[_a_a_a_]

I appreciate the detail you've given and you clearly know your stuff, but I think your looking at it too deeply, at least compared to me. Basically, use a familiar notation where a familiar notation would be appropriate. Your complex ad example is a good case where it probably isn't.

> What about adding two decimals?

  rx = ry +bcd rz

I'm really thinking of simple, simple changes. As you point out some situations aren't appropriate for it, in other cases maybe it is. Or maybe I'm just plain wrong and it never is appropriate. But it's just a suggestion and worth considering, no?

[inkyoto]

> […] where a familiar notation would be appropriate.

And this is the problem I have been trying to point out. «+» comes from math, and – in the world of math – there are no bytes, no half-words, no overflows, no carry overs, no branches and no traps, and the imaginary «register» size is infinite – an addition always succeeds however large is the number. There are no decimals, no floating point numbers, either – in math, there is no distinction. There is just a lone exception being the handling of the explicit infinity values (-∞ and +∞). «Add and branch» or «add and trap» simply do not exist in math – math is abstract, and computing is concrete.

That is not the case in computing. The semantics of «add» varies across different CPU architectures, as the assembly language exposes the internal machinery and the internal state of a given CPU which may or may not be appropriate for another CPU. For example, RISC-V does not support the integer overflow flag, and most other CPU's do. Assembly is a 1:1 representation of the binary code for a given CPU, and that is where it stops.

In fact, I do find the charm in your proposal being along the lines of «r3 = r1 +.u8 r2», «r3 = r1 +.c r2 or branch label1», «r3 = r1 +.c r2 or trap overflow» etc. It will not be assembly though, more of a meta-assembly, which is fine. The real trouble is that the grammar will be able to handle just one ISA and might quickly become complex and unwieldy if ported to another ISA that has a rich set of addition operations that do not fit in the narrow constraints of such a design.

[_a_a_a_]

I'm glad you like the possibility of using the addition symbol or some variation on it. The idea that it would be ISA independent never crossed my mind, and perhaps just as well because as you pointed out, it would bomb. For that (ie. portability), use an HLL.

I fully understand your criticism, entirely correct, that machine arithmetic does not behave like mathematical arithmetic. I diverged from you where you say that '+' is mathematical therefore has a predetermined meaning. It has a conventional mathematical interpretation, often related to number addition, but it is a convention only and can be bent as far as you like provided you're clear about it (and a bit of common sense too; defining '+' as a square root operation would be pretty bloody stupid). No symbol in mathematics has any intrinsic meaning, including '+'.

Thanks for interesting discussion!