20 lines
936 B
Markdown
20 lines
936 B
Markdown
Natural Transformation Examples (2/4)
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<pre><code class="haskell small">data Tree a = Empty | Node a [Tree a]
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toList :: Tree a -> [a]
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toList Empty = []
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toList (Node x l) = [x] ++ concat (map toList l)</pre></code>
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`toList` is a natural transformation.
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It is also a morphism from `Tree` to `[]` in the Category of \\(\\Hask\\) endofunctors.
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<img style="float:left;width:30%" src="categories/img/mp/nattrans-tree-list.png" alt="natural transformation commutative diagram"/>
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<figure style="float:right;width:60%">
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<img style="width:40%" src="categories/img/mp/tree-list-endofunctor-morphism.png" alt="natural transformation commutative diagram"/>
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<figcaption><code>toList . toTree = id</code> & <code>toTree . toList = id</code> <span style="visibility:hidden">&</span><br/>
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therefore <code>[]</code> & <code>Tree</code> are <span class="yellow">isomorph</span>.
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</figcaption>
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</figure>
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