# [Haskell-cafe] help understanding lazy evaluation

Xavier Noria fxn at hashref.com
Wed Aug 22 19:08:25 EDT 2007

```I am learning Haskell with "Programming in Haskell" (an excellent
book BTW).

I have background in several languages but none of them has lazy
evaluation. By now I am getting along with the intuitive idea that
things are not evaluated until needed, but there's an example I don't
understand (which means the intuitive idea needs some revision :-).

We have factors(), defined on page 39 like this[*]:

factors :: Int -> [Int]
factors n = [x | x <- [1..n], n `mod` x == 0]

and we base prime() on it this way:

prime :: Int -> Bool
prime n = factors n == [1, n]

Now, the books says prime does not necessarily compute all of the
factors of n because of lazy evaluation. Meaning that if n is
composite as soon as some non-trivial divisor appears we halt
computation and return False.

My vague intuition said "we either need factors or we don't, we do
because we need to perform the test, so we compute it". That's wrong,
so a posteriori the explanation must be something like this:

1. someone knows we want factor() to perform an equality test

2. someone knows an equality test between lists is False as soon as
we have a mismatch, left to right

3. thus, instead of evaluating factors completely we are going to
build sublists of the result and perform the tests on those ones
against [1, n].

That's a lot of *context* about that particular evaluation of
factors, in particular step puzzles me. Can anyone explain how lazy
evaluation fits there? I suspect the key is the implementation of ==
together with the fact that list comprehensions are lazy themselves,
is that right?

-- fxn

[*] Which notation do you use for functions in text? is f() ok?

```