Hello Robert, Thanks for the comments. The lazy list with Double phi embedded does indeed begin to deviate, at the 81st Fibonacci number, if I'm not mistaken. Another fellow in this thread calculated the deviation points for Double, Float and CReal. By way of further explanation, I'm writing up various approaches and solutions to the problems posed at Project Euler, discussing the various defects to each approach, comparing the runtimes of solutions and, hopefully, deriving interesting tidbits of math along the way. The project was begun to improve my Haskell ability by exercising it in as many ways on a single idea as possible. I'd not thought of the algorithm you pointed out in SICP and will now happily include it. Thanks. Brian On Wednesday 11 July 2007 07:00:05 you wrote:
Brian,
I am also a Haskell newbie, and unfortunately can not answer your type question, but wish to make a 'side comment'. The use of a floating point phi to calculate Fibonacci numbers makes me a bit nervous. In 'Structure and Interpretation of Computer Programs' 2n Edition Exercise 1.19 there is an algorithm for calculating the n'th Fibonacci number in order of log n steps. Take a look at:
http://mitpress.mit.edu/sicp/full-text/sicp/book/node18.html
I would use the type Integer, with this algorithm, for arbitrary precision Fibonacci numbers. My concern is that your lazy list will start to deviate at some point from Fibonacci numbers because of the floating point calculations. Comments welcome, and I look forward to seeing the experts answer your type question.
Best Regards, Robert
On Wednesday 11 July 2007 05:11, Brian L. Troutwine wrote:
I'm rather new to Haskell and need, in typical newbie style, a bit of help understanding the type system.
The Nth even Fibonacci number, EF(n) can be defined by the recursive relation EF(0) = 2, EF(n) = [EF(n-1) * (phi**3)], where phi is the golden ratio and [] is the nearest integer function. An infinite lazy list of this sequence would be nice to have for my Project Euler, er, project. Defining phi thusly,
phi :: (Floating t) => t phi = (1+sqrt(5))/2
With phi in place, if I understood types properly (and if I understand iterate correctly as I think), the lazy list should be a relatively quick matter.
even_fibs :: (Num t) => [t] even_fibs = iterate (\x -> round(x * (phi**3))) 2
Dynamically typed even_fibs :: (Floating t, Integral t, RealFrac t) => [t], assuming I pass -fno-monomorphism-restriction to ghci. That's not at all the type I assumed even_fibs would take, as can be seen from above. So, I went on a bit of sojourn. Having seen the sights of the Haskell Report section 6.4, the marvels of the references cited in the wiki's article on the monomorphism restriction and the Gentle Introduction's chapter 10 I must say I'm rather more terribly confused than when I started out, possibly.
Can someone explain where my type statements have gone wrong? _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe