Re: A Logical Model for Lists as Relations

Jay Dee wrote:
> vc wrote:
> > What's an 'operator' ?
>
> Something that yields a value. Nilary booleans give false and true,
> the boolean prefix unary NOT gives the complement of its input, the
> number infix + give the sum of two operands... Like that. Operator.

Why don't you revisit your school algebra book ? There, you might discover that the operator is just a convenience notation for the function.

>
> One math guy I often speak with says function when I like to say
> operator. Some programming types like to distinguish between procedures
> and functions while others use the words mutators and selectors.
>
> Go figure.

You'd better listen to the 'one math guy [you] often speak with'. You might be able to figure out what all this stuff is about.

> > How do you define an operator without using the notion of the set first
> > ? What is the 'operator' in your language ?
>
> Well, that's why bunch is there -- something to build on when
> defining sets.

One does not need no bunches to define a set .

> >
> > The 'union on elements' is a beast inconnu in math.
>
> How do you describe the comma that appears in {a, b, c}?
> Punctuation?

Yes, commas and curly brackets are just readiblity markers (punctuation). Have you ever seen a pack of dogs running around with curly brackets around them and commas in their midst ? If not, how different then is a bunch of dogs from a set of dogs ?

>Is it wrong to define it as an infix union operator?
> As such, it is associative - {a, b} = {b, a} - and the appeal is
> that there's no stray ink on the page.

Any good book on set theory (e.g. Halmos's) may (or may not) put you straight. Received on Fri May 12 2006 - 13:17:27 CEST