Re: [Haskell-cafe] A question about "monad laws"

On Feb 12, 2008, at 1:50 AM, David Benbennick wrote:

On Feb 11, 2008 10:18 PM, Uwe Hollerbach wrote:

...

If I fire up ghci, import Data.Ratio and GHC.Real, and then ask about the type of "infinity", it tells me Rational, which as far as I can tell is Ratio Integer...?

Yes, Rational is Ratio Integer. It might not be a good idea to import GHC.Real, since it doesn't seem to be documented at http://www.haskell.org/ghc/docs/latest/html/libraries/. If you just import Data.Ratio, and define

...

pinf :: Integer pinf = 1 % 0

...

ninf :: Integer ninf = (-1) % 0

Then things fail the way you expect (basically, Data.Ratio isn't written to support infinity). But it's really odd the way the infinity from GHC.Real works. Anyone have an explanation?

An educated guess here: the value in GHC.Real is designed to permit fromRational to yield the appropriate high-precision floating value for infinity (exploiting IEEE arithmetic in a simple, easily- understood way). If I'm right, it probably wasn't intended to be used as a Rational at all, nor to be exploited by user code. -Jan-Willem Maessen