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
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