18 Dec
2007
18 Dec
'07
4:29 p.m.
Nicolas Frisby writes:
Extensionality says that the only observable properties of functions are the outputs they give for particular inputs. Accepting extensionality as a Good Thing implies that enabling the user to define a function that can differentiate between f x = x + x and g x = 2 * x is a Bad Thing.
Provided you subsume what you subsume, in general case there is no reason that the "standard math" equality x+x == 2*x be true. You may write whatever Num instances (for some data "x") please you. Your multiplication may have nothing to do with the addition, and your fromInteger function may do horrible things. In any case, confusing math and Haskell is not safe. Jerzy Karczmarczuk