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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 21:15

There's nothing implicit in the example I've posted.
More lies. There's an implicit type mismatch (or domain error if you prefer.)

Oh and you haven't posted any proof that OCaml's multicore support has been improved.
I'll play Google for you once you prove a single one of your ridiculous claims.

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