On Thu, 2007-07-12 at 12:49 -0400, Doug McIlroy wrote:

For lovers of things small and beautiful, http://www.cs.dartmouth.edu/~doug/powser.html boils down basic operations on power series with numeric coefficients to the bare minimum--each is a one-liner. Included are overloaded arithmetic operators, integration, differentiation, functional composition, functional inverse and coercion from scalars. --A telling demonstration of the power of lazy evaluation and of Haskell's attunement to math.

and a link to your earlier Functional Pearl, http://citeseer.ist.psu.edu/mcilroy98power.html

This is really interesting. I love how the typechecker can resolve 1:0:1 (representing (1+x^2)) 1 : 0 : 1 => 1 : 0 : (fromInteger 1 :: [Integer]) => 1 : 0 : (series (fromInteger 1 :: Integer)) => 1 : 0 : (series 1) => 1 : 0 : 1 : repeat 0 (I'm going to go on a bit of a soapbox here...) I feel that Haskell could learn from one of C++'s goals here: provide at least as good support for user-defined-types as for built-in types. Automatic conversion to numeric types via fromInteger could be extended to other types; fromList and fromString could be applied automatically to convert other literals: class LiteralString a where fromString :: String -> a class LiteralList a b where fromList :: [a] -> b