On Jul25, apfelmus wrote:
> The point is to be
> able to define both zip and pairs with one and the same operator :< .
There's actually a quite simple way of doing this. You make the view
type polymorphic, but not in the way you did:
type Queue elt
empty :: Queue elt
cons :: elt -> Queue elt -> Queue elt
data ViewL elt rec = EmptyL
| elt :< rec
view :: Queue elt -> ViewL elt (Queue elt)
view2 :: Queue elt -> ViewL elt (ViewL elt (Queue elt))
That is, the result of the view type is a parameter, so you can
instantiate it with both the viewed type and another view (and so on if
you want more levels).
Then the client code looks like this:
myzip :: Queue a -> Queue b -> Queue (a,b)
myzip a b = case (view a, view b) of
(EmptyL, _) -> empty
(_, EmptyL) -> empty
(h1 :< t1, h2 :< t2) -> (h1,h2) `cons` myzip a b
pairs :: Queue a -> Queue (a,a)
pairs a = case view2 a of
h1 :< (h2 :< t) -> (h1, h2) `cons` pairs t
_ -> empty
The only difference with view patterns is that you can do the view2
inside the pattern itself:
pairs (view2 -> h1 :< (h2 :< t)) = (h1,h2) `cons` pairs t
pairs _ = empty
This would be useful if the thing you were viewing were deep inside
another pattern.
This is a well-known technique in the ML community; see, e.g.,
http://www.cs.cmu.edu/~tom7/papers/wizard.pdf
-Dan
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