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initial_algebra [2014/09/28 17:36] nikolaj |
initial_algebra [2014/09/28 18:00] nikolaj |
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=== Examples === | === Examples === | ||
- | In the following, we give some examples. Note that one can "automatize" some of repeating features of the discussed catamorphisms, see [[http://www.haskell.org/haskellwiki/Catamorphisms|haskellwiki/Catamorphisms]]. I've also translated the examples and the general case Haskell code on the Wikipedia page [[http://en.wikipedia.org/wiki/Catamorphism|Catamorphism]]. | + | In the following, we give some examples. Note that one can "automatize" some of repeating features of the discussed catamorphisms, see [[http://www.haskell.org/haskellwiki/Catamorphisms|haskellwiki/Catamorphisms]]. I've also translated the examples and the general case Haskell code on [[http://en.wikipedia.org/wiki/Catamorphism|wikipedia/Catamorphism]]. |
$\{\text{Nothing}\}$ is any fixed singleton/unit type, $L+R$ denotes the disjoint union/sum type of $L$ and $R$ and "[left,right]" is notation for a conditional function on $L+R$. Instead of ${\bf Set}$, any category with terminal object, sums and products will do. | $\{\text{Nothing}\}$ is any fixed singleton/unit type, $L+R$ denotes the disjoint union/sum type of $L$ and $R$ and "[left,right]" is notation for a conditional function on $L+R$. Instead of ${\bf Set}$, any category with terminal object, sums and products will do. | ||
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Haskellwiki: | Haskellwiki: | ||
- | [[http://www.haskell.org/haskellwiki/Catamorphisms|haskellwiki/Catamorphisms]] | + | [[http://www.haskell.org/haskellwiki/Catamorphisms|Catamorphisms]] |
==== Parents ==== | ==== Parents ==== | ||
=== Context* === | === Context* === |