"use strict"; const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { code: "code", li: "li", p: "p", pre: "pre", span: "span", strong: "strong", ul: "ul", ..._provideComponents(), ...props.components }; return _jsxs(_Fragment, { children: [_jsxs(_components.p, { children: ["下面通过一个综合示例，展示 Functor、Applicative、Monad 三种抽象是如何在 Haskell 中配合使用的。考虑一个简单的场景：我们想从配置中读取两个整数，然后将它们相加，但在读取过程中可能会失败（比如键不存在）。我们可以使用 ", _jsx(_components.code, { className: "language-auto", children: "Maybe" }), " Monad 来处理可能的失败，通过组合 Functor 和 Applicative 的功能来方便地进行计算："] }), "\n", _jsx(_components.pre, { className: "language-haskell", children: _jsxs(_components.code, { className: "language-haskell code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsxs(_components.span, { className: "token import-statement", children: [_jsx(_components.span, { className: "token keyword", children: "import" }), " Data", _jsx(_components.span, { className: "token punctuation", children: "." }), "Maybe"] }), " ", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token hvariable", children: "fromMaybe" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "-- 假设的配置读取函数" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "lookupInt" }), " ", _jsx(_components.span, { className: "token operator", children: "::" }), " ", _jsx(_components.span, { className: "token constant", children: "String" }), " ", _jsx(_components.span, { className: "token operator", children: "->" }), " ", _jsx(_components.span, { className: "token constant", children: "Maybe" }), " ", _jsx(_components.span, { className: "token constant", children: "Int" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "lookupInt" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token operator", children: "..." }), " ", _jsx(_components.span, { className: "token comment", children: "-- （这里省略实现，假设从配置中取整数）" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "-- 使用 Functor 提升纯函数到带上下文的计算" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "incrementConfig" }), " ", _jsx(_components.span, { className: "token operator", children: "::" }), " ", _jsx(_components.span, { className: "token constant", children: "String" }), " ", _jsx(_components.span, { className: "token operator", children: "->" }), " ", _jsx(_components.span, { className: "token constant", children: "Maybe" }), " ", _jsx(_components.span, { className: "token constant", children: "Int" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "incrementConfig" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token operator", children: "+" }), _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token operator", children: "<$>" }), " ", _jsx(_components.span, { className: "token hvariable", children: "lookupInt" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "-- (<$>) 是 fmap 的别名，将 lookupInt 返回的 Maybe Int 中的值加1" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "-- 使用 Applicative 同时读取两个配置项并相加" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "addConfigs" }), " ", _jsx(_components.span, { className: "token operator", children: "::" }), " ", _jsx(_components.span, { className: "token constant", children: "String" }), " ", _jsx(_components.span, { className: "token operator", children: "->" }), " ", _jsx(_components.span, { className: "token constant", children: "String" }), " ", _jsx(_components.span, { className: "token operator", children: "->" }), " ", _jsx(_components.span, { className: "token constant", children: "Maybe" }), " ", _jsx(_components.span, { className: "token constant", children: "Int" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "addConfigs" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key1" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key2" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token operator", children: "+" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token operator", children: "<$>" }), " ", _jsx(_components.span, { className: "token hvariable", children: "lookupInt" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key1" }), " ", _jsx(_components.span, { className: "token operator", children: "<*>" }), " ", _jsx(_components.span, { className: "token hvariable", children: "lookupInt" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key2" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "-- (<*>) 将第一个 Maybe 中的函数应用到第二个 Maybe 中的值" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "-- 使用 Monad 串联多个步骤的计算" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "combinedCalc" }), " ", _jsx(_components.span, { className: "token operator", children: "::" }), " ", _jsx(_components.span, { className: "token constant", children: "String" }), " ", _jsx(_components.span, { className: "token operator", children: "->" }), " ", _jsx(_components.span, { className: "token constant", children: "String" }), " ", _jsx(_components.span, { className: "token operator", children: "->" }), " ", _jsx(_components.span, { className: "token constant", children: "Maybe" }), " ", _jsx(_components.span, { className: "token constant", children: "Int" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token hvariable", children: "combinedCalc" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key1" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key2" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token keyword", children: "do" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token hvariable", children: "x" }), " ", _jsx(_components.span, { className: "token operator", children: "<-" }), " ", _jsx(_components.span, { className: "token hvariable", children: "lookupInt" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key1" }), " ", _jsx(_components.span, { className: "token comment", children: "-- Monad: 取出第一个配置值，若 Nothing 则传播" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token hvariable", children: "y" }), " ", _jsx(_components.span, { className: "token operator", children: "<-" }), " ", _jsx(_components.span, { className: "token hvariable", children: "incrementConfig" }), " ", _jsx(_components.span, { className: "token hvariable", children: "key2" }), " ", _jsx(_components.span, { className: "token comment", children: "-- Monad: 取出第二个配置值并在 Monad 内部加1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token builtin", children: "return" }), " ", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token hvariable", children: "x" }), " ", _jsx(_components.span, { className: "token operator", children: "+" }), " ", _jsx(_components.span, { className: "token hvariable", children: "y" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token comment", children: "-- 返回相加结果（自动包装为 Just 或 Nothing）" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" })] }) }), "\n", _jsx(_components.p, { children: "在上述代码中：" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.code, { className: "language-auto", children: "incrementConfig" }), " 利用 Functor (", _jsx(_components.code, { className: "language-auto", children: "<$>" }), ") 将普通加法函数提升为可作用于 ", _jsx(_components.code, { className: "language-auto", children: "Maybe" }), " 的函数，实现读取配置值后加 1 的操作。如果配置缺失导致 ", _jsx(_components.code, { className: "language-auto", children: "lookupInt key" }), " 返回 ", _jsx(_components.code, { className: "language-auto", children: "Nothing" }), "，那么 ", _jsx(_components.code, { className: "language-auto", children: "fmap" }), " 会让结果依然是 ", _jsx(_components.code, { className: "language-auto", children: "Nothing" }), "（因为无法对不存在的值加1）。"] }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.code, { className: "language-auto", children: "addConfigs" }), " 使用 Applicative (", _jsx(_components.code, { className: "language-auto", children: "<$>" }), " 和 ", _jsx(_components.code, { className: "language-auto", children: "<*>" }), ") 实现", _jsx(_components.strong, { children: "并行的" }), "计算：同时读取两个配置项，并将它们相加。如果任意一个配置项不存在，整个结果就是 ", _jsx(_components.code, { className: "language-auto", children: "Nothing" }), "；只有当两个都是 ", _jsx(_components.code, { className: "language-auto", children: "Just" }), " 时才会得到 ", _jsx(_components.code, { className: "language-auto", children: "Just" }), " 的和。这体现了 Applicative 可以方便地组合独立的效果。"] }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.code, { className: "language-auto", children: "combinedCalc" }), " 则使用 Monad 的 ", _jsx(_components.code, { className: "language-auto", children: "do" }), " 表达式串联步骤：首先读取 ", _jsx(_components.code, { className: "language-auto", children: "key1" }), " 对应的值赋给 ", _jsx(_components.code, { className: "language-auto", children: "x" }), "，如果失败直接返回 ", _jsx(_components.code, { className: "language-auto", children: "Nothing" }), "；接着在 Monad 上下文中调用前面的 ", _jsx(_components.code, { className: "language-auto", children: "incrementConfig key2" }), "（这实际上使用了先 Functor 再 Monad 的组合能力），取得 ", _jsx(_components.code, { className: "language-auto", children: "y" }), "；最后返回 ", _jsx(_components.code, { className: "language-auto", children: "x+y" }), "。这里，", _jsx(_components.code, { className: "language-auto", children: "do" }), " 表达式背后用到了 ", _jsx(_components.code, { className: "language-auto", children: ">>=" }), " 来传递 ", _jsx(_components.code, { className: "language-auto", children: "x" }), " 和 ", _jsx(_components.code, { className: "language-auto", children: "y" }), "，使我们无需手动检查 ", _jsx(_components.code, { className: "language-auto", children: "Nothing" }), "，逻辑更清晰。"] }), "\n"] }), "\n"] }), "\n", _jsxs(_components.p, { children: ["通过这个例子可以看到，Functor 提供了对", _jsx(_components.strong, { children: "单一上下文" }), "中的值进行映射的能力，Applicative 提供了处理", _jsx(_components.strong, { children: "独立多个上下文" }), "的手段，而 Monad 则允许表达", _jsx(_components.strong, { children: "顺序依赖的上下文计算" }), "。它们各自对应的范畴论结构（函子、带单位元的函子、幺半群）确保了这些操作符满足良好的代数规律，使我们能够在代码中放心地组合它们而不引入歧义或不一致。"] })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = { ..._provideComponents(), ...props.components }; return MDXLayout ? _jsx(MDXLayout, { ...props, children: _jsx(_createMdxContent, { ...props }) }) : _createMdxContent(props); } return { default: MDXContent };

Links to this page: