As it happens, I am just studying a presentation [1] Martin Escardo gave to students at the University of Birmingham. It contains Haskell code for exact real number computation. Among other things, there is a function that computes a signed digit representation of pi/32. It computes several thousand digits in a few seconds. I did not try it yet, but many irrational numbers are fixed points of simple arithmetical expressions. For example, the golden ratio is the fixed point of \x -> 1+1/x. Infinite streams of digits should be a type where such a fixed point is computable. Or you could use a sufficiently precise rational approximation and convert that do decimal in the usual way. import Data.Ratio import Data.List (iterate) -- one step of Heron's algorithm for sqrt(a) heron :: (Fractional a) => a -> a -> a heron a x = (x+a/x)/2 -- infinite stream of approximations to sqrt(a) approx :: (Fractional a) => a -> [a] approx a = iterate (heron a) 1 -- Find an interval with rational end-points -- for a signed-digit real number type SDReal = [Int] -- use digits [-1,0,1] interval :: Int -> SDReal -> (Rational,Rational) interval precision x = let f = foldr (\d g -> (a d).g) id (take precision x)) a d = \x -> ((fromIntegral d)+x)/2 in (f(-1),f(1)) Cheers, Olaf [1] www.cs.bham.ac.uk/~mhe/.talks/phdopen2013/realreals.lhs