[Haskell-cafe] MonadRandom and traversing infinite streams

[Petr Pudlák]

Hi Brent and Wouter,

looking at SO questions

http://stackoverflow.com/q/14494648/1333025
http://codereview.stackexchange.com/q/52149/15600

threre are monads and applicative functors that support

```
sequenceInf :: S.Stream (f a) -> f (S.Stream a)
```

that is, allow lazy traversals of streams (infinite lists). Namely those
that don't produce any additional output.

And instances of MonadRandom seem to have valid implementations of
`sequenceInf`, which would allow to produce lazy infinite randomized lists
(basically a generalization of `getRandoms`).

My proposal is to add

```
class Applicative f => LazyApplicative f where
    sequenceInf :: S.Stream (f a) -> f (S.Stream a)
    sequenceInf = traverseInf id

    traverseInf :: (a -> f b) -> S.Stream a -> f (S.Stream b)
    traverseInf f = sequenceInf . S.map f
```

to a module in Stream package (for example `Control.Applicative.Lazy`), and
add its instances into `MonadRandom`.

What do you think? I'd be willing to send patches.

  Best regards,
  Petr
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