[Haskell-cafe] Re: appending an element to a list

[Tillmann Rendel]

Abhay Parvate wrote:
> I think I would like to make another note: when we talk about the complexity
> of a function, we are talking about the time taken to completely evaluate
> the result. Otherwise any expression in haskell will be O(1), since it just
> creates a thunk.

I don't like this notion of complexity, since it seems not very suited 
for the analysis of composite expression in Haskell. For example,

   repeat 42

has infinite complexity according to your definition (it doesn't even 
terminate if completely evaluated), but

   take 5 $ repeat 42

has only constant complexity even if fully evaluated. It is not clear 
how to reuse the finding about the complexity of (repeat 42) to 
determine the complexity of (take 5).

Instead, my view of complexity in lazy languages includes the 
interesting behaviour of the rest of the program as variables. For 
example, (repeat 42) needs O(n) steps to produce the first n elements of 
its output. Now, (take 5 x) restricts x to the first 5 elements, so 
(take 5 $ repeat 42) needs O(min(n, 5)) = O(1) steps to produce the 
first n elements of its output.

Is this intuitive view generalizable to arbitrary datatypes (instead of 
lists) and formalized somewhere?

   Tillmann