Re:Ask HN: How to be fluent in functional language speak?
by pacala on Wednesday May 06, 2020 @01:24AM
(#23088120)
I like the way you frame CT. Never got too deep down this rabbit hole, the terminology is just too atrocius. I wonder though how useful it is in practice. It is easier for me to take a formula and generalize it among one dimension at a time as the needs arise, see the catamorphism example above. As opposed to correctly divine 5-10-15 very specific concretizations of an uber-abstract scheme to arrive to the same result. Echoes of premature abstraction.
Perhaps the world lacks CT for dummies. Teach it in primary school. New Math was not aggressive enough ;)
Yup, category theory is often called "general abstract nonsense" precisely because it manages to talk about many disparate parts of math (or programming!) in a way that purposely avoids any reference to the specific. To usefully interpret the above, you specifically need to know that your domain often uses the category (C) of types (as objects) and functions (as morphisms), and that this category features certain generic types (such as Option, List, Array etc.) as endofunctors - and then literally plug all of those into the definition and work out the result.
It's exactly the difference between (in an elementary context) a word problem, vs. the general theory of equations of type foo which could be used to solve any number of word problems - except replicated at a higher level.