[Haskell-cafe] Re: Theory about uncurried functions

[Achim Schneider]

Peter Verswyvelen <bugfact at gmail.com> wrote:

> Maybe this raises a new question: does understanding category theory
> makes you a better *programmer*?
>
Possibly yes, possibly no. In my experience, you have to have a look at
how CT is applied to other fields to appreciate its clarity. Doing so,
you may succeed in promoting some of your understanding of code to a
more general level. I see abstract nonsense as way less fuzzy than
lambda-based abstraction, and a lot more flexible (mentally speaking)
than type theory, or logic, in general. The fact that it encompasses
both makes it even more attractive (although you can express both of
them in terms of the other as it stands)

There's not much to understand about CT, anyway: It's actually nearly
as trivial as set theory. One part of the benefit starts when you begin
to categorise different kind of categories, in the same way that
understanding monads is easiest if you just consider their difference
to applicative functors. It's a system inviting you to tackle a problem
with scrutiny, neither tempting you to generalise way beyond
computability, nor burdening you with formal proof requirements or
shackling you to some other ball and chain.

Sadly, almost all texts about CT are absolutely useless: They
tend to focus either on pure mathematical abstraction, lacking
applicability, or tell you the story for a particular application of CT
to a specific topic, loosing themselves in detail without providing the
bigger picture. That's why I liked that Rosetta stone paper so much: I
still don't understand anything more about physics, but I see how
working inside a category with specific features and limitations is the
exact right thing to do for those guys, and why you wouldn't want to do
a PL that works in the same category.


Throwing lambda calculus at a problem that doesn't happen to be a DSL
or some other language of some sort is a bad idea. I seem to understand
that for some time now, being especially fond of automata[1] to model
autonomous, interacting agents, but CT made me grok it. The future will
show how far it will pull my thinking out of the Turing tarpit.


[1] Which aren't, at all, objects. Finite automata don't go bottom in
    any case, at least not if you don't happen to shoot them and their
    health drops below zero.

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