Re: 3DLDF

[Hans Aberg]

At 19:51 +0100 2004/08/14, Frank Heckenbach wrote:
>You started the rant about terminology, didn't you?

You was the guy who started the rant, jumping and inflating a small rematk
I had in a discussion with Laurence Finston. You wanted to start a language
war, remember? :-)

>You get upset...

I am not upset, I just want to straighten out the terminology as to becoe
less confusing.

>about using "real" for a type to represent some real values and
>claim that using "float" for a type to represent some real values in
>a floating point representation was "mathematically correct".

The thing is there will be clash in names when one introduces real
representation of real numbers into computers. So it is better to stick to
the terminology, simply.

> While
>at the same time using "int" for a type to represent some integer
>values or integral values (which means the same AFAIK).

Same here. I already pointed out that Haskell has both the types Integer
and Int.

You are free to call them whatever you want in your own computer language,
of course.

>> > You can represent a different subset that
>> >floating point numbers (say, expressions involving pi, e and certain
>> >integrals), but it's still a small subset, and calling such a type
>> >"real" is/isn't just as justified than calling a floating-point type
>> >"real".
>>
>> So this your statement probably declares null and void all the pure math
>> about real numbers, that presumably is formally expressible via a
>> metamathematical theory.
>
>Are you trolling now? I suppose you know that mathematical
>statements about real numbers (and most anything) are not made by
>performing computations on examples (whether by hand or by
>computers), but by using quantors.

(Is "quantor" what is usually called quantifier?)

I think I pointed out that the set of real numbers is in math, as well in
computers, when done correctly, developed using an axiomatic system.

>> (If one wants to implement properly implement the
>> set of real numbers in a computer, one does that exactly the same way as in
>> pure math, via a finite, but potentially infinite via substitutions,
>> axiomatic system.)
>
>Yes. If that's your point, then all of "real", "float", "int" etc.
>as used in most programming languages are incorrect,
>and should be
>reserved for the sets of all real, floating point or integer
>numbers.

The use of float and int in say is is more or less correct, as one
speficies which values can be used, and all those values are potentially
reachable. This is not the case of real as thought as representation of
mathematical real nimbers, as many real numbers are not potentially not
reachable (as say pi or e).

>Then usual computer languages could only...

Usual computer languages such as Haskell <http://haskell.org/> has
potentially infinite types, for example Integer. In fact the Haskell lists
are also (potentially) infinite, so it is for example possible to define a
list of all the Fibonacci numbers.

>... talk about
>limited-integers-represented-in-twos-complement,
>limited-reals-with-limited-precision-represented-in-floating-point
>etc.

This is indeed the development in computer languages: For example C, now
admits integral types of specific sizes.

>I just don't think that many programmers would appreciate such
>type names.

They have names like int32 and the like. I think of creating a type
binary<n> of n bits.

>> >AFAIK, "integral" is just the adjective to "integer".
>>
>> Yes, but this difference is exploited to technically distinguish integral
>> type from integer number. :-)
>>
>> > Since "real"
>> >is both a noun and an adjective, it seems just as well suited.
>>
>> To denote real numbers or floating point numbers?
>
>In your terminology, I guess I should say a real (adjective) type,
>as distinguished from the set of real numbers!?

It is not my terminology; it is what is used in the C/C++ standards.

  Hans Aberg