I recently implemented some new Haskell numeric types that, instead of performing calculations, can generate a rendering of the requested calculation or store units with it.
good old Haskell rule (with apologies to Daniel Düsentrieb, I think;): "impossible things are delayed immediately, miracles may take a little longer" you can't get an expression representation from a value, but you can generate a representation while building the expression, so that you have it at hand if/when needed. I did something similar once (pairing values with representations instead of calculating values from representations), which you might find interesting for comparison (note that the focus in this one was on simplicity, eg. string representation only, no simplification, etc.): http://www.cs.kent.ac.uk/~cr3/toolbox/haskell/R.hs btw, that kind of thing gets even more interesting with ho-functions like foldr, foldl, map. try it!-) nice for explaining these hofs.. (the code still works, but if you use ghci -fglasgow-exts instead of hugs +98, the defaulting doesn't seem to kick in, so you'll need to give explicit type annotations, eg. "map (+) [1..4::R Integer]" or "foldl (-) 0 [1..4::R Integer]"). cheers, claus --------------------------------------------------------------------------------------- Do you have late-breaking research results in FP but have missed the other deadlines? Submit to TFP'05: http://www.tifp.org/tfp05/ --------------------------------------------------------------------------------------- extended abstracts: 8th July 2005 <==== full papers: 2nd September 2005 symposium: 23/24 September 2005, Tallinn, Estonia (w.ICFP/GPCE) ---------------------------------------------------------------------------------------