Re: Integers and Mathematical Correctness

["G.B." <bauhaus@futureapps.invalid>]

On 01.10.14 21:48, vincent.diemunsch@gmail.com wrote:
> But now that we have operator overloading and that I use it for rationals or symbolic expression, I am bothered that an integer division has exactly the syntax I would like to use for a rational number...

A story about John von Neumann has him say something like
"what a waste of valuable programmer time", when approached by
someone enthusiastically demonstrating early Fortran syntax,
assuming that source texts looking "like math" rather than "like
assembler" would help.

In fact, I think that, provided that one is using languages
not specifically made for mathematics, distracting peoples'
attention from computing devices by way of "math like"
syntax is a terrible mistake.  It is the prime invitation
to not think about the thing you are programming, and then
make corresponding mistakes, led by the wrong assumptions.

Computer formalisms deserve their own syntax. It does not
make them non-mathematical. Operators that are not operating
like the ones you learned at school should never look like
those.  Cf. C's INT_MAX + 1 ... or feed the following program
to GNAT's default compilation to watch "+" in action:

procedure Plus is
    X : Integer := Integer'Last;
begin
    for Y in Integer loop
       X := X + 1;
    end loop;
end Plus;