[racket] arity of + versus <=

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?

--Carl