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> This relational framework captured Smolin’s imagination, as did Leibniz’s enigmatic text The Monadology, in which Leibniz suggests that the world’s fundamenta
by pcj_1000x 7y ago
> This relational framework captured Smolin’s imagination, as did Leibniz’s enigmatic text The Monadology, in which Leibniz suggests that the world’s fundamental ingredient is the “monad,”
If this is not evidence that Haskell is the language of the Gods, I don't know what is...
- avmich 7y agoMonads were used in APL language long before Haskell came to be. Surely all those are different monads though.
- 6thaccount2 7y agoThey are different...I can understand the APL ones. I have no idea what a "monoid in the category of endofunctors" means :)
- avmich 7y agoLook at this statement enough times over long enough period, and it starts making sense. "Category" is that central thing of the science of nodes and arrows between them. "Functor" is a mapping - a function - from a category to another category, where each node is mapped and each arrow is mapped according to node mapping. Like, if 1 in number category maps to A in character category, 2 maps to B, and there is an arrow 1->2 in number category, then this arrow should map to arrow A->B in character category. "Endofunctor" adds that the resulting category should in fact be the same as original. So, 1->2 can e.g. map to 3->4 in the same number category. "Monoid" is requirement that with the category we also have defined binary operation (let's call it X), that the operation is associative and also that category has "identity" node (let's call it I) - that is, for any A both operations A X I and I X A both produce A. It's like adding with zero. Now, this is not enough to understand monads - but it provides a foundation for what those monads, mathematically speaking, are. Consequences of these definitions can lead far :) .
- criloz2 7y agoI will not say Haskell, I will say the category theory, is all right there :)