# [racket] arity of + versus <=

 From: John Clements (clements at brinckerhoff.org) Date: Fri Oct 28 12:07:36 EDT 2011 Previous message: [racket] arity of + versus <= Next message: [racket] arity of + versus <= Messages sorted by: [date] [thread] [subject] [author]

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

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