[r6rs-discuss] Comparison procedures' number of arguments

[Thomas Lord]

Ken Dickey wrote:
> On Tuesday 21 October 2008 08:32:12 Abdulaziz Ghuloum wrote:
>   
>> On Oct 21, 2008, at 11:04 AM, Ken Dickey wrote:
>>     
>>> No.  Actually, I'd like a holds-for-all which returns #f as the
>>> base case.
>>>       
>> You can push it down, but you can't escape making these
>> exceptions.
>>     
>
> The law of the excluded third has a number of possible outcomes:
>   #t #f not-applicable undecided unknown outcome
>
> undecided is sometimes divided into undecidable, here are a list of conditions 
> which would make the preposition decidable, ..
>   

That's a good reason to use exceptions in the math system
where different choices of axiom really matter.

That's not a good reason to hair up relations and sequences
since no changes to axioms, only definitions, are in play.


>
> I am not saying that there is no check for existence of elements.  I am saying 
> that there is no relation holding between elements when there are no 
> elements.
>   

There is an element: the "possibly empty relation".

< is a binary relation of two numbers, let's say.

<... is a singleton relation (a property or predicate or subclass) of 
sequences.

(<)  ; ill formed expression
(< 1) ; ill formed expression
(< 1 2) => #t
(< 1 2 3) ; ill formed expression

(<...) => #t   ; the empty sequence is well-ordered
(<... 1) => #t ; a singleton sequence is well-ordered
(<... 1 2) => #t ; that two element sequence is well-ordered
(<... 1 3 2) => #f ; that three element sequence is not well-ordered

etc.

-t


>
> Cheers,
> -KenD
>
> "In theory, theory and practice are the same, but in practice they differ."  
> Engineer's axiom
>
>
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