[om] result of cubic formula

[Richard Fateman]

In lisp, an alternative syntax is available
which might be less suprising to receivers of
solutions to cubic equations, namely "let".
((lambda(x)(f x)) y)  is the same as

(let ((y x))
    (f x))

so a cubic solution might be
(let ((r ..resolvent..))   ;; or whatever
   (SolutionList
       ..solution1 in terms of r
       ... etc))

If this is surprising to people, then frankly
it is surprising to me that any human would
look at the openmath text, except perhaps as
punishment.  The human would see it via
some front end that could expand this information
into some pleasing form, and paint it on a
display device in variable width font, on a
pastel background, encoding the relevant pieces
in different colors so as to portray the
sharing.  Or not.

The more typical recipient would parse the expression
and (pardon the anthropomorphism) say
"oh goodie, a lambda (or let):  I better get
ready to set up an association of names and their
bindings if I am going to make sense of the insides
of this expression".

In no way is the recipient compelled to evaluate the insides
any more than a lisp program would be compelled by  receiving
the 7 character string "(+ 3 4)"  in lisp to add.  The program
could just as easily say "Oh thanks, a three element list.  I'll
store it.  Or display it as '3+4' "  etc.

RJF


jhd at cs.bath.ac.uk wrote:

> On Thu, 4 Apr 2002, Richard Fateman wrote:
> 
> 
>>If OM has an intention of providing notation and
>>semantics for an assign operation, then it is
>>
> I never said that it should (though this is atopic of debate), I was 
> merely using assignment on intervals as an example of how there's a 
> difference between "two different [-1,1]" and "two occurrences of the same 
> "[-1,1]". John Abbott's example needs no assignment.
> 
>>  seems to me it has become a programming language with 
>>all that baggage as well.
>>   If you want to define "semantic sharing" it can
>>be done, in most reasonable cases, with lambda-binding.
>>
> It can be done, though people might be surprised to see the result of 
> solving a cubic to be the application of a lambda-expression to 
> sqrt(-4a^3-27b^2).
> 
> James
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