Proposal: unify constant functors

[wren ng thornton]

On 5/3/12 7:23 PM, Henning Thielemann wrote:
>
> On Thu, 3 May 2012, wren ng thornton wrote:
>
>> Indeed. I'm fine with Const (we don't call the value-level function k,
>> afterall), but Constant is just too much. Ditto for the excessively
>> lengthy naming of the identity functor. For things this basic and this
>> widely used, all that verbosity gives me flashbacks to coding in Java.
>
> It's not all bad in imperative languages ...

There's a difference between imperative programming in general, and Java 
programming in particular ;)


> Do you really use "Identity" everywhere? I use it only implicitly as
> part of transformers:State monads and friends.

Everywhere would be an exaggeration, but I do use it rather frequently. 
It helps reduce boilerplate when you want both pure and 
monadic/functorial (i.e., *->*) versions of things and don't care too 
much about performance. It's the monad of choice when instantiating 
rank-2 quantifiers. It's a primitive of generic programming with 
polynomial types, as Conor mentioned. etc.


> Identity's meaning is immediately clear. 'Ident' or 'Id' could also be
> 'identifier'.
>
> 'Const' could also mean 'constructor'.
>
> I also prefer 'Integer' to \mathbb{Z} and 'Rational' to \mathbb{Q}.

Should we rename 'id' to 'identity' and 'const' to 'constant' then? The 
purported confusion is exactly the same since there must be values to 
inhabit your identity and constructor types. If anything, you're only 
making an argument for K and I in lieu of Const and Id.

I'm fine with Integer, in virtue of the fact that it's unbounded and we 
have Int for the bounded version, so the lengthiness of the name 
actually conveys valuable information. Rational is in a similar position 
in virtue of the Ratio type it's an alias for. In mathematics I refer to 
those types often enough that having the names \mathbb{N}, \mathbb{Z}, 
\mathbb{Q}, \mathbb{R}, \mathbb{C},... is extremely helpful for brevity 
and clarity. In programming, I use them infrequently enough (compared to 
other types) that little would be gained by such brevity.

-- 
Live well,
~wren