On 11 Oct 2007, at 1:34 pm, Dan Weston wrote:
Actually, [pi] is a constant: piDecimalExpansion :: String.
No, that's another constant.
A translation from piDecimalExpansion :: String to pi :: Floating a => a is already well defined via read :: Read a => String -> a
Wrong. piDecimalExpansion would be infinite. pi is, after all, a transcendental number. It can be computed incrementally by a finite algorithm, true. The problem is that read has to read *all the way to the end*, and there is no end. (More precisely, either to the end of the string or to the first character that is not part of a floating point literal.)
Any definition of pi in the Floating class that differs from (read piDecimalExpansion) is erroneous.
In effect, you are proposing that the only non-erroneous definition of pi is bottom. I don't think that is very helpful.