Lazy Patterns (was: Curry module system and other proposals)

From: Wolfgang Lux <wlux_at_uni-muenster.de>
Date: Tue, 28 Feb 2006 13:50:25 +0100

Michael Hanus wrote:

> Moreover, I am not sure whether the semantic consequences of
> the little tilde in definitions like
>
> f x ~(False:ys) = if x==0 then ys else []
> f x (True:ys) = ys
>
> (note that without the tilde f is inductively sequential, whereas
> with the tilde f is overlapping) should be made explicit by
> a let declaration as in
>
> f x y = let (False:ys)=y in if x==0 then ys else []
> f x (True:ys) = ys

I agree that in the latter definition it is more obvious that f has
overlapping patterns, but I doubt that anybody would intend to write
such as definition.

> Do you have examples showing that it is worth to hide these
> consequences
> in a tilde annotation instead of a let?

Quite obviously, lazy patterns are most useful in declarations with
only a single rule (because otherwise they are likely to give rise to
unintended non-determinism).

One kind of such examples is tuples. For instance, you can define the
prelude function unzip with a simple fold and a lambda as follows

   unzip = foldr (\(x,y) ~(xs,ys) -> (x:xs,y:ys)) ([],[])

using a let declaration in the lambda expression

   unzip = foldr (\(x,y) xys -> let (xs,ys) = xys in (x:xs,y:ys)) ([],
[])

looks a bit clumsy to me.

Another kind of examples where lazy patterns are useful are lazy stream
processors. As an example, consider a stream of integers where after
every
third integer you want to a insert a sum of those numbers, but at the
same time want to be as lazy as possible so that
   head (process (1:undefined)) = 1
With lazy patterns you would do this as follows

   process (x : ~(y : ~(z : rest)) = x : y : z : (x+y+z) : process rest

Without lazy patterns, you would have to use something like

   process (x : rest1) = x : y : z : (x+y+z) : process rest3
     where y : rest2 = rest1
           z : rest3 = rest2

which, IMHO, is considerably less readable than the version using lazy
patterns and also in danger of mixing up the rest? variables.

Regards
Wolfgang


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Received on Di Feb 28 2006 - 16:59:33 CET

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