Lazy pattern match

From HaskellWiki

What does "lazy pattern match" mean and what is the meaning of the tilde in pattern matches?

1 Syntax

These are all lazy pattern matches:

let (a,b) = p

f ~(a,b) = ...

case p of ~(a,b) -> ...

(\ ~(a,b) -> ... )

This seems to be quite arbitrary but this is how it is defined. That is, if you want to match constructors lazily in two levels then you have to write:

let (a, ~(b,c)) = p

f ~(a, ~(b,c)) = ...

case p of ~(a, ~(b,c)) -> ...

(\ ~(a, ~(b,c)) -> ... )

2 Meaning

What is the meaning of a lazy pattern match and why is it required sometimes?

The lazy pattern match on a pair as in

f ~(a,b) = g a b

can be translated to

f p = g (fst p) (snd p)

Generally, a lazy pattern match is translated to calling corresponding record field accessors.

The key difference between strict pattern match

f (a,b) = g a b

and lazy pattern match

f ~(a,b) = g a b

is that the strict pattern match requires to check for the pair constructor

In contrast to that, the lazy pattern match allows

without looking at its arguments

before matching the pair constructor.

This difference can be essential.

with lazy and strict pattern match. Here is the (correct) lazy implementation:

import Prelude hiding (splitAt)
 
splitAt :: Int -> [a] -> ([a], [a])
splitAt n xs =
   if n<=0
     then ([], xs)
     else
        case xs of
           [] -> ([], [])
           y:ys ->
              case splitAt (n-1) ys of
                 ~(prefix, suffix) -> (y : prefix, suffix)

Now try

Test> splitAt 1000000 $ repeat 'a'

With lazy pattern match

you see an answer immediately whereas with a strict pattern match the Haskell interpreter requires some time and memory before showing something. The reason is that the strict pattern match forces

in order to check whether they actually generate a pair constructor. This might look silly since the pair type has only one constructor

Furthermore this behavior is consistent with data types with more than one constructor.

then it might help to translate the tilde into pair element accessors

3 Implications

The lazy pattern match has some consequences. First of all a lazy pattern matches immediately always. Remember,

f ~(x:xs) = x:xs

is translated to

f ys = head ys : tail ys

That is with the lazy pattern match the order of matches counts. E.g.

f :: [a] -> [a]
f [] = []
f ~(x:xs) = x:xs

is fine but stupid, because the first match already requires the decision whether the list is empty or not. But the reversed order

f :: [a] -> [a]
f ~(x:xs) = x:xs
f [] = []

because the first case already matches always.

You may have also noted the danger caused by a lazy pattern match. Since the lazy pattern match on a non-empty list

because these functions are not total. That is, generally it is good style to avoid lazy pattern matches on types with more than one constructor.

Categories: Glossary | Idioms