Re: [Haskell-beginners] Extend instance for List

On December 15, 2015 12:36:58 PM GMT+02:00, Kim-Ee Yeoh wrote:

On Tue, Dec 15, 2015 at 12:43 AM, Graham Gill wrote:

I guessed that the correct Extend instance for List is needed for Comonad,

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but didn't have any intuition about it.

List is not comonadic. In this case, the function copure must be of type [a] -> a, which must necessarily be partial.

(Non-empty lists, on the other hand, are comonadic.) In fact, it seems this distinction is true of any type that has an empty case, i.e. f s.t. exists g. f a = 1 + g a. What blinded me was the fact that for such types, usually the definition of extend extends naturally to the empty case. So obviously the possibly-empty types have an Extend instance inherited from their nonempty counterparts, but it is only the latter who have Comonad instances.

Graham's "Extend" -- I'll explain the scare quotes in a minute -- instance for List obeys the associative law. So it's a valid instance but a bit boring. The exercise asks for an interesting instance. Indeed, the same problem exists dually for Monad, where one can force the empty case always and obtain a Monad isomorphic to Const ().

Thanks for the correction and illumination, Gesh

The way the NICTA course is structured, there's no mention of the

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dependence between "extend" and "copure" (equivalent to extract and duplicate I suppose) via the Comonad laws when considering Extend first by itself.

It's a bit terse, but you can find "class Extend f => Comonad f" in Comonad.hs. After all, we're only looking at the exercises. The live lecture version probably does talk about the dependence.

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I'm not knocking the NICTA course. I've found it useful. A quick paragraph or two as you've written, stuck into the source files as comments, would improve it.

Most folks are neutral about the course. If parts of it work for you, great. If not, no worries. The whole comonadic business is a bit obscure and some of the strongest haskell programmers don't bat an eyelid over not knowing it.

p.s. "Extend" doesn't agree with the CT literature. See the paragraph that starts "The dual problem is the problem of lifting a morphism" here:

http://ncatlab.org/nlab/show/extension

But calling it a "lift" or "lifting" will only add to the confusion since monad transformers got first dibs on the terminology. Which is why you sometimes see "coextend" or (for the flipped version) "cobind".

-- Kim-Ee

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