On Sun, Jun 01, 2008 at 03:34:00PM +0100, Ian Lynagh wrote:
On Sun, Jun 01, 2008 at 05:39:49PM +0400, Serge D. Mechveliani wrote:
This is why res and 1*res are not equivalent in Haskell-98 for res :: Num a => a.
Am I missing something?
The library functions assume that class instances obey some unwritten laws; it's all a bit vague, but if your instances don't obey them then you might find that things go wrong when using library functions. For example, if your (*) isn't associative then (^) is going to give odd results, and if the type of the second argument to (^) doesn't do arithmetic in the normal way then very strange things could happen.
Anyway, I've just tweaked the (^) definition again, so your code should work in 6.8.3.
Thank you. This helps -- in that the public DoCon-2.11 test will run (I hope). But I think that you have found a bug in the DoCon test program. Thank you. More precisely, here are my indeas. 1. Generally, for t = Num a => a, the expessions res :: t and ((fromInteger 1) :: t) * res are not equivalent in Haskell-98, and the compiler has not rigth to replace the former with the latter. Right? 2. But I guess, our current questions are different: (2.1) For t = Num a => a, has a Haskell implementation for (f^n) :: t right to base on certain natural properties of the operation fromInteger :: Integer -> t ? (2.2) Has a reliable mathematical application right to base on that for n > 0 the expression (f^n) :: Polynomial Integer does not imply computing fromInteger 1 :: Polynomial Integer ? Concerning (2.1): I do not know whether Haskell-98 allows to rely on that f^3 is equivalent to (fromInteger 1)*(f^3). But concerning (2.2), I think that (independently of the question (2.1)) a reliable mathematical application must not presume the above properties of (^) and fromInteger. Concerning f^3 :: UPol Integer in my test for DoCon: 1) fromInteger _ :: UPol _ is defined as error "... use fromi instead". 2) (*) is defined via polMul ... 3) The expression f ^ 3 relies on the Haskell-98 library for (^). The Haskell library defines (^) via (*) -- all right. 4) DoCon has the function `power' to use instead of (^), and its library avoids (^). But for n > 0, I considered f^n :: UPol _ as also correct. Because the Haskell library performs this via repeated application of (*). And I thought that if n > 0, then (fromInteger _ :: UPol _) will not appear. Maybe it does not appear in old GHC-s and does appear 6.8.3 ? I was using expressions like [(f ^ n) :: UPol Integer | n <- [2 .. 9]] in my _test programs_ for DoCon. But this relies on a particular property of the Haskell library definition for (f^n) :: a -- on that if n > 0 then (fromInteger _ :: a) does not appear in this computation. Now, I think, either I need to hide the standard (^) and overload it or to replace (^) with `power' in my examples too. Regards, ----------------- Serge Mechveliani mechvel@botik.ru