
Oleg rewrote my power-series one-liners to illustrate the fact that lazy lists defined in a strict language need not be very clumsy to use. I had implemented those funstions in many strict languages, one of which was ML using a lazy-list implementation from Dave MacQueen. But after I finally did it in Haskell, I never looked back. Though ML was the best of the strict bunch. Haskell's overloading and cleaner notation made for more perspicuous code. It also enabled elegant code like this for the exponential series: exps = 1 + integral exps As Oleg pointed out, this won't work in a strict language, and must be replaced with something much less vivid: exps = fix (\s 1 + integral s) In slightly more involved cases, such as sins = integral coss coss = 1 - integral sins the strict equivalent becomes murky: sins = fix (\s -> integral (1 - integral s)) coss = derivative sins or (sins, cosx) = fix (\sc -> (integral $ snd sc, 1 - integral $ fst sc) Further, because lazy lists are a new type, they can't be manipulated directly with the standard list vocabulary (map, take, filter, etc.). All such functions must be lifted to the new type. Thus, while lazy lists can be *programmed* in a strict language, they *play* somewhat awkwardly in it. In fairness, I must admit that the beauty of representation by naked lists may not survive when power series are embedded in a more comprehensive algebraic system. For example, if both matrices and power series were defined as list instances of Num, matrices might be confusEd with nested power series. Combinations--matrices of power series and vice versa--could be similarly ambiguous. But it could also turn out to cause no more difficulty than the already extensive degree of polymorphism in arithmetic expressions. Doug