On Mon, Mar 10, 2008 at 3:12 PM, Neil Mitchell <[email protected]> wrote:
> > "The Ord class is used for totally ordered datatypes."
> > This *requires* that it be absolutely impossible in valid code to
> > distinguish equivalent (in the EQ sense, not the == sense) things via
> > the functions of Ord. The intended interpretation of these functions is
> > clear and can be taken as normative:
> > forall f . (compare x y == EQ and (f x or f y is defined))
> > ==> f x == f y)
> Are you sure? I would have read this as the ordering must be
> reflexive, antisymetric and transitive - the standard restrictions on
> any ordering. See http://en.wikipedia.org/wiki/Total_ordering
This is my reading, too. In addition, to make it total, the property
that any two elements are comparable (this is the property that a
partial order does not necessarily have).
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