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Coalgebra December 8, 2008

Posted by dcorfield in Uncategorized.
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I posted on coalgebra over at my other blog. I won’t rehash the material of the discussion over here. But I’m still searching for an answer to the question I had of whether coalgebra has been formalised slowly due to algebraic blinkers.

A highlight for me was this comment from Dan Piponi, where he explains about how one needs to employ guarded recursion to work with ‘codata’. He says

In the real world of open ended loops like OSes and word processors, it’s often not computability we need, but productivity (absolutely no pun intended). And that makes coalgebraic reasoning an important topic.

Operating systems don’t require the totality of input in order to calculate a response by recursively breaking it into its atomic parts and deriving a function’s value by recomposition. They respond as each piece of new input arrives.

Coalgebra throws up a whole load of infinitely large entities.