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Stop pretending studying arrow theory improves your apping

Name: Anonymous 2015-03-11 7:12

Given two functors S,T:C→B, a natural transformation τ:S→T is a function which assigns to each object c of C an arrow τc=τc:Sc→TC of B in such a way that every arrow f:c→c' in C yields a diagram
ᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠτc
c ᅠᅠ Sc---→Tc
|ᅠᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠᅠᅠᅠᅠ|
|fᅠᅠᅠᅠᅠSf↓ᅠᅠᅠᅠᅠ↓Tf
↓ᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠτc'ᅠᅠ|
c', ᅠᅠᅠ Sc'--→Tc'


which is commutative. When this holds, we also say that τc=τc:Sc→Tc is natural in c. If we think of the functor S as giving a picture in B of (all the objects and arrows of) C, then a natural transformation τ is the set of arrows mapping (or, translating) the picture S to the picture T, with all squares (and parallelograms!) like that above commutative:
ᅠaᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠSa----------→Ta
ᅠ|ᅠ╲fᅠᅠᅠᅠᅠᅠᅠ ᅠ|ᅠ╲Sfᅠᅠᅠᅠᅠᅠᅠᅠᅠ|ᅠ╲Tf
ᅠ|ᅠᅠᅠ↘ᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠ↘ᅠᅠᅠτbᅠᅠᅠ|ᅠᅠᅠ↘
ᅠ|ᅠᅠᅠᅠᅠbᅠᅠᅠᅠ ᅠ|ᅠᅠᅠᅠSb----------→Tb
ᅠ|ᅠᅠᅠ╱ᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠ╱ᅠᅠᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠ╱
↓ᅠ↙ᅠᅠᅠᅠᅠᅠ ᅠ↓↙Sgᅠᅠᅠᅠᅠᅠᅠᅠ↓ᅠ↙Tg
ᅠcᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠSc----------→Tc

Name: Anonymous 2015-03-14 18:13

>>34
You can add numbers in OCaml. It doesn't do implicit conversions for you because that is some weakass shit right there.

No it hasn't.
If Haskell sucks so hard you need to deny reality to support your choice that's your problem.

I don't get why people even bother with Haskell when things like Idris exists. You might as well take advantage of the code inference and so on.

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