13 lines
596 B
HTML
13 lines
596 B
HTML
<h2 id="we-reinvented-monads">We reinvented Monads!</h2>
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<p>A monad is a triplet <code>(M,⊙,η)</code> where</p>
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<ul>
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<li>\(M\) an <span class="yellow">Endofunctor</span> (to type <code>a</code> associate <code>M a</code>)</li>
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<li>\(⊙:M×M→M\) a <span class="yellow">nat. trans.</span> (i.e. <code>⊙::M (M a) → M a</code> ; <code>join</code>)</li>
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<li>\(η:I→M\) a <span class="yellow">nat. trans.</span> (\(I\) identity functor ; <code>η::a → M a</code>)</li>
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</ul>
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<p>Satisfying</p>
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<ul>
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<li>\(M ⊙ (M ⊙ M) = (M ⊙ M) ⊙ M\)</li>
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<li>\(η ⊙ M = M = M ⊙ η\)</li>
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</ul>
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