evaluation - Why does this pattern with Plus not work for numbers?

I have a very simple question about redefining basic built-in functions, such as Plus. I'm pretty sure someone must have asked a similar question around here, but I couldn't find one. Consider the following code:

Unprotect[Plus];
x_ + y_ := x y
Protect[Plus];

For symbols this works as expected:

x+y

(* ---> x y *)

For numbers, however, the new definition does not work:

1+2
(* ---> 3 *)

Of course I know that it is stupid to use something like this and that defining functions or using upvalues etc. is the way to go here, but I'm really interested in why this happens. Can the pattern for Plus be defined in such a way that it works for numbers as well? Is Plus[1,2] evaluated internally before the pattern can be matched?

Answer

See Plus in the reference manual:

Unlike other functions, Plus applies built-in rules before user-defined ones. As a result, it is not possible to make definitions such as 2+2=5.

The ability for user-defined rules to supersede built-in ones was lost in Version 3

Comments

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