Tue, 13 Feb 2001 14:01:25 -0500, Dylan Thurston
Consequences: you cannot, e.g., raise a Double to an Integer power without an explicit conversion or calling a different function (or declaring your own instance). Is this acceptable?
I don't like it: (-3::Double)^2 should be 9, and generally x^(2::Integer) should be x*x for all types of x where it makes sense. Same for Int. (**) does not work for negative base. Neither of (^) and (**) is a generalization of the other: the knowledge that an exponent is restricted to integers widens the domain of the base. x^2 = x*x cannot actually work for any x in Num, or whatever the class of (*) is called, if (^) is not defined inside the same class. This is because (^) is unified with (^^): the unified (^) should use recip if available, but be partially defined without it if it's not available. So I propose to put (^) together with (*). With a default definition of course. It means "apply (*) the specified number of times", and for fractional types has a meaning extended to negative exponents. (^) is related to (*) as discussed times or scale is related to (+). (**):: a -> a -> a, together with other analytic functions. Sorry, the fact that they are written the same in conventional math is not enough to force their unification against technical reasons. It's not bad: we succeeded in unification of (^) and (^^). -- __("< Marcin Kowalczyk * qrczak@knm.org.pl http://qrczak.ids.net.pl/ \__/ ^^ SYGNATURA ZASTÊPCZA QRCZAK