On Wed, Apr 21, 2010 at 5:25 AM, Max Rabkin <max.rab...@gmail.com> wrote:
> On Wed, Apr 21, 2010 at 1:44 AM, Edward Kmett <ekm...@gmail.com> wrote: > > Eq doesn't state anywhere that the instances should be structural, though > in > > general where possible it is a good idea, since you don't have to worry > > about whether or not functions respect your choice of setoid. > > Wikipedia's definition of structural equality is an object-oriented > one, but if by structural equality you mean the natural equality on > algebraic datatypes (as derived automatically), I don't believe this > is quite the case. If the type is abstract, surely the Eq instance > need only be a quotient w.r.t. the operations defined on it. Thus, for > example, two Sets can be considered equal if they contain the same > elements, rather than having identical tree shapes (except that > Data.Set exports unsafe functions, like mapMonotonic which has an > unchecked precondition). Yes. My point about why falling back on structural equality is a good idea when possible, is that then you don't have to work so hard to make sure that x == y => f x == f y holds. When your equality instance isn't structural you need to effectively prove a theorem every time you work with the structure to avoid violating preconceptions. My post was acknowledging the expedience of such methods. I think we are using a lot of words to agree with one another. ;) -Edward Kmett > --Max >
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