[Haskell-cafe] Haskell function composition commutivity?

Dominic Steinitz dominic at steinitz.org
Wed Apr 14 12:42:18 UTC 2021

I’d recommend *not* reading Categories for the Working Mathematician unless you are a mathematician (lots of background assumed) and even then it’s a bit of a dull read.

Dominic Steinitz
dominic at steinitz.org
Twitter: @idontgetoutmuch

> From: Viktor Dukhovni <ietf-dane at dukhovni.org>
> To: haskell-cafe at haskell.org
> Subject: Re: [Haskell-cafe] Haskell function composition commutivity?
> Message-ID: <YHYPMnJcYzdEolzl at straasha.imrryr.org>
> Content-Type: text/plain; charset=us-ascii
> On Tue, Apr 13, 2021 at 02:19:46PM -0500, Galaxy Being wrote:
>> Your answers seem to originate outside of normal Haskell tutorials. Where
>> can I start with this higher superset theory?
> There's a reason why the tutorials don't cover this, the categorical
> foundations of Haskell types are not beginner material.  It is perhaps
> best to defer going down this rabbit hole until you're more comfortable
> with the Haskell generally.
> You could start with:
>    https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/
>    https://bartoszmilewski.com/2015/04/07/natural-transformations/
> For the Yoneda Lemma specifically, I'd recommend:
>    http://blog.sigfpe.com/2006/11/yoneda-lemma.html
> Parametricity is covered in "Theorems for free":
>    https://www2.cs.sfu.ca/CourseCentral/831/burton/Notes/July14/free.pdf
> but it is by no means elementary, though skimming it for the essential
> facts and skipping the gory details is not too difficult.
> You could also read "Categories for the Working Mathematician" by
> Saunders Mac Lane.

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