Are stacks mainly used in software design while registers are mainly used in hardware design? What is the trade off?
The instructions can also execute faster because I don't have to do things like decode registers and look them up in the register rename table but modern CPUs pipeline this shit so well you never have to worry about instruction latencies.
For register based machines one big advantage is that it's way easier for compilers to optimize for register based systems. If I have a common value that I'm using constantly if I was using a stack based arch I'd have to keep pushing that value to the stack. With a register machine I just slap the value in a register and use it as an operand as many times as I need.
Quite. In practice, a high-performance processor today, either stack or register, will internally have little resemblance to the presented instruction set. The stack will become a huge array of registers that are the inputs and outputs to various computation units, and they will be tracked and renamed as necessary to align with the various slots in the stack, rather than actually moving things around on the stack. Just as the integer register file on a register machine, becomes a huge array of registers that are renamed as necessary. Any difference between them, in terms of hardware implementation, has largely disappeared over the last couple decades.
And to a point.. pointfree in haskell is an extreme of that, albeit at some point you start having to remember more information if you stack too many operators.
On the other hand, the circuitry is simpler and implementing a compiler for such an architecture is close to trivial. Early stack computers, especially from Burroughs, were the first to be mainly programmed in a high level language, assembly was barely used if at all. This was revolutionary at the time.
Not necessarily. BEAM, the Erlang VM, used by Erlang, Elixir and other languages is a register software machine. https://www.erlang.org/blog/a-brief-beam-primer/