[Haskell-beginners] laziness and optimization

[Michael Mossey]

I understand a bit about the concept of "lazy evaluation." I think of 
that as saying an imperative language would always make one evaluation, 
whereas Haskell might make 0 evaluations. I have another similar 
situation where an imperative language would make N evaluations of the 
same expression, and I would like Haskell to make only 1.

This is the situation: the graphical score editor displays 
"LayoutItems." A LayoutItem can be a single displayed entity, like a 
round notehead, or it can be composed of several entities.

A common situation in my code is the need to determine the size and 
shape of a LayoutItem. For a fundamental item, this can be looked up in 
a table or read from the font properties. For a composite item, some 
computation is required: the code must determine the positions of each 
sub-item and compute the bounds of a shape containing all of them.

It's this latter computation, finding the bounds of a composite item, 
which might come up multiple times. Consider that I ask for the bounds 
of a composite-composite item (a composite item composed of composite 
items). It will run the computation associated with each composite 
sub-item, even though it is very likely I already make that computation 
when I first constructed and placed that sub-item.

In an imperative language, one might cache values for later lookup. This 
raises the problem of keeping the cache current to the current state.

So I'm wondering to what extent the haskell compiler recognizes 
computations it's done before. In a purely functional language this 
should be pretty easy, right? If it sees the same expression, it knows 
it will have the same value. That's my understanding, so far.

Thanks,
Mike