add nats: natural numbers for lazy unfoldable

[matthewleon]

following conversation here: #11

This adds a dependency.

I've tested the laziness here: https://github.com/matthewleon/purescript-lists/tree/test-nats

[paf31]

I don't think you need defer here, since any lazy structure should use it anyway. Did you try this on lazy lists?

[matthewleon]

Yes, you are right. Will fix.

[paf31]

No need for this any more, right?

[paf31]

f might be lazy but in the wrong way. I think we need a comment to say that the result is actually infinite.

[matthewleon]

done

…

On Sun, Dec 10, 2017 at 6:45 PM, Phil Freeman ***@***.***> wrote: ***@***.**** commented on this pull request. ------------------------------ In src/Data/Unfoldable.purs <#12 (comment)> : > @@ -88,6 +89,13 @@ none = unfoldr (const Nothing) unit singleton :: forall f a. Unfoldable f => a -> f a singleton = replicate 1 +-- | Produce a Lazy Unfoldable structure representing the natural numbers. +nats :: forall f a. Unfoldable f => Semiring a => Lazy (f a) => f a f might be lazy but in the wrong way. I think we need a comment to say that the result is actually infinite. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#12 (review)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AARBS_j8t9nZUVDrtCkIjfe34rZglR8Rks5s_G0NgaJpZM4Q1cF4> .

[hdgarrood]

Can we generalise this to iterate :: forall f a. Unfoldable f => Lazy (f a) => (a -> a) -> a -> f a? So you could reconstruct nats via nats = iterate add zero?

[matthewleon]

Good call.

[hdgarrood]

A couple nitpicks I've noticed which are no longer relevant if we are generalising to iterate, but you might want to think about if you're defining nats elsewhere: some definitions of the natural numbers include zero and others don't, so I guess you'd at least want to say which one your nats is using (in fact, I guess it's more or less equally likely for people to want to use either version, which is mostly what led me to the above suggestion). Also, the result can't really be described as representing the natural numbers in cases where your semiring is finite; a good example of a finite semiring is the integers modulo n.