Re: if vs. when vs. and: style question

["Pascal J. Bourguignon" <pjb@informatimago.com>]

Rusi <rustompmody@gmail.com> writes:

> On Wednesday, March 25, 2015 at 8:10:18 AM UTC+5:30, Emanuel Berg wrote:
>> "Pascal J. Bourguignon"  writes:
>> 
>> > But then, why stop with +?
>> >
>> > You could use instead:
>> >
>> >    (funcall (additive-operator (ring integer))
>> > (neutral-element (multiplicative-operator (ring
>> > integer))) 5) ; 6
>> >
>> > or something even more general?
>
> I find Pascal's example brilliant and hilarious.
> In this case though, I slightly err on your (Emanuel) side.
>
> When I see the 1+, I have a stop (like um... er...)
> Is that a number, an expression, a constant, a comment?
>
> Oh Oh.. Functions can start with digits (Yeah this is lisp...)


Indeed, it is clear that the names 1+ and 1- are ill-choosen.
Notably 1-!!!

            (1- x) == (- x 1)


BUT

Those are actually fundamental operators, more fundamental than addition
and substration, both in a theoric way, and in practice with a lot of
processors.

They are the operators named succ(x) and pred(x) in pascal (which C
lacks as independent operators, but have combined with updating with the
pre- and post- complifications of ++x, x++, --x, and x--; C is THE crazy
language).


In axiomatic number/set theory, we only assume a number noted 0, and a
succ(x) operation that let us build a new number from any number x.

so 1 = succ(0) by definition.  (= 1 (1+ 0))

You do not program it the other way around, defining 1+ from x and 1,
you define 1 from 1+ and 0!

And the proof, is that processors usually have an increment and a
decrement operation even while they may lack a general load operation
(working or any immediate word-sized number).

So when you write x:=512; you may actually obtain a "load #511; incr"
instruction sequence, ie. (1+ 511).



So write: 

   (defun succ (x) (1+ x)) 
   (defun pred (x) (1- x)) 

or in elisp:

   (defalias 'succ '1+)
   (defalias 'pred '1-)

and use (succ x) instead of (1+ x) or (+ x 1).


(Remember that the only literal numbers allowed in a program source are
0 and 1; well, it's even better if you allow only 0 and (succ x)).

-- 
__Pascal Bourguignon__                 http://www.informatimago.com/
“The factory of the future will have only two employees, a man and a
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