Is there a programming language which allows the redefinition of numbers?

Question

My first stab at this problem was in C

#define 2 5
assert(2+2 == 10);

Unfortunately

error: macro name must be an identifier

I also tried Scheme

(define 2 5)

but

can't define a non-symbol: (define 2 5)

I was wondering if there are any programming languages where this is possible.

Just a thought, but in C++ it might be possible to overload the `+` operator and then redefine how each operand behaves during addition. — Tim Biegeleisen, Jun 15 '16 at 15:01
@TimBiegeleisen: that's difficult since `2 + 2`, for example, is a compile time evaluable constant expression. I don't see a way of doing this in standard C++. — Bathsheba, Jun 15 '16 at 15:05
@TimBiegeleisen That's a neat idea. Unfortunately I don't think you can overload operators for builtin types like int. I tried to define a class, overload `+`, `int` operators on that and then cast the numeric literals to that new class. Which gives code that looks looks like `(T)2 + (T)2 == 5`. Which looks pretty weird and suspicious, but cool thanks. :) — 2pjwul, Jun 15 '16 at 16:12

score 3 · Answer 1 · edited Apr 13 '17 at 12:38

I sincerely hope not.

But that said, I do know of a way in Java: you can use reflection to adjust the values of the cached boxed Integers: a JVM must cache all values in the range -128 to +127, and there does exist a mechanism to adjust the numeric values in that cache!

See https://codegolf.stackexchange.com/questions/28786/write-a-program-that-makes-2-2-5/28818#28818 for more details. Here's the code in full:

import java.lang.reflect.Field;
public class Main {
    public static void main(String[] args) throws Exception {
        Class cache = Integer.class.getDeclaredClasses()[0];
        Field c = cache.getDeclaredField("cache");
        c.setAccessible(true);
        Integer[] array = (Integer[]) c.get(cache);
        array[132] = array[133];

        System.out.printf("%d", 2 + 2);
    }
}

The output is 5, essentially achieved by redefining the number 4.

I'm a bit resentful about installing Java but it worked. This is pretty cool, thanks for the answer. Sorry, I don't have enough virtual stackoverflow points to up vote. — 2pjwul, Jun 15 '16 at 16:04

score 1 · Answer 2 · answered Sep 12 '22 at 20:19

I remembered hearing a story about this long ago, and today I decided to follow-up on it. That follow-up lead me to this question which unfortunately isn't exactly answered. This isn't exactly an answer, either, but ... here ya go.

I believe this can be done with early Fortran compilers.

From that post (which is a copy of an original post to comp.lang.python which I haven't been able to track-down):

>     subroutine munge (i)
>     i = 3
>     return
>and then in your main program did:
>     j = 7
>     call munge (7)
>     write (6, 11) j
> 11    format ('j = ', i6)
>it would print 3!

The reason seems to be due to a combination of:

Constant interning
Fortran's pass-by-reference semantics

The compiler interns the constant value (7) and then calls the munge function with a pointer to the interned "constant" 7. The munge function changes the value of the passed-by-reference integer value and so now the interned constant value is 3.

So, this won't universally change the value of 7 to 3 across the whole program, but anywhere that interned "constant" value is used will now be using 3 as its numeric value.

This can be extraordinarily surprising (and rightly so, IMO) to younger programmers who have only dealt with languages whose arguments are almost always passed by value (unless otherwise specified). C, C++, C#, Erlang, Java, javascript, Perl, Python, Ruby, etc. all use pass-by-value. For those languages, pass-by-reference semantics are achieved either using encapsulation (e.g. passing a mutable complex type such as an object) or explicitly passing a pointer to a value instead of the value (e.g. using the & operator in C and similar languages).

Is there a programming language which allows the redefinition of numbers?

2 Answers2