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# Question 2.9 - Programming with categories

edited January 19

Programming with categories.

Tell a story about what's going on in this course. Is there an example you find interesting or enlightening, or just fun? Have you had any a-ha! moments? Share one.

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1.
edited January 20

I appreciated seeing -- through the course videos -- that the concept of a functor is exactly what is needed to define the meaning of a polymorphic datatype.

And similarly the concept of a natural transformation is just what the doctor ordered for describing the meaning of a polymorphic function.

Comment Source:I appreciated seeing -- through the course videos -- that the concept of a functor is exactly what is _needed_ to define the meaning of a polymorphic datatype. And similarly the concept of a natural transformation is just what the doctor ordered for describing the meaning of a polymorphic function.
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2.
edited January 20

I appreciate this as a meaningful application of category theory. True, it's being applied to other theory, but that's still an application. And it is useful.

Category theory describes the semantics of Haskell programs, which can do empirically useful things. The theory can be used to prove the correctness of these programs. That's empirically useful!

Comment Source:I appreciate this as a meaningful application of category theory. True, it's being applied to other theory, but that's still an application. And it is useful. Category theory describes the semantics of Haskell programs, which can do empirically useful things. The theory can be used to prove the correctness of these programs. That's empirically useful! 
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3.

I had an a-ha moment when they showed the intuition of Functors from trivial categories (like 1, 2, 3) to any category C and how they describe ways of picking objects and morphisms. :)

Comment Source:I had an a-ha moment when they showed the intuition of Functors from trivial categories (like 1, 2, 3) to any category C and how they describe ways of picking objects and morphisms. :)