅,只是给大家一个直观的感受。有兴趣的同学可以进行拓展学习。 + 除了捕获错误外,还有几种常见的错误处理方式。 + 第一种方式是重新抛出。 + 很多时候,我们不知道该如何处理某个错误,或是这个错误不应当在某个函数中处理,可以直接使用会抛出错误的表达式。此时,若该表达式抛出了错误,那么这个错误会被重新抛出。 + 例如这里,函数 div reraise 函数直接调用了可能抛出错误的 div 函数,因此也可能抛出错误。所以 div reraise 函数的签名也需要指明 raise Div Error。 + 第二种方式是直接崩溃。 + 有时我们能确信某个表达式一定不会抛出错误,或者,该错误的发生,表明程序内发生了严重的问题,此时让程序崩溃,而不是带着错误运行下去,是一个更好的选择。在月兔中,可以使用 try 加上一个感叹号的语法来使用某个会抛出错误的表达式,以此来达到当错误发生时直接崩溃的目的。 + 例如这里的 div panic 函数会在 y 为 0 时导致程序崩溃。注意,这种情况下,div panic 函数的签名不再需要标注 raise。因为这个函数并不会抛出错误。 + 最后一种方式是将可能带有错误的值转化为 Result,让我们来详细看看这种处理方式。

- 这里还有几个例子。我们定义的硬币的数据类型,可以看作是1+1, - 因为每一个情况:Head 和 Tail,事实上都是只有一个值的集合,因此它们每一个都和单值类型同构; - 用禾类型结合起来的 Coin 类型就是1 + 1 = 2,是一个有两个值的集合,它也与其他任何有两个值的类型同构。 - 同样的,DaysOfWeek 就是有七个值的集合,与任何有七个值的类型同构。 - 而比较有趣的是 List,我们这里以 List Int 为例。 - List[Int] 的定义是,空列表或者一个整数和一个子列表,而空列表同样与单值类型同构,因此可以写作 1 + Int 乘 List。 - 而这里的 List 是递归的,因此可以被替换为 1 + Int 乘 List。 - 之后,我们可以使用乘法结合律,获得 1 + Int 乘 1 + Int 乘 Int 乘 List。 - 继续进行替换与化简,于是我们便可以发现,整数的列表的集合, - 是一个单值集合、一个整数集合、两个整数集合的笛卡尔积乃至无数整数集合的笛卡尔积的可区分并集。而这也符合事实。 + 所谓 Result,其实就是一种枚举类型,它有两种可能的情形。OK 和 Error。OK 的负载值是一个类型 R,Error 的负载值是另一个类型 E。 + 对于一个类型为 R、可能抛出类型为 E 错误类型的表达式,使用 try 加上一个问号可以将这个表达式的值转化为一个 Result R E 类型的值。 + 如果表达式化简得到了正常结果,这个值就会转化成 OK。例如 9 除以 3 经过 try 问号转换后就得到了 OK 3. + 如果表达式抛出了错误,那么错误会转化成一个 Error。例如 3 除以 0,经过 try 问号转换后就得到了 Error Div Error,division by zero 这个值。

总结一下,今天的课程中,我们学习了月兔中的诸多自定义数据类型, - 包括多元组、结构体、枚举类型,同时介绍了代数数据类型的概念。 - 我们推荐大家阅读 Category Theory for Programmers 第六章。 + 包括多元组、结构体、枚举类型和错误类型。 + 并学习了每一种类型的模式匹配、以及错误处理方式。 我们下节课再见。

From 2039b8505fb114360b6bc50bd56f1722639575f4 Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Fri, 12 Sep 2025 13:20:11 +0800 Subject: [PATCH 13/14] feat: slides update for course 4. --- course4/lec4.mbt.md | 240 ++++++++++++++++++++++++++++++++++++-------- course4/lec4.pdf | Bin 520389 -> 569708 bytes 2 files changed, 196 insertions(+), 44 deletions(-) diff --git a/course4/lec4.mbt.md b/course4/lec4.mbt.md index b62be79..43a7a6d 100644 --- a/course4/lec4.mbt.md +++ b/course4/lec4.mbt.md @@ -8,11 +8,11 @@ headingDivider: 1 # 现代编程思想 -## 多元组,结构体与枚举类型 +## 多元组,结构体、枚举与错误类型 ### 月兔公开课课程组 -# 基础数据类型:多元组与结构体 +# 基础数据类型:多元组、结构体、元组结构体 # 回顾:多元组 @@ -27,12 +27,11 @@ headingDivider: 1 - 列表:**任意**长度的**相同**类型数据的集合 - 例如: - 字符的序列:`Cons('H', Cons('i', Cons('!', Nil)))` - - `Cons`:`construct`的缩写 # 笛卡尔积 - 一个多元组类型的元素即是每个组成类型的元素构成的有序元素组 - - 集合的笛卡尔积,又称积类型 + - 集合的笛卡尔积 - 例:扑克牌的所有花色:{ ♥️ ♦️ ♠️ ♣️ } $\times \{ n \in \mathbb{N} | 1 \leq n \leq 52 \}$ ![](../pics/product.drawio.png) @@ -40,11 +39,13 @@ headingDivider: 1 # 结构体 - 元组的问题在于,难以理解其所代表的数据 - - `(String, Int)`:一个人的姓名和年龄?姓名和手机号?地址和邮编? + - `(String, Int)`:一个人的姓名和年龄?地址和邮编? + - `(Double, Double, Double)`:三维空间中的坐标?向量? - 结构体允许我们赋予**名称** - `struct PersonalInfo { name : String; age : Int }` - - `struct ContactInfo { name : String; telephone : Int }` - `struct AddressInfo { address : String; postal : Int }` + - `struct Vector3 { x: Double; y: Double; z: Double }` + - `struct Point3 { x: Double; y: Double; z: Double }` 通过名称,我们能明确数据的信息以及对应字段的含义 # 结构体的定义 @@ -52,8 +53,8 @@ headingDivider: 1 - 结构体的定义形如`struct <结构体名称> { <字段名> : <类型> ; ... }` - `struct PersonalInfo { name : String; age : Int}` - 定义结构体的值时,形如`{ <字段名>: <值> , ... }` - - `let info : PersonalInfo = { name : "Moonbit", age : 1, }` - - 结构体的值的定义不在意顺序:`{ age : 1, name : "Moonbit", }` + - `let info : PersonalInfo = { name : "Moonbit", age : 3 }` + - 结构体的值的定义不在意顺序:`{ age : 3, name : "Moonbit" }` - 如遇到字段名相同的定义无法区分时,可在后面加上类型声明以作区分 - `struct A { val : Int }` - `struct B { val : Int }` @@ -62,11 +63,13 @@ headingDivider: 1 # 结构体的访问与更新 - 访问结构体时,我们通过`<结构体>.<字段名>` + ```moonbit - let old_info : PersonalInfo = { name : "Moonbit", age : 1, } + let old_info : PersonalInfo = { name : "Moonbit", age : 3, } let a : Int = old_info.age // 1 ``` - 更新原有的结构体时,我们可以复用原有的部分,如 + ```moonbit let new_info = { .. old_info, age : 2, } let other_info = { .. old_info, name : "Hello", } @@ -96,16 +99,36 @@ headingDivider: 1 # 元组结构体 +- 考虑如下情况: + - 同样的字段,不同的类型 + + ```moonbit + struct Vector3 { x: Double; y: Double; z: Double } + struct Point3 { x: Double; y: Double; z: Double } + ``` + + - 类型名称和字段的顺序,比字段名称更有代表性 + + ```moonbit + struct IntPair { first : Int; second : Int } + struct Interval { start : Int; end : Int } + ``` + +# 元组结构体 + - 元组结构体: - 命名的元组 - 字段不命名的结构体 -- 元组结构体的定义:`struct <结构体名称>(<类型>, ...)` +- 元组结构体的定义:`struct <元组结构体名称>(<类型>, ...)` +- 值的定义:`<元组结构体名称>(<表达式>, ...)` - 通过索引访问:`<元组结构体>.<索引>` - 例子: - ``` + ```moonbit struct IntPair(Int, Int) - let info : IntPair = IntPair(0, 1) - inspect(info.0, content="0") + let pair : IntPair = IntPair(0, 1) + test { + inspect(pair.0, content="0") + } ``` - 元组结构体是 nominal:类型名相同,且字段类型一一对应则类型兼容 @@ -167,11 +190,11 @@ headingDivider: 1 } ``` -- 元组结构体模式匹配和元组类似 +- 元组结构体模式匹配和元组类似,需要加上类型名称 ```moonbit - fn second(pair : Pair) -> Int { + fn second(pair : IntPair) -> Int { match pair { - Pair(first, second) => second + IntPair(first, second) => second } } ``` @@ -218,19 +241,6 @@ fn zip(l1 : List[Int], l2 : List[Char]) -> List[(Int, Char)] { } ``` -# 本地定义中的匹配 - -我们还可以在**本地**定义中利用模式进行匹配 - -- `let <模式> = <表达式>` - -此时会根据模式将表达式的值的子结构绑定到定义的标识符上,如: - -- `let (first, second) = (1, 2) // first == 1, second == 2` -- `let Pair(first, second) = Pair(1, 2) // first == 1, second == 2` -- `let Cons(1, x) = List::Cons(1, Nil) // x == Nil` -- `let Cons(2, x) = List::Cons(1, Nil) // 运行时错误,程序中止` - # 枚举类型 # 不同情况的并集 @@ -321,10 +331,12 @@ enum DaysOfWeek { ```moonbit expr let opt : Option[Int] = Some(10) inspect(opt is None, content="false") + inspect(0 is 1, content="false") + let pair = Pair(1, 2) + inspect(pair is Pair(_, _), content="true") ``` -- 同时,is 表达式也会对模式进行匹配 - - ```moonbit expr +- is 表达式也会对标识符进行绑定 + ```moonbit fn get_or_else2(option_int : Option[Int], default : Int) -> Int { if option_int is Some(value) { value @@ -334,21 +346,48 @@ enum DaysOfWeek { } ``` -# 错误处理 +# 本地定义中的匹配 + +我们还可以在**本地**定义中利用模式进行匹配 + +- `let <模式> = <表达式>` + +此时会根据模式将表达式的值的子结构绑定到定义的标识符上,如: + +- `let (first, second) = (1, 2) // first == 1, second == 2` +- `let Pair(first, second) = Pair(1, 2) // first == 1, second == 2` +- `let Cons(1, x) = List::Cons(1, Nil) // x == Nil` +- `let Cons(2, x) = List::Cons(1, Nil) // 运行时错误,程序中止` +- ```moonbit + fn unsafe_get(option_int : Option[Int]) -> Int { + let Some(value) = option_int + value + } + ``` + +# 错误类型 + +# 当程序出现问题 + +- 当程序的输入不符合预期 +- 当试图访问的文件不存在 +- 当传输数据时网络突然中断 +- ... # 错误类型 - 月兔中的错误有一个统一的类型 `Error` - `Error` 类型无法直接构造,必须使用 `suberror` 定义 `Error` 的子类型 - 定义错误类型: - - 无负载数据的错误类型:`suberror <错误类型1>` - - 有单一负载的错误类型:`suberror <错误类型2> <负载类型>` + - 无负载数据的错误类型:`suberror <错误类型1>`,例如 `suberror E1` + - 有单一负载的错误类型:`suberror <错误类型2> <负载类型>`, + 例如 `suberror E2 Int` - 类似枚举的错误类型:`suberror <错误类型3> { <情形1>; <情形2>; ... }` + 例如 `suberror E3 { Case1; Case2(Int); }` - 所有的错误类型都可以被自动提升为 `Error` 类型 -# 错误的构造 +# 构造错误类型的值 -- 每一种定义错误的方式 - 定义错误类型: - `suberror <错误类型1>`,例如 `suberror E1` - `suberror <错误类型2> <负载类型>`,例如 `suberror E2 Int` @@ -363,16 +402,131 @@ enum DaysOfWeek { # 函数中抛出错误 - 错误类型和错误的值可以当作普通的类型和值使用 -- 关键字 `raise` 用于抛出错误:`raise <错误表达式>` -- 函数 +- 关键字 `raise` 用于从函数中抛出错误:`raise <错误表达式>`。抛出错误后,函数的执行将被中断,并将错误传递给调用者。 +- 函数签名中使用 `raise` 关键字来指明可能抛出的错误类型 ```moonbit - + suberror DivError String + fn div(x : Int, y : Int) -> Int raise DivError { + if y == 0 { + raise DivError("division by zero") + } else { + x / y + } + } ``` +- 在这个例子中,`div(1, 0)` 会抛出 `DivError("division by zero")` 错误。 + +# 函数中抛出错误 + +- 不关心错误的具体类型时,可以用 `Error` 来表示: + `let e : Error = DivError("division error")` +- `Error` 出现在函数签名中时,可以省略: + `fn div(x : Int, y : Int) -> Int raise Error { ... }` 等价于 + `fn div(x : Int, y : Int) -> Int raise { ... }` +- 对于不抛出错误的函数,签名中可以标注 `noraise`: + `fn add(x : Int, y : Int) -> Int noraise { x + y }` # 处理错误 -# 错误多态 +# 捕获错误的 try-catch 表达式 + +- 使用 try-catch 表达式可以捕获错误并进行处理 +- 捕获错误的语法: + ``` + try <可能抛出错误的表达式0> catch { + <模式1> => <表达式1> + <模式2> => <表达式2> + ... + } noraise { + <模式3> => <表达式3> + } + ``` +- `catch` 部分的每一个分支都可以匹配不同的错误类型,并提供一个表达式作为整个 try-catch 表达式的结果。 +- `noraise` 部分用于处理没有错误发生的情况。如果 `<表达式0>` 没有抛出错误,其化简的值会匹配 `模式3`。此时 `<表达式3>` 为整个 try-catch 表达式的结果。 +- 当 `noraise` 部分没有任何处理过程时,可以省略。 + +# 捕获错误的化简 + +- 化简 `<可能抛出错误的表达式>`。 +- 如果发生错误,查找匹配的 `catch` 分支进行处理。 +- 如果没有错误发生,进入 `noraise` 块。 +- 无论进入哪个分支,最终的计算结果即是整个 try 表达式的结果 + +# 捕获错误的化简 + +``` +try div(1, 0) catch { + DivError(s) => 0 +} noraise { v => v } +``` +$\mapsto$ 计算会抛出错误的表达式 +``` +try (raise DivError("division by zero")) catch { + DivError(s) => 0 +} noraise { v => v } +``` +$\mapsto$ 匹配错误并将结果作为整个 try-catch 表达式的结果 +``` +0 +``` + +# 混合错误 + +try-catch 表达式中可以捕获多个错误类型 + +```moonbit +fn f1() -> Unit raise E1 { ... } + +fn f2() -> Unit raise E2 { ... } + +try { + f1() + f2() +} catch { + E1 => ... + E2 => ... + e => ... // 捕获其它错误 +} +``` + +当在 try-catch 表达式中捕获多个错误类型时,必须用标识符或者通配符 `_` 来捕获所有可能的错误。 + +# 其它错误处理方式 + +- 重新抛出错误:当不想要处理错误时,直接使用表达式,可以重新抛出错误: + + ```moonbit + fn div_reraise(x : Int, y : Int) -> Int raise DivError { + div(x, y) // 如果 `div` 引发错误,则重新抛出错误 + } + ``` + +- 直接崩溃:使用 `try! <表达式>` 可以在发生错误时直接引发程序崩溃 + + ```moonbit + fn div_panic(x : Int, y : Int) -> Int { + try! div(x, y) // 如果 `div` 引发错误,则程序崩溃 + } + ``` + +- 转化为 Result:使用 `try? <表达式>` 把一个类型为 `R`、可能抛出 `E` 类型的表达式转化为 `Result[R, E]` 类型的值 + +# 其它错误处理方式 + +- 转化为 Result:使用 `try? <表达式>` 把一个类型为 `R`、可能抛出 `E` 错误类型的表达式转化为 `Result[R, E]` 类型的值 + + ```moonbit + enum Result[R, E] { + Ok(R) + Err(E) + } + + test { + inspect(try? div(9, 3), content="Ok(3)") + inspect(try? div(3, 0), content="Err(DivError(\"division by zero\"))") + } + ``` # 总结 @@ -380,6 +534,4 @@ enum DaysOfWeek { - 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z)*k0@^?wKBxv==mJ6=qaIbVE3a=zGHxY#VY?DhtHhTdX)1*bV>xApTOl1bOX@FJQ4 zpD*Ion_HYh+vxfCqjDA|qHUyjv%c0p*=B{q5Z`)xs4zN^YBb8{>Fdh8YRNJKZgIlX z0!2!dIhD6D2+V+#Dgl+&Q-VFuNT+ShGVYV=_Gx#gqj7!LBa_L+%EC9>FUx&LX~g%; zBEsm;?YcaqfZJ8U%EgiIUwkmxWVwY9!4DKVp_6q#_fW^dcXBpybar>Nc#Xov#>L9U Mj`H-Wq>|MC16vc67ytkO From 644827825f0353cf94d3d9d91ce0b32943f23a97 Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Sun, 28 Sep 2025 17:23:22 +0800 Subject: [PATCH 14/14] feat: ssml for course 5. --- course5/lec5.mbt.md | 200 ++++++++++++++----------- course5/lec5.pdf | Bin 1070007 -> 1072474 bytes course5/script.xml | 356 ++++++++++++++++++++++++++++++++++++++++++++ 3 files changed, 468 insertions(+), 88 deletions(-) create mode 100644 course5/script.xml diff --git a/course5/lec5.mbt.md b/course5/lec5.mbt.md index 91a5af7..038f9ab 100644 --- a/course5/lec5.mbt.md +++ b/course5/lec5.mbt.md @@ -10,7 +10,7 @@ headingDivider: 1 ## 树 -### Hongbo Zhang +### 月兔公开课课程组 # 数据结构:树 - 树 @@ -37,20 +37,20 @@ headingDivider: 1 - 如果没有子节点的节点可称为叶节点 - 任何节点不能是自己的后代节点:树中不能有环路 - 树的一条边指的是一对节点(u, v),其中u是v的父节点或者v是u的父节点 -![](../pics/abstract-tree.drawio.png) + ![](../pics/abstract-tree.drawio.png) # 树的逻辑结构 - 这不是一颗树 -![](../pics/not-a-tree.drawio.png) + ![](../pics/not-a-tree.drawio.png) # 树的逻辑结构 - 计算机中的树根节点在上,子节点在父节点下方 - 相关术语 - - 节点的**深度**:根节点下到这个节点的路径的长度(边的数量) + - 节点的**深度**:从根节点向下,到这个节点的路径的长度(边的数量) - 根节点深度为0 - - 节点的**高度**:节点下到叶节点的最长路径的长度 + - 节点的**高度**:从节点向下,到叶节点的最长路径的长度 - 叶节点高度为0 - 树的**高度**:根节点的高度 - 只有一个节点的树高度为0 @@ -77,8 +77,8 @@ headingDivider: 1 - 线段树:每一个节点都存储了一根线段及对应的数据,适合一维查询 - 二叉树:每个节点至多有两个分支:左子树与右子树 -- KD-Tree:支持K-维度的数据(例如平面中的点、空间中的点等)的存储与查询的二叉树,每一层更换分叉判定的维度 - B-Tree:适合顺序访问,利于硬盘存储数据 +- KD-Tree:支持K-维度的数据(例如平面中的点、空间中的点等)的存储与查询的二叉树,每一层更换分叉判定的维度 - R-Tree:存储空间几何结构 - …… @@ -87,12 +87,20 @@ headingDivider: 1 - 二叉树要么是一棵空树,要么是一个节点;它最多具有两个子树:左子树与右子树 - 叶节点的两个子树都是空树 - 基于**递归枚举类型**的定义(本节课默认存储数据为整数) -```moonbit -enum IntTree { - Node(Int, IntTree, IntTree) // 存储的数据,左子树,右子树 - Empty -} -``` + + ```moonbit + enum IntTree { + Node(Int, left~ : IntTree, right~ : IntTree) // 存储的数据,左子树,右子树 + Empty + } + + let tree : IntTree = Node(1, left=Node(2, left=Empty, right=Empty), Empty) + + match tree { + Empty => ... + Node(value, left=l, right~) => ... // 左子树和右子树被绑定到 l 和 right + } + ``` # 二叉树的遍历 @@ -109,7 +117,7 @@ enum IntTree { - 后序遍历:先访问左子树,再访问右子树,再访问根节点 - `[3, 5, 4, 1, 2, 0]` - 广度优先遍历:`[0, 1, 2, 3, 4, 5]` -![height:6em](../pics/traversal.drawio.png) + ![height:6em](../pics/traversal.drawio.png) # 深度优先遍历:查找为例 @@ -117,24 +125,24 @@ enum IntTree { - 结构化递归 - 先对基本情形进行处理:空树 - 再对递归情形进行处理,并递归 -```moonbit -fn dfs_search(target: Int, tree: IntTree) -> Bool { - match tree { // 判断当前访问的树 - Empty => false // 若为空树,则已抵达最深处 - Node(value, left, right) => // 否则,再对子树轮流遍历 - value == target || dfs_search(target, left) || dfs_search(target, right) - } -} -``` + ```moonbit + fn dfs_search(target : Int, tree : IntTree) -> Bool { + match tree { // 判断当前访问的树 + Empty => false // 若为空树,则已抵达最深处 + Node(value, left~, right~) => // 否则,再对子树轮流遍历 + value == target || dfs_search(target, left) || dfs_search(target, right) + } + } + ``` - 前序、中序、后序遍历只是改变顺序 # 逻辑值的短路运算 - 短路运算:当发现当前求解值可以被确定,则中断计算并返回结果 - - `let x = true || { abort("程序中止") }`:因为`true || 任何值`均为真,因此不会计算`||`右侧表达式 - - `let y = false && { abort("程序中止") }`:因为`false && 任何值`均为假,因此不会计算`&&`右侧表达式 + - `let x = true || { abort("程序中止") }`:因为 `true || 任何值` 均为真,因此不会计算 `||` 右侧表达式 + - `let y = false && { abort("程序中止") }`:因为 `false && 任何值` 均为假,因此不会计算 `&&` 右侧表达式 - 树的遍历 - - `value == target || dfs_search(target, left) || dfs_search(target, right)`在找到后即会中止遍历 + - `value == target || dfs_search(target, left) || dfs_search(target, right)` 在找到后即会中止遍历 # 广度优先遍历 @@ -148,42 +156,45 @@ fn dfs_search(target: Int, tree: IntTree) -> Bool { - 就像生活中排队一样,先进入队伍的人最先获得服务 - 对于数据的插入和删除遵循先进先出(First In First Out, FIFO)的原则 - 队尾插入数据,队头删除数据 -![](../pics/queue.drawio.png) + + ![](../pics/queue.drawio.png) # 数据结构:队列 - 我们在此使用的队列由以下接口定义: -```moonbit -fn[T] empty() -> Queue[T] { ... } // 创建空队列 -fn[T] enqueue(q: Queue[T], x: T) -> Queue[T] { ... } // 向队尾添加元素 -// 尝试取出一个元素,并返回剩余队列;若为空则为本身 -fn[T] pop(q: Queue[T]) -> (Option[T], Queue[T]) { ... } -``` + ```moonbit + fn[T] empty() -> Queue[T] { ... } // 创建空队列 + fn[T] enqueue(q : Queue[T], x : T) -> Queue[T] { ... } // 向队尾添加元素 + // 尝试取出一个元素,并返回剩余队列;若为空则为本身 + fn[T] pop(q : Queue[T]) -> (Option[T], Queue[T]) { ... } + ``` - 例如 -```moonbit -let q = enqueue(enqueue(empty(), 1), 2) -let (head, tail) = pop(q) -assert_eq(head, Some(1)) -assert_eq(tail, enqueue(empty(), 2)) -``` + ```moonbit + test { + let q = enqueue(enqueue(empty(), 1), 2) + let (head, tail) = pop(q) + assert_eq(head, Some(1)) + assert_eq(tail, enqueue(empty(), 2)) + } + ``` # 广度优先遍历:查找为例 - 我们想要在树的节点中查找是否有特定的值 -```moonbit -fn bfs_search(target: Int, queue: Queue[IntTree]) -> Bool { - match pop(queue) { - (None, _) => false // 若队列为空,结束搜索 - (Some(head), tail) => match head { // 若队列非空,对于取出的树进行操作 - Empty => bfs_search(target, tail) // 若树为空树,则对剩余队列进行操作 - Node(value, left, right) => - if value == target { true } else { - // 否则,操作根节点并将子树加入队列 - bfs_search(target, enqueue(enqueue(tail, left), right)) - } + ```moonbit + fn bfs_search(target : Int, queue : Queue[IntTree]) -> Bool { + match pop(queue) { + (None, _) => false // 若队列为空,结束搜索 + (Some(head), tail) => match head { // 若队列非空,对于取出的树进行操作 + Empty => bfs_search(target, tail) // 若树为空树,则对剩余队列进行操作 + Node(value, left~, right~) => + if value == target { true } else { + // 否则,操作根节点并将子树加入队列 + bfs_search(target, enqueue(enqueue(tail, left), right)) + } + } } } -} -``` + ``` # 数据结构:二叉搜索树 @@ -206,17 +217,17 @@ fn bfs_search(target: Int, queue: Queue[IntTree]) -> Bool { - 对于一棵树 - 如果为空,则替换为插入值构成的子树 - 如果为非空,则与当前值进行比较,选择适当的子树替换为插入值后的子树 -```moonbit -fn insert(tree: IntTree, value: Int) -> IntTree { - match tree { - Empty => Node(value, Empty, Empty) // 若为空,则构建新树 - Node(v, left, right) => // 若非空,则基于更新后的子树构建新的树 - if value == v { tree } else - if value < v { Node(v, insert(left, value), right) } else - { Node(v, left, insert(right, value)) } + ```moonbit + fn insert(tree : IntTree, value : Int) -> IntTree { + match tree { + Empty => Node(value, left=Empty, right=Empty) // 若为空,则构建新树 + Node(v, left~, right~) => // 若非空,则基于更新后的子树构建新的树 + if value == v { tree } else + if value < v { Node(v, left=insert(left, value), right~) } else + { Node(v, left~, right=insert(right, value)) } + } } -} -``` + ``` # 二叉搜索树的删除 @@ -238,19 +249,19 @@ fn insert(tree: IntTree, value: Int) -> IntTree { 我们使用辅助函数`fn remove_largest(tree: IntTree) -> (IntTree, Int)`来找到并删除子树中的最大值。我们一路向右找到没有右子树的节点为止 ```moonbit match tree { - Node(v, left, Empty) => (left, v) - Node(v, left, right) => { - let (newRight, value) = remove_largest(right) - (Node(v, left, newRight), value) + Node(v, left~, Empty) => (left, v) + Node(v, left~, right~) => { + let (new_right, value) = remove_largest(right) + (Node(v, left~, right=new_right), value) } } ``` -我们定义删除操作`fn remove(tree: IntTree, value: Int) -> IntTree` +我们定义删除操作`fn remove(tree : IntTree, value : Int) -> IntTree` ```moonbit match tree { ... - Node(root, left, right) => if root == value { - let (newLeft, newRoot) => remove_largest(left) - Node(newRoot, newLeft, right) + Node(root, left~, right~) => if root == value { + let (new_left, new_root) => remove_largest(left) + Node(new_root, left=new_left, right~) } else ... } ``` @@ -273,10 +284,11 @@ match tree { ... ```moonbit enum AVLTree { Empty - Node(Int, AVLTree, AVLTree, Int) // 当前节点值、左子树、右子树、树高度 + // 当前节点值、左子树、右子树、树高度 + Node(Int, left~ : AVLTree, right~ : AVLTree, height~ : Int) } -fn create(value: Int, left: AVLTree, right: AVLTree) -> AVLTree { ... } -fn height(tree: AVLTree) -> Int { ... } +fn create(value : Int, left : AVLTree, right : AVLTree) -> AVLTree { ... } +fn height(tree : AVLTree) -> Int { ... } ``` # 二叉平衡树 AVL Tree @@ -288,18 +300,27 @@ fn height(tree: AVLTree) -> Int { ... } 我们对一棵树进行再平衡操作 ```moonbit -fn balance(left: AVLTree, z: Int, right: AVLTree) -> AVLTree { - if height(left) > height(right) + 1 { - match left { - Node(y, left_l, left_r, _) => - if height(left_l) >= height(left_r) { - create(left_l, y, create(lr, z, right)) // x在y z同侧 - } else { match left_r { - Node(x, left_right_l, left_right_r, _) => // x在y z中间 - create(create(left_l, y, left_right_l), x, create(left_right_r, z, right)) - } } +fn balance(tree : AVLTree) -> AVLTree { + match tree { + Empty => Empty + Node(z, left~, right~, ..) if height(left) > height(right) + 1 => { + match left { + Node(y, left=left_l, right=left_r, ..) => + if height(left_l) >= height(left_r) { + create(y, left_l, create(z, left_r, right)) // x在y z同侧 + } else { + match left_r { + Node(x, left=left_right_l, right=left_right_r, ..) => // x在y z中间 + create(x, + create(y, left_l, left_right_l), + create(z, left_right_r, right), + ) + } + } + } } - } else { ... } + ... + } } ``` @@ -308,12 +329,15 @@ fn balance(left: AVLTree, z: Int, right: AVLTree) -> AVLTree { 我们在添加后对生成的树进行再平衡 ```moonbit -fn add(tree: AVLTree, value: Int) -> AVLTree { +fn add(tree : AVLTree, value : Int) -> AVLTree { match tree { - Node(v, left, right, _) as t => { - if value < v { balance(add(left, value), v, right) } else { ... } - } - Empty => ... + Node(v, left~, right~, _) => + if value < v { + balance(create(v, add(left, value), right)) + } else { + balance(create(v, left, add(right, value))) + } + Empty => create(value, Empty, Empty) } } ``` diff --git a/course5/lec5.pdf b/course5/lec5.pdf index 438435aeb0807a51ca6b961faeea363d1dbf2b42..b066f933511d103187f0df116d639b85d8975c75 100644 GIT binary patch delta 143569 zcmZU4b8uik)OKxKTifo|TXVOzZJW2YZQJeE+PYiY?$);P_4m&A{qfE>bI;68a&wYN zo+RfvC%2_kXtiCa4z(PVHFZW9o+fpn7!et0O4O0*XT}J*yrr9L()aw;4PRVWeOl8g z5AVr)!imDWk+nUQO0Ls^%q!X$oY3ttm3YTbgUyPFO-!tP8>m)|auQ;bwny%qb}8Y~ z5A){375II*Mx8aW&eO~{CrG3Y%%DSG#&wKSNF@wL_=s3gyZ0sb=yPI=S?(Z=+VB@( z5bavt4$E<5;4s~vAOSgedg=OCN*Y!h$H<>fPEg^+WC&A68hq4#N&<8tL1CT7-$gsn z9zvy`^(VLT6g|y(y%sJZPc2BkXTW$-^_0%T&$|0!!97%6POQSNct(5^_Fr^EQgPQi 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+ 大家好,欢迎来到由IDEA研究院基础软件中心为大家带来的现代编程思想公开课。 + 上节课我们学习了如何自定义数据结构。 + 那么今天的课程,就让我们来看一个常用的数据结构:树,以及相关的算法。 + +

+

+ 这节课我们将会从最简单的树结构开始,了解树的概念,然后学习一种特化的树:二叉树。 + 之后,我们会对二叉树进行特化,变成二叉搜索树。 + 在二叉搜索树的基础上,我们还会学习二叉平衡树。 + +

+

+ 树在我们生活中是十分常见的植物,例如左下图所示。 + 我们所常见的树都是有一个树根,从树根上逐渐分化出多个树枝,每个树枝上有着叶子,或者其他小树杈,树杈又继续分化。 + 事实上,生活中很多的数据结构都有着一种类似的结构,长得像一棵树。 + 比如,我们所常见的谱系图,或者又被称为家族树。 + 从一对先祖出发,家族不断壮大。我们也会用开枝散叶来形容这一过程。 + 又比如文件结构,一个文件夹中可能有着一些文件和其他的文件夹,就像叶子和树杈。 + 数学表达式也可以用类似一棵树表示,每一个节点都是运算符,每一片叶子都是数字,越靠近根部的运算符越晚被计算。 + +

+

+ 在数据结构中,树是由有限个节点构成的具有层次关系的集合。 + 每一个节点是存储数据的结构。而节点与节点之间存在着层次关系。 + 习惯上,我们一般用家庭关系来描述。 + 例如,我们会说相邻的节点之间存在亲子关系,称为父节点和节点,也有的翻译称为双亲节点。 + 同时,我们也会用祖先和后代来描述关系稍远一些的节点。 + +

+

+ 对于一棵树而言,如果不为空,那么它应该有着唯一一个节点,这个节点只有父节点,没有节点。 + 而除了节点以外的所有节点都应当有且仅有一个父节点。 + 对于没有节点的节点,也就是最外侧一圈的节点,我们称为节点,就像树的叶子。 + 另外,任何节点不能是自己的后代节点,也就是说,树中不能出现环路。 + +

+

+ 在树中,一条边指的是一对节点 u, v,其中 u 是 v 的父节点,或者 v 是 u 的父节点; + 简单说,这两个节点应该存在亲子关系。 + 我们在图中用箭头标识亲子关系,由长辈指向晚辈。 + +

+

+ 在下面的例子当中,这就不是一棵树。 + 每一个红色的地方都违反了树结构的要求。 + 右上方,出现了一个节点以外的没有父节点的节点,也就是有两个节点,这不符合要求; + 最下面的两个节点,左侧多了一个指向节点的箭头,也就意味着它成了节点的父节点; + 而这也就意味着,节点成为了本身的节点的节点的节点,自己成了自己的后辈,这也不符合要求; + 右侧的节点则出现了两个父节点,这也不符合要求。 + +

+

+ 在计算机程序语境中,一般把节点放在上方,节点都放在父节点的下方。 + 我们以这种方式来定义相关的术语。 + 首先是节点的深度。 + 节点的深度对应从节点向下,到这个节点的路径的长度,或者说经过的边的数量。 + 也就是说,从节点出发,只向下,不向上所经过的边的数量。 + 因此,节点的深度是0。 + 之后是节点的高度。节点的高度对应从这个节点向下,到节点的最长路径的长度。 + 也就是说,如果在节点的后代中有多个节点,我们以距离最远的那个为准。 + 同理,节点的高度为0。最后则是树的高度,它等同于节点的高度。 + 如果一个树只有一个节点,那么这个节点既是节点,也是节点,高度为0,因此树的高度为0。 + 而如果一棵树为空,也就是说没有任何的节点,那么我们定义它的高度为-1。 + 当然,有的书本可能采取不同的定义,以“层次”来“定义”树的高度,以根为第一层,如果遇到了,大家也不要感觉奇怪。 + +

+

+ 说完了树的逻辑结构,让我们来看看树的存储结构。 + 逻辑结构定义了数据之间的关系,而存储结构则定义了数据的具体的表示。 + 我们以二叉树为例。这样的树,至多只有两个节点。 + 我们在这里省略节点存储的数据,用数字来代表每个节点。 + 例如,节点的编号为0,其他节点从1开始编号。 + 一种方式是以一个二元组的列表来表示树。 + 其中,每一个二元组定义了亲子关系,例如,0 1 表示编号0的节点是编号1的节点的父节点。 + 而 0 2 则代表编号0的节点是编号2的节点的父节点。 + 之后,编号1的节点又是编号3的节点的父节点。 + 通过这种形式,我们能够定义一棵树。 + 另一种方式则是用我们上节课学习过的代数数据结构来定义。 + 我们用枚举类型来定义几种情况:Node 代表一颗普通的树,它具有自身的编号以及两个树; Leaf 代表一个只有个节点的树,也就是节点,它只有本身的编号,Empty则代表一个空树。 + 这种情况下,我们同样能定义与刚才同样的树结构。 + 当然,这只是一种可能的实现。 + 最后一种方式则是一个列表,其中每一层的结构从左到右连续排布。 + 例如,第一层的节点被放在第一位; + 之后两位则是第二层的节点,从左到右排布; + 再之后则是第三层的节点,从左到右排布。 + 因此,3以及右侧一个节点是1的节点,而后两者则是2的节点。 + 当然,目前都是空。我们可以看到,这三者都定义了相同的一棵树,而它们的存储结构大相径庭。 + 因此,我们可以得出结论,数据的逻辑结构独立于存储结构,这点希望大家注意。 + +

+

+ 最后,树这一数据结构有着众多的衍伸。 + 例如,线段树,每一个节点都存储了一个区间以及对应的数据,因此十分适合一维查询。 + 二叉树则是一个特别的树,每个节点至多有两个分支,分别为左树与右树。 + B树则适合顺序访问,利于硬盘存储数据。 + KD-Tree和R-Tree则适合存储空间集合结构。 + 其中,KD-Tree和R-Tree分别是二叉树和B树的衍伸。 + 除此以外还有众多的树结构,大家可以自行学习了解。 + +

+

+ 接下来让我们从树出发,进入更加特殊的树,二叉树的学习。 + 二叉树刚才已经见过了,它要么是一颗空树,要么是一个节点,这个节点最多具有两个树,分别是左树和右树。 + 其中,叶节点意味着两个树都是空树。 + 我们这里采用基于递归枚举类型的定义,默认存储的数据为整数。 + 当枚举类型的一个情形包含多个负载值时,为了更清晰的区分每个负载值,可以在定义负载值类型时加上标签。 + 带标签的负载值定义为标签名、波浪号、冒号、和类型。 + 例如二叉树节点的定义中,我们分别为左树和右树这两个负载值添加标签,left 和 right,它们的类型都是二叉树。 + 例子中也可以看出,带标签和不带标签的负载值,可以同时出现在一个枚举情形的定义中。 + 在定义 Node 情形的枚举值时,使用标签和等号,来标明定义的是哪一个负载值。 + 如 tree 这个变量所示。 + 模式匹配时,可以使用等号和标识符来绑定带标签的负载值,也可以使用波浪号来重复使用标签本身的名字进行绑定。 + 下面的例子中,在对 Node 情形进行模式匹配时,左子树和右子树分别被绑定到 l 和 right 这两个标识符。 + +

+

+ 我们首先要谈到的算法是二叉树的遍历。 + 树的遍历是指以某种规律,不重复的访问树的所有节点的过程。 + 通常,有两种方式可以遍历:深度优先遍历,和广度优先遍历。 + 深度优先遍历总是先访问一个树,再访问另一个树。 + 而在访问这个树的过程中,也总是访问其中的一个树。 + 如此递归,总是先访问到深度最深的节点,再进行返回。 + 例如左图中,我们首先访问左树,之后再次访问左树,于是3被访问了。 + 之后我们不断访问右树,于是访问了5。 + 最后,我们才访问了整棵树的右树2。 + 而广度优先遍历则不同,它从节点开始,一层一层进行访问,将一定深度的节点访问完才会访问更深的节点。 + 例如同样的一棵树,广度优先遍历会先访问节点,之后是树1和2,再之后是3和4,最后才是深度最深的5。 + +

+

+ 深度优先遍历通常也分几种情况:前序遍历、中序遍历和后序遍历。 + 它们的区别是,在走遍整棵树的过程当中,访问节点的时机不同。 + 例如,前序遍历会先对节点进行访问,之后再对左树进行访问,最后对右树进行访问。 + 以我们刚才看到的这棵树为例,这就意味着先从0开始,再访问左树; + 而访问左树的时候也是先从节点开始,也就是从 1 开始; + 之后则是3,4,5,2。而中序遍历,则是先访问左树,再访问节点,最后访问右树。 + 于是,它会先对左树访问。此时左树还有左树,于是我们找到 3 这棵树。 + 此时这是一个节点,没有左树,因此我们对节点3进行访问。 + 之后我们向上返回,访问树的节点1,之后再对右树进行访问。 + 后序遍历同理,先访问左树,再访问右树,最后访问节点。 + 而广度优先遍历,我们刚才已经解释过了,从左到右,顺序便是 0, 1, 2, 3, 4, 5。 + +

+

+ 我们以查找树的节点中的具体的值来看一下两种遍历的具体实现。 + 首先是深度优先遍历。 + 如刚才所介绍,这是一个基于结构化递归的遍历。 + 我们首先对基本情形进行处理,也就是树为空的情况。 + 如第三行所示。这种情况下,我们没有找到我们所要找的值,因此返回 false。 + 之后,我们对递归情形进行处理。对于一个节点,我们判断它的值是不是我们要找的结果,如第5行所示。 + 如果找到,那么结果就是 true。 + 否则,我们继续对左右树轮流遍历,结果是左树有当前值或右树有当前值。 + 在目前的二叉树中,要找到给定的值,我们需要遍历左右树才能找到结果。 + 之后介绍的二叉搜索树将会优化这一过程。 + 前序、中序、后序遍历只需改变对当前节点操作、对左节点遍历以及对右节点遍历这三者的顺序即可。 + +

+

+ 我们在这里补充一下第二节课没有提到的内容,那就是逻辑值的短路运算。 + 逻辑值的-操作是短路的。 + 也就是说,如果发现当前求解的值的结果可以被确定了,那么我们会中止计算并直接返回结果。 + 例如第一个例子中,我们在求 true 和一个值的或。 + 事实上,我们清楚 true 和任何值的或,均为真, + 因此,我们只需要完成对运算的左侧计算即可结束,右侧不会被计算。 + 即便我们在这里写了一个令程序中止的指令 abort,程序依然会正常运行,因为右侧根本没有被计算。 + 同理,如果我们求 false 和一个值的与。 + 我们清楚 false 和任何值的与,均为假,因此我们也不会计算运算的右侧。 + 回到我们刚才的树的遍历上来。 + 我们运用运算,任何一项条件满足,遍历即会立刻终止。 + +

+

+ 让我们继续学习广度优先遍历。 + 广度优先遍历,如刚才所说,是要对每一层树挨个访问。 + 这种情况下,为了能够记录我们将要访问的所有的树,我们需要一个全新的数据结构:队列。 + +

+

+ 队列,是一个先进先出的数据结构。 + 我们每次对队列中的树,取出一个进行判断,它的节点的值是否是我们所搜索的值。 + 如果不是,那么我们把它的非空树从左到右加到队尾,并且继续进行计算,直到队列为空。 + +

+

+ 我们具体看一下队列。 + 就像生活中排队一样,最先进入队伍的人最先获得服务,要讲究先来后到。 + 对于数据的插入和删除遵循同样的顺序,如下图所示。 + 我们按照顺序添加了0到5。可以看到,之后在添加6的时候,它是跟在5的后面; + 而我们接下来要进行删除操作的话,则从最早加入队列的0开始。 + +

+

+ 我们在这里使用的队列通过以下的接口定义: + 和 Option 类型一样,队列也是一个泛型类型,这意味着一个 Queue T 类型的队列可以包含类型为 T 的元素。 + empty 构筑一个空的队列; + enqueue 往队列中添加元素,也就是往队尾添加; + pop 尝试取出一个元素,并且返回剩下的队列,如果队列已经为空,那么返回的值就会是None,以及一个空队列。 + 例如下方,我们在一个空列表中前后添加了1和2。 + 之后,当我们尝试取出一个元素,我们应该能获得 Some(1),而剩下的应当等同于往一个空列表中加2。 + +

+

+ 我们回到我们的广度优先遍历的实现上来。 + 如果我们想要在树的节点中查找是否有特定的值,我们需要维护一个装有树的队列,通过参数可以看到这一点。 + 之后,我们判断当前队列是否为空。 + 通过 pop 操作后对队列头进行模式匹配, + 如果为空,那么我们已经完成了所有的搜索,也就是没有找到,返回 false。 + 如果队列还有元素,那么我们对这个树进行操作。 + 如果这个树为空,那么我们直接对剩余队列进行操作;如果树不为空,那么和刚才一样,我们判断当前节点是否是我们要找的值。 + 如果是,那我们就返回真; + 否则,我们把左右树 left 和 right 加入队列中,并且继续对队列进行搜索。 + +

+

+ 到这里为止,我们对于树的遍历的介绍就结束了。 + 当然我们会注意到,这样的搜索似乎不太高效,因为每一个树都可能有我们要找的值。 + 那有没有什么办法减少搜索的次数呢?这就是我们下节课要介绍的二叉搜索树。 + +

+

+ 大家好,欢迎来到由IDEA研究院基础软件中心为大家带来的现代编程思想公开课。 + 在上节课,我们介绍了树这一数据结构和树的遍历。 + 接下来,我们学习二叉搜索树。 + +

+

+ 我们之前提到,二叉树要查找树中的元素很可能要找遍整棵树。 + 例如下图中,我们尝试查找树中是否存在8这个元素。 + 对于左侧的二叉树,我们不得不找遍整棵树,最后得出结论:树中没有8。 + +

+

+ 为了方便搜索,我们在二叉树的基础上对于树中的数据排列进行规定,从左到右的数据从小到大,于是我们便获得了基于二叉树的二叉搜索树。 + 我们规定,左树中的所有数据都应当小于节点的数据; + 而节点的数据又应当小于右树的数据,如右下图所示。 + 我们可以注意到,如果我们进行一次中序遍历,我们可以从小到大依次遍历排序后的数据。 + 大家可以在课后练习中尝试实现二叉搜索树的判断。 + 而二叉搜索树的搜索操作十分简单,只需要对于每个节点判断当前值是小于、等于、还是大于我们要找的树,便可以判断我们要找的值应该在哪个树中。 + 例如在下图的例子当中,我们判断8大于5,因此应当向右查找。 + 而当我们找到7之后,我们发现它右侧没有树,也就意味着没有比7更大的数字了,因此我们可以得出结论,8不在树中。 + 可以看到,我们的查找效率有了很大的提升。 + 事实上,我们最多需要进行的查找次数,也就是最坏情况,等同于树的高度加一,而非元素总数。 + 当然,树的高度也可能会等于元素总数,我们将会在稍后看到。 + +

+

+ 为了维护这样的一棵树,我们需要特殊的插入与删除的算法,确保修改后的树依然保持着顺序。 + 我们分别来看这两个算法。 + +

+

+ 对于一棵树的插入操作,我们同样是利用结构化递归进行。 + 首先我们讨论基础情形,也就是树为空的情况。 + 那么这个时候,我们只需要把树替换为一棵只有一个节点的树,而节点的值,就是我们想要插入的值。之后我们讨论递归的情形。 + 如果一棵树非空,那么我们将想要插入的值,与节点的值进行比较。 + 如果小于它,那么我们将值插入左树,并且将左树替换为插入值后的树。 + 如果大于,那么就替换右树。 + 例如,我们想要插入3,那我们就需要与节点进行逐个判断。 + 例如,它小于5,那我们对左面的树进行操作。 + 之后,它大于2,那我们对右面的树进行操作。 + 我们将这个树放大。可以看到,3小于4,因此我们应该将它插入左面的树。 + 而这是一棵空的树,因此我们构建一个只有一个节点的树,并且将根为4的树的左树替换为它。 + +

+

+ 我们这里可以看到完整的插入代码。 + 第3行,如果原来的树是空的,我们重新构建一棵树; + 第6第7行,如果我们需要“更新”树,我们在更新后的树的基础上重新利用 Node 构造器构建一棵树。 + +

+

+ 之后,我们讨论删除的操作。 + 同样的,我们利用结构化递归进行。 + 如果树为空,那么很简单,我们什么都不用做。 + 如果树非空,那么我们就需要和当前值进行比较,判断当前的值是否要进行删除操作。 + 如果要进行删除操作,那我们就删除它,这个我们之后再讨论; + 如果不是我们要删除的值,那同样,我们要进行比较,找到值可能存在的树,在进行删除操作后重新创建新的树。 + 那么这个流程中最关键的就在于,如何删除一棵树的节点。 + 如果这棵树没有树或者只有一棵树,那么是最简单的,因为只需要替换为空树或者唯一的树即可。 + 比较棘手的是如果有两棵树。 + 这种情况下,我们要找一个新的值来做节点,并且这个节点需要依然大于左树中的所有值,小于右树中的所有值。 + 那么满足这个条件的值其实有两个:左树的最大值,右树的最小值。 + 我们在这里以左树的最大值为例。我们这里再看一下示意图。 + 如果没有树,直接替换为空树,如果有一棵树,替换为树。 + 如果有两棵树,那么我们需要将左树的最大值设为最新的节点的值,并且从左树中删除该值。 + 好消息是,这次这个值,至多只有一个树,因此操作比较简单。 + +

+

+ 我们在这里展示部分的二叉搜索树的删除操作。 + 我们定义了一个辅助函数,来从左树中查找并删除最大值。 + 我们一路向右找到没有右树的节点为止,因为没有右树意味着没有值比它更大了。 + 之后,基于此,我们定义一个删除操作,其中在删除两个树均非空的情况时,我们便可以利用这个辅助函数,获得新的左树和新的节点。 + 我们在这里省略具体的代码实现,留给大家作为课后练习。 + +

+

+ 最后,我们进入到二叉平衡树的学习中。 + 我们在解释二叉搜索树的时候提到过,二叉搜索树中的搜索次数的最坏情况取决于树的高度。 + 当我们在对二叉搜索树进行操作的时候,很可能会发生不平衡的现象,也就是一边的树高度远远高于另一边的树。 + 比如,如果我们按照1到5的次数进行插入的话,我们便会得到如左下图所示的一棵树。 + 我们可以看到,对于整棵树来说,左侧树高度为-1,因为是一颗空树;而右侧树高度为3。 + 在这种情况下,搜索次数的最坏情况等同于树的元素数量,也就是五次。 + 而如果树比较平衡,也就是两边树的高度差不多的话,例如右图,那节点的深度最多也就是2,大约只是log2n次,n为树的元素数量。 + 大家回忆一下对数函数的曲线便可知道,在树的元素数量较多的时候,这两种情况下查询的最坏时间差距会很大。 + 因此,我们希望能够避免这种最坏的情况的发生,来保证我们总是能有较好的查询性能。 + 为此,我们可以引入二叉平衡树这一类数据结构,使得任意节点的左右树的高度相差无几。 + 常见的二叉平衡树有AVL树、二三树或者红黑树等多种实现。 + 我们在这里讨论AVL树这种比较简单的树。 + +

+

+ 二叉平衡树保持平衡的关键点就在于,当树出现不平衡的现象之后,我们可以通过对树进行重新排列,来重新获得平衡。 + AVL树的插入、删除都和标准的二叉搜索树相类似。 + 不同的是,AVL树在每次插入、删除后都会进行调整,以保证树的平衡。 + 为了方便维护,我们在之前的树的定义的基础上,在每个节点中添加当前树的高度属性。 + 我们定义一个创建方法,用于创建一颗新的AVL树而不用显式维护它的高度。 + AVL树的插入、删除操作都类似于标准的二叉搜索树,因此我们按下不表。 + +

+

+ 我们在插入一个元素或者删除一个元素之后,从修改的地方向上返回,直到找到第一个出现不平衡的位置,我们称之为 z。 + 之后,我们用y表示z的树中更高的那一个。 + 而x则是y的树中更高的那个。 + 之后,我们对平衡进行讨论。 + 第一种情况,x在y和z中间。这种情况下,我们可以将x移到父亲和祖父的上方。 + 我们可以看到,x的两棵树所处的深度减小了1,从而整棵树的高度降低了。 + 而T4虽然深度增加了一,但是原本高度就比左树要低,因此依然是平衡的。 + 另一种情况则是x在y和z的同侧,那么我们可以通过让父亲y成为新的节点来降低树的高度,目的同样是降低最深的两棵树的深度,从而减小左树的高度。 + +

+

+ 大家看到的是平衡树的代码片段。大家只需要理解了我们刚才讨论的情况,就能简单的将算法转化为实际的代码。 + 我们对于一棵树,首先判断是否已经失衡、如何失衡,也就是两个树的高度差是不是大于特定的值,以及哪边更高。 + 在判断之后,我们就会进行平衡操作。 + 此时我们传入的节点就是z,而更高的那边通过模式匹配分解以后,节点就是y。 + 这里我们不需要用到这个树自身的高度,因此我们使用两个点,忽略未匹配的负载值。 + 此时,我们再根据y的两边树的高度比较结果,进一步作出判断,看x是在y和z的同侧还是异侧,如第7行所示。 + 之后,我们再根据刚才讨论的情形进行重新的组合,如第8、10行所示。 + +

+

+ 以插入元素为例,我们在插入元素之后,直接对将要生成的树进行一个平衡操作。 + +

+

+ 总结一下,今天的课程中,我们介绍了树这一数据结构,包括树的定义以及相关的术语、二叉树的定义以及遍历的算法、二叉搜索树的定义以及增删操作、二叉平衡树AVL树的平衡操作。 + 我们推荐大家阅读《算法导论》第12、13章。 + 我们下节课再见。 +

+ + + \ No newline at end of file

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za^9U<>sntgwBbw%6=?|lVD~DT1l|0sg;vt`V#-USm#bteJ=R+x7wWjoaifP}JfXqG z83=`d1S&F%XXvK3E65hvrOZ;}ID3YOZfkG<;H-h`R`R#;=ln2V=OvMz+od{n8EjT; z`r-5j)05dEEe0xiZ%FzLar#$q=7x_a0y122XtS~+CyLQ7n~h+M@Tvy~@pd)0Ulp@~ zoOUnk1VhSg_CmYz$7f;I@AeR$IyTO26O<*Y^*l?C^mxb-%Km;ou4i4=vTMnxvByCR ziw0I-J^S#I{bB%ckg5Gl4 zX7t@8oe#%pi6xNGq3th~Hb(_^_KCSXH<*|fmnpt{Wifqe4qefs)&C76EiFHCkUWOyR3jiwTyuNAOB1Gf0O Date: Tue, 26 Aug 2025 11:05:06 +0800 Subject: [PATCH 10/14] feat: ssml for course4. --- course4/script.xml | 226 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 226 insertions(+) create mode 100644 course4/script.xml diff --git a/course4/script.xml b/course4/script.xml new file mode 100644 index 0000000..b00531f --- /dev/null +++ b/course4/script.xml @@ -0,0 +1,226 @@ + + +

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z{ipaY&uL%q*Klp`=!xEcf5S}qf2JblLYDy{0TUK;bYXIIcyeWC3O6@6G%_#>B_%~q EMks7IO#lD@ From 538e1dd1271cb4b51d6cbdb7eb6ca9b2fc164791 Mon Sep 17 00:00:00 2001 From: Milky2018 <842376130@qq.com> Date: Tue, 26 Aug 2025 11:04:57 +0800 Subject: [PATCH 09/14] feat: slides update for course4. --- course4/lec4.mbt.md | 92 ++++++++++++++++++++++---------------------- course4/lec4.pdf | Bin 494128 -> 520389 bytes course4/zip.drawio | 58 ++++++++++++++-------------- pics/zip.drawio.png | Bin 28258 -> 27864 bytes 4 files changed, 75 insertions(+), 75 deletions(-) diff --git a/course4/lec4.mbt.md b/course4/lec4.mbt.md index ba143e7..22c4f58 100644 --- a/course4/lec4.mbt.md +++ b/course4/lec4.mbt.md @@ -41,71 +41,71 @@ headingDivider: 1 - 元组的问题在于,难以理解其所代表的数据 - `(String, Int)`:一个人的姓名和年龄?姓名和手机号?地址和邮编? - 结构体允许我们赋予**名称** - - `struct PersonalInfo { name: String; age: Int }` - - `struct ContactInfo { name: String; telephone: Int }` - - `struct AddressInfo { address: String; postal: Int }` + - `struct PersonalInfo { name : String; age : Int }` + - `struct ContactInfo { name : String; telephone : Int }` + - `struct AddressInfo { address : String; postal : Int }` 通过名称,我们能明确数据的信息以及对应字段的含义 # 结构体的定义 -- 结构体的定义形如`struct <结构体名称> { <字段名>: <类型> ; ... }` - - `struct PersonalInfo { name: String; age: Int}` +- 结构体的定义形如`struct <结构体名称> { <字段名> : <类型> ; ... }` + - `struct PersonalInfo { name : String; age : Int}` - 定义结构体的值时,形如`{ <字段名>: <值> , ... }` - - `let info: PersonalInfo = { name: "Moonbit", age: 1, }` - - 结构体的值的定义不在意顺序:`{ age: 1, name: "Moonbit", }` + - `let info : PersonalInfo = { name : "Moonbit", age : 1, }` + - 结构体的值的定义不在意顺序:`{ age : 1, name : "Moonbit", }` - 如遇到字段名相同的定义无法区分时,可在后面加上类型声明以作区分 - - `struct A { val: Int }` - - `struct B { val: Int }` + - `struct A { val : Int }` + - `struct B { val : Int }` - `let x = ( { val : 1, } : A )` # 结构体的访问与更新 - 访问结构体时,我们通过`<结构体>.<字段名>` ```moonbit -let old_info: PersonalInfo = { name: "Moonbit", age: 1, } -let a: Int = old_info.age // 1 +let old_info : PersonalInfo = { name : "Moonbit", age : 1, } +let a : Int = old_info.age // 1 ``` - 更新原有的结构体时,我们可以复用原有的部分,如 ```moonbit -let new_info = { .. old_info, age: 2, } -let other_info = { .. old_info, name: "Hello", } +let new_info = { .. old_info, age : 2, } +let other_info = { .. old_info, name : "Hello", } ``` # 多元组与结构体的关系 - 结构体与相同类型集合构成的多元组**同构** - 集合`A`与`B`之间存在一一映射的关系 - - 存在一对映射`f: (A) -> B`与`g: (B) -> A`使得 + - 存在一对映射`f : (A) -> B`与`g : (B) -> A`使得 - `g(f(a)) == a` - `f(g(b)) == b` - 例:`struct PersonalInfo { name: String; age: Int }`与`(String, Int)`同构 ```moonbit -fn f(info: PersonalInfo) -> (String, Int) { (info.name, info.age) } -fn g(pair: (String, Int)) -> PersonalInfo { { name: pair.0, age: pair.1, }} +fn f(info : PersonalInfo) -> (String, Int) { (info.name, info.age) } +fn g(pair : (String, Int)) -> PersonalInfo { { name: pair.0, age: pair.1, }} ``` ![](../pics/isomorphism.drawio.png) # 多元组与结构体的关系 -- 多元组是structural:只要结构相同(字段类型一一对应)就类型兼容 +- 多元组是 structural:只要结构相同(字段类型一一对应)就类型兼容 ```moonbit -fn accept_tuple(tuple: (Int, String)) -> Bool { +fn accept_tuple(tuple : (Int, String)) -> Bool { true } -let accepted: Bool = accept_tuple((1, "Yes")) +let accepted : Bool = accept_tuple((1, "Yes")) ``` -- 结构体是nominal:只有类型名相同(字段顺序可以打乱)才类型兼容 +- 结构体是 nominal:只有类型名相同(字段顺序可以打乱)才类型兼容 ```moonbit -struct A { val : Int ; other: Int } -struct B { val : Int ; other: Int } -fn accept_a(a: A) -> Bool { +struct A { val : Int ; other : Int } +struct B { val : Int ; other : Int } +fn accept_a(a : A) -> Bool { true } -let not_accepted: Bool = accept_a(({ val : 1, other : 2 }: B)) // DO NOT COMPILE -let accepted: Bool = accept_a(({other: 2, val: 1}: A)) +let not_accepted : Bool = accept_a(({ val : 1, other : 2 } : B)) // DO NOT COMPILE +let accepted : Bool = accept_a(({other : 2, val : 1} : A)) ``` # 模式匹配 @@ -113,7 +113,7 @@ let accepted: Bool = accept_a(({other: 2, val: 1}: A)) - 回顾:我们可以通过模式匹配查看列表和Option的结构 ```moonbit -fn head_opt(list: List[Int]) -> Option[Int] { +fn head_opt(list : List[Int]) -> Option[Int] { match list { Nil => None Cons(head, _tail) => Some(head) @@ -122,7 +122,7 @@ fn head_opt(list: List[Int]) -> Option[Int] { ``` ```moonbit -fn get_or_else(option_int: Option[Int], default: Int) -> Int { +fn get_or_else(option_int : Option[Int], default : Int) -> Int { match option_int { None => default Some(value) => value @@ -134,7 +134,7 @@ fn get_or_else(option_int: Option[Int], default: Int) -> Int { - 模式匹配可以匹配值(逻辑值、数字、字符、字符串)或者构造器 ```moonbit -fn is_zero(i: Int) -> Bool { +fn is_zero(i : Int) -> Bool { match i { 0 => true 1 | 2 | 3 => false @@ -146,7 +146,7 @@ fn is_zero(i: Int) -> Bool { - 构造器中可以嵌套模式进行匹配,或定义标识符绑定对应结构 ```moonbit -fn contains_zero(l: List[Int]) -> Bool { +fn contains_zero(l : List[Int]) -> Bool { match l { Nil => false Cons(0, _) => true @@ -159,7 +159,7 @@ fn contains_zero(l: List[Int]) -> Bool { - 多元组模式匹配需数量一一对应 ```moonbit -fn first(pair: (Int, Int)) -> Int { +fn first(pair : (Int, Int)) -> Int { match pair { (first, second) => first } @@ -168,7 +168,7 @@ fn first(pair: (Int, Int)) -> Int { - 结构体模式匹配可以匹配部分字段;可以不用另外命名标识符 ```moonbit -fn baby_name(info: PersonalInfo) -> Option[String] { +fn baby_name(info : PersonalInfo) -> String? { match info { { age: 0, .. } => None { name, age } => Some(name) @@ -181,7 +181,7 @@ fn baby_name(info: PersonalInfo) -> Option[String] { 我们试图缝合两个列表,生成一个数字与字符的二元组的列表,以最短者为准 ```moonbit -fn zip(l1: List[Int], l2: List[Char]) -> List[(Int ,Char)] { +fn zip(l1 : List[Int], l2 : List[Char]) -> List[(Int, Char)] { match (l1, l2) { (Cons(hd, tl), Cons(hd2, tl2)) => Cons((hd, hd2), zip(tl, tl2)) _ => Nil @@ -196,7 +196,7 @@ fn zip(l1: List[Int], l2: List[Char]) -> List[(Int ,Char)] { 需要注意到模式匹配的顺序是从上到下的 ```moonbit -fn zip(l1: List[Int], l2: List[Char]) -> List[(Int, Char)] { +fn zip(l1 : List[Int], l2 : List[Char]) -> List[(Int, Char)] { match (l1, l2) { _ => Nil // 编辑器会提示未使用的模式及无法抵达的代码 @@ -253,8 +253,8 @@ enum DaysOfWeek { - 每一种可能的情况即是构造器 ```moonbit -let monday: DaysOfWeek = Monday -let tuesday: DaysOfWeek = Tuesday +let monday : DaysOfWeek = Monday +let tuesday : DaysOfWeek = Tuesday ``` - 枚举类型定义可能重复,需要加上`<类型>::`加以区分 @@ -262,20 +262,20 @@ let tuesday: DaysOfWeek = Tuesday ```moonbit enum Repeat1 { A; B } enum Repeat2 { A; B } -let x: Repeat1 = Repeat1::A +let x : Repeat1 = Repeat1::A ``` # 枚举类型的意义 - 对比一下两个函数,枚举类型可以与现有类型区分开,更好地实现抽象 ```moonbit -fn tomorrow(today: Int) -> Int -fn tomorrow(today: DaysOfWeek) -> DaysOfWeek +fn tomorrow(today : Int) -> Int +fn tomorrow(today : DaysOfWeek) -> DaysOfWeek let tuesday = 1 * 2 // 这是周二吗? ``` - 禁止不合理数据的表示 ```moonbit -struct UserId { email: Option[String]; telephone: Option[Int] } +struct UserId { email : Option[String]; telephone : Option[Int] } enum UserId { Email(String) Telephone(Int) @@ -320,20 +320,20 @@ enum ComputeResult { - $1 \times n = n$ - 对于任意类型`T`,`(T, Unit)`与`T`同构 ```moonbit - fn[T] f1(t: T) -> (T, Unit) { (t, ()) } - fn[T] g1(pair: (T, Unit)) -> T { pair.0 } + fn[T] f1(t : T) -> (T, Unit) { (t, ()) } + fn[T] g1(pair : (T, Unit)) -> T { pair.0 } ``` - $0 + n = n$ - - 对于任意类型`T`,`enum PlusZero[T] { CaseT(T); CaseZero(Nothing) }`与`T`同构 + - 对于任意类型 `T`,`enum PlusZero[T] { CaseT(T); CaseZero(Nothing) }` 与 `T` 同构 ```moonbit - fn[T] f2(t: PlusZero) -> T { + fn[T] f2(t : PlusZero) -> T { match t { CaseT(t) => t CaseZero(_) => abort("对应集合为空,即不存在这样的值") } } - fn[T] g2(t: T) -> PlusZero { CaseT(t) } + fn[T] g2(t : T) -> PlusZero { CaseT(t) } ``` # 代数数据类型 @@ -342,14 +342,14 @@ enum ComputeResult { - $\texttt{Coins} = 1 + 1 = 2$ - `enum DaysOfWeek { Monday; Tuesday; ...; }` - $\texttt{DaysOfWeek} = 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7$ -- `List`的定义(以`List[Int]`为例): +- `List` 的定义(以 `List[Int]` 为例): $$ \begin{array}{r@{}l} \texttt{enum} \;\; \texttt{List} & = \texttt{Nil} + \texttt{Int} \times \texttt{List} \\ & = \texttt{1} + \texttt{Int} \times \texttt{List} \\ & = \texttt{1} + \texttt{Int} \times (\texttt{1} + \texttt{Int} \times \texttt{List} ) \\ & = \texttt{1} + \texttt{Int} \times \texttt{1} + \texttt{Int} \times \texttt{Int} \times 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