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On 16-07-13 15:03, Alexey Radul wrote:
> On Tue, Jul 16, 2013 at 3:19 AM, Marijn <hkBst@gentoo.org> wrote:
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>> On 16-07-13 06:21, Alexey Radul wrote:
>>> In addition to the weight of tradition, -1, 0, and 1 have the
>>> benefit of being naturally correctly totally-ordered amongst
>>> themselves. Semantically chosen symbols are unlikely to share
>>> this advantage.
>>
>> What exactly is ``naturally correct'' about this inherited total
>> ordering?
>
> Precisely that any currying of (the second argument of) any
> compare procedure becomes a homomorphism of totally ordered sets.
>
>> Do you also think  (< (< 0 1) (< 1 0))  should be #t or #f?
>
> That example is irrelevant, but (let ((<=>
> (comparator-compare-procedure integer-comparator))) (< (<=> -2 0)
> (<=> 2 0))) absolutely should return #t.

   (let ((<=> (comparator-compare-procedure integer-comparator)))
     (< (<=> 1 0) (<=> 2 0)))

shows that this is not a homomorphism, since (< 1 2) is true (or LT or
- -1), but (< 0 0) is false (or EQ or 0).  Unless you meant homomorphism
differently?

Marijn

>> If we could compare functions for equality, we could have the
>> return values be the respective equivalents of <, > and =.
>> Failing that maybe '<, '> and '= would be appropriate?
>
> I like Haskell's choice of a new, disjoint type for the answers of
> compare.  In Scheme, however, such a thing adds considerable extra
> weight, so I am not even sure I would support it.  In addition to
> being traditional (and therefore quite recognizable), integers
> have the (debatable) advantage over symbols of allowing comparator
> puns, such as (define (abs x) ; Look Ma, no branch! (* x
> ((comparator-compare-procedure real-comparator) 0))) which may even
> be important numerical computations.

I don't think multiplication is a very efficient way of implementing
the absolute value function; an implementation could just fix the sign
bit directly.  But if there are other reasons for such traditional
compare procedures, then they can exist separately from the default
compare procedures.

Marijn
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