blocks|key|2582897|text|重要的是要知道，能够组合事物并不一定意味着它们是么半群。要成为么半群，它必须具有结合性、左单位和右单位。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2582898|C#：|2582899|public+static+Func<Guid,+int>+Combine(
++++Func<Guid,+int>+f,
++++Func<Guid,+int>+g)
{
++++return+x+=>+f(x)+%2B+g(x);
}|code-block|syntax|javascript|2582900|JS：|2582901|function+combine(f,g)+{
++++return+x+=>+f(x)+%2B+g(x)
}

function+addOne(x)+{
++return+x+%2B+1;
}

function+addTwo(x)+{
++return+x+%2B+2;
}

let+newFunction+=+combine(addOne,+addTwo);
let+result+=+newFunction(0);
console.log(result)|2582902|​|2582903|entityMap^0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|Q|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|R|8|@]|9|@]|A|$]]|$1|D|3|E|5|F|7|S|8|@]|9|@]|A|$G|H]]|$1|I|3|J|5|6|7|T|8|@]|9|@]|A|$]]|$1|K|3|L|5|F|7|U|8|@]|9|@]|A|$G|H]]|$1|M|3|N|5|6|7|V|8|@]|9|@]|A|$]]|$1|O|3|-4|5|6|7|W|8|@]|9|@]|A|$]]]|P|$]]

<p>It's important to know that being able to combine things doesn't necessarily mean they are a monoid.  For something to be a Monoid, it must have associativity, left identity, and right identity.  </p>

<p>C#:</p>

<pre class="lang-cs prettyprint-override"><code>public static Func&lt;Guid, int&gt; Combine(
    Func&lt;Guid, int&gt; f,
    Func&lt;Guid, int&gt; g)
{
    return x =&gt; f(x) + g(x);
}
</code></pre>

<p>JS:
<div class="snippet" data-lang="js" data-hide="false" data-console="true" data-babel="false">
<div class="snippet-code">
<pre class="snippet-code-js lang-js prettyprint-override"><code>function combine(f,g) {
    return x =&gt; f(x) + g(x)
}

function addOne(x) {
  return x + 1;
}

function addTwo(x) {
  return x + 2;
}

let newFunction = combine(addOne, addTwo);
let result = newFunction(0);
console.log(result)</code></pre>
</div>
</div>
</p>


blocks|key|2794637|text|Monoid+Laws|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|2794638|2794639|同一性法则：|blockquote|2794640|2794641|combine+(identity,+a)+==+combine+(a,+identity)|style|CODE|2794642|结合性定律：|2794643|combine+(a,+combine+(b,+c))+==+combine+(combine+(a,+b),+c)|2794644|2794645|我们可以为函数实现身份元素(identity)和二元运算(combine)+-|2794646|​|2794647|//+identity+element
const+identity+=
++x+=>+x

//+binary+operation
const+combine+=+(a,+b)+=>
++x+=>+a+(b+(x))
+
//+sample+functions
const+a+=
++x+=>+x+%2B+3
++
const+b+=
++x+=>+x+-+1

const+c+=
++x+=>+x+*+x

//+uphold+laws
console.log
++(+combine+(identity,+a)+(2)+===+combine+(a,+identity)+(2)
++,+combine+(a,+combine+(b,+c))+(2)+===+combine+(combine+(a,+b),+c)+(2)
++)
++
//+=>+true
//+=>+true|code-block|syntax|javascript|2794648|2794649|根据您的域，二元运算和标识元素会有所不同。有关如何为各种集合实现标识元素和二进制操作的更多信息，请参阅Wikipedia上的表格。|2794650|当然，您并不局限于这些域。您的自定义类型可能具有满足么半群定律的各种二元运算和标识元素。如果法律得到支持，你的类型就属于么半群类别。|2794651|entityMap|0|LINK|mutability|MUTABLE|url|https://en.wikipedia.org/wiki/Monoid|1|https://en.wikipedia.org/wiki/Identity_element^0|0|B|0|0|0|0|0|0|1A|0|0|0|1M|0|0|E|8|T|7|0|0|0|0|1F|9|1|0|0^^$0|@$1|2|3|4|5|6|7|1F|8|@]|9|@$A|1G|B|1H|1|1I]]|C|$]]|$1|D|3|-4|5|6|7|1J|8|@]|9|@]|C|$]]|$1|E|3|F|5|G|7|1K|8|@]|9|@]|C|$]]|$1|H|3|-4|5|6|7|1L|8|@]|9|@]|C|$]]|$1|I|3|J|5|6|7|1M|8|@$A|1N|B|1O|K|L]]|9|@]|C|$]]|$1|M|3|N|5|6|7|1P|8|@]|9|@]|C|$]]|$1|O|3|P|5|6|7|1Q|8|@$A|1R|B|1S|K|L]]|9|@]|C|$]]|$1|Q|3|-4|5|6|7|1T|8|@]|9|@]|C|$]]|$1|R|3|S|5|6|7|1U|8|@$A|1V|B|1W|K|L]|$A|1X|B|1Y|K|L]]|9|@]|C|$]]|$1|T|3|U|5|6|7|1Z|8|@]|9|@]|C|$]]|$1|V|3|W|5|X|7|20|8|@]|9|@]|C|$Y|Z]]|$1|10|3|U|5|6|7|21|8|@]|9|@]|C|$]]|$1|11|3|12|5|6|7|22|8|@]|9|@$A|23|B|24|1|25]]|C|$]]|$1|13|3|14|5|6|7|26|8|@]|9|@]|C|$]]|$1|15|3|-4|5|6|7|27|8|@]|9|@]|C|$]]]|16|$17|$5|18|19|1A|C|$1B|1C]]|1D|$5|18|19|1A|C|$1B|1E]]]]

<p><a href="https://en.wikipedia.org/wiki/Monoid" rel="nofollow noreferrer">Monoid Laws</a></p>
<blockquote>
<p>identity law:<br />
<code>combine (identity, a) == combine (a, identity)</code></p>
<p>associativity law:<br />
<code>combine (a, combine (b, c)) == combine (combine (a, b), c)</code></p>
</blockquote>
<p>We can implement an <em>identity element</em> (<code>identity</code>) and <em>binary operation</em> (<code>combine</code>) for functions -</p>
<p><div class="snippet" data-lang="js" data-hide="false" data-console="true" data-babel="false">
<div class="snippet-code">
<pre class="snippet-code-js lang-js prettyprint-override"><code>// identity element
const identity =
  x =&gt; x

// binary operation
const combine = (a, b) =&gt;
  x =&gt; a (b (x))
 
// sample functions
const a =
  x =&gt; x + 3
  
const b =
  x =&gt; x - 1

const c =
  x =&gt; x * x

// uphold laws
console.log
  ( combine (identity, a) (2) === combine (a, identity) (2)
  , combine (a, combine (b, c)) (2) === combine (combine (a, b), c) (2)
  )
  
// =&gt; true
// =&gt; true</code></pre>
</div>
</div>
</p>
<p>The binary operation and identity element is different depending on your domain. See the table on <a href="https://en.wikipedia.org/wiki/Identity_element" rel="nofollow noreferrer">Wikipedia</a> for more insight on how to implement the identity element and binary operation for various sets.</p>
<p>Of course you are not limited to those domains. Your custom type may have various binary operations and identity elements that satisfy the monoid laws. If the laws are upheld, your type belongs to the monoid category.</p>


<p>In <a href="https://blog.ploeh.dk/2017/11/06/function-monoids/" rel="nofollow noreferrer">this article</a> Function Monoids are introduced with C# code and Haskell Type definition.</p>

<blockquote>
  <p>A function <code>a -&gt; b</code> is a monoid if <code>b</code> is a monoid. This means that
  you can combine two functions with the same type. In an
  object-oriented context, it means that you can combine two methods
  with the same signature into one method as long as the return type
  forms a monoid.</p>
  
  <h2>Generalisation</h2>
  
  <p>While the above C# code is only an example, the general rule is that
  any function that returns a monoid is itself a monoid. In Haskell,
  this rule is articulated in the standard library:</p>

<pre><code>instance Monoid b =&gt; Monoid (a -&gt; b)
</code></pre>
  
  <p>This means that for any monoid <code>b</code>, a function <code>a -&gt; b</code> is also
  (automatically) a monoid.</p>
</blockquote>

<p>The problem is the example in C# is too specific about "GUID" and I have no idea what the author trying to do in the code, and the Haskell Type Definition is merely the type definition.</p>

<p>What is an example code in JavaScript to implement this Function Monoids?</p>

<p>cf)
<a href="https://www.reddit.com/r/haskellquestions/comments/6j4ct9/why_is_instance_monoid_b_monoid_a_b_in_base/" rel="nofollow noreferrer">Why is <code>instance Monoid b =&gt; Monoid (a -&gt; b)</code> in base?</a></p>


What is the binary operator of Function Monoids in example of JavaScript

在函数中，通过C#代码和Haskell类型定义引入了么半群。如果b是么半群，则函数a -> b是么半群。这意味着您可以组合两个相同类型的函数。在面向对象的上下文中，这意味着只要返回类型形成monoid，就可以将具有相同签名的两个方法组合成一个方法。泛化虽然上面的C#代码只是一个示例，但一般规则是，任何返回么半群的函数本...

问在JavaScript的例子中，函数么半群的二元算子是什么
EN

社区

活动

资源

关于

腾讯云开发者

热门产品

热门推荐

更多推荐

问在JavaScript的例子中，函数么半群的二元算子是什么EN

社区

活动

资源

关于

腾讯云开发者

热门产品

热门推荐

更多推荐

问在JavaScript的例子中，函数么半群的二元算子是什么
EN