Re: [Haskell-cafe] Formalizing lazy lists?

Greg Woodhouse wrote:

--- Lennart Augustsson wrote:

...

How about:

nil = \ n c . n cons x xs = \ n c . c x xs

zero = \ z s . z suc n = \ z s . s n

listFromZero = Y ( \ from n . cons n (from (suc n))) zero

(Untested, so I might have some mistake.)

-- Lennart

Okay, I see what you mean here. What I was thinking is that repeatedly unfolding Y give us kind of an algorithm to extract initial segments of the list (like "from"), but there's something disquieting about all of this.

Unfolding Y is indeed part of the algorithm to generate the list. The lambda calculus is "just" another programming language, so why does this disturb you? Maybe it's just my lack of familiarity with lambda calculus, but

I think one thing I got used to as a student was the idea that if I started peeling back layers from an abstract defintion or theorem, I'd end up with something that looked familiar. Now, to me a list comprehension is something like an iterative recipe. Maybe [0, 1, ..] is something "primitive" that can only really be understood recursively, and then a comprehension like

[ x*x | x <- [0, 1..] ]

is something easily built from that (or itself defined as a fixed point), but it would be nice to see the iterative recipe somehow "fall out" of the more formal definition in terms of Y.

List comprehensions are just a different way of writing concats and maps, both of which have recursive definitions. What is an "iterative recipe"? -- Lennart