[racket] arity of + versus <=

On Fri, Oct 28, 2011 at 11:44 AM, Carl Eastlund <cce at ccs.neu.edu> wrote:
> On Fri, Oct 28, 2011 at 12:07 PM, John Clements
> <clements at brinckerhoff.org> wrote:
>>
>> On Oct 28, 2011, at 8:12 AM, Joe Marshall wrote:
>>
>>> On Wed, Oct 26, 2011 at 8:32 PM, Dan Grossman <djg at cs.washington.edu> wrote:
>>>> Very minor point, but is there a rationale beyond historical precedent
>>>> for + and * to allow any number of arguments but, =, <=, <, >, >= to
>>>> require at least two arguments?
>>>
>>> 0 is the additive identity. 1 is the multiplicative identity.
>>> What is the equality identity?
>>
>> No, I don't buy that. operators in \alpha X \alpha -> \beta can never have identities, but that doesn't mean they can't be generalized.
>>
>> I can definitely imagine that you would choose to disallow unary use of comparison operations to prevent a certain class of programming errors, but it seems pretty clear to me that the generalization of, e.g., <= is "is every sequential pair of items in the argument list related by the given operator."
>>
>> Am I missing something here?
>>
>> John
>
> Furthermore, that generalization is useful, as it makes (apply <= xs)
> into a simple implementation of "is xs monotonically non-decreasing?",
> just as (apply + xs) implements "the sum of the elements of xs".  If
> <= must accept 2 or more arguments (or even 1 or more), that does not
> work for all lists.  Personally, I'd prefer if <= and friends were
> generalized.  It seems more in tune with Racket's permissive Scheme
> heritage -- if append accepts "improper" lists, + mixes precise
> numbers with floating point, and all values act as booleans, why can't
> <= accept 0 or 1 arguments?

Does this rationale also suggest that it is fine that (cdr '()) = '()?

Robby