Fortunately these rules are natural and easy to remember, especially the details of how different languages choose different orders, relative to the confusing and abhorrent prefix notation (- (^ 3 2)) or (^ (- 3) 2).
(- (expt 3 2))
(expt -3 2)
Likewise, in dc
3 _ 2 ^ p
_3 2 ^ p
3 2 ^ _ p
When you start touching infix, you get into https://en.wikipedia.org/wiki/Shunting_yard_algorithm which was not a fun part of my compiler class.
(And yes, I do recognize your credentials ... I still think that lisp and forth (above examples for dc) are better notational systems for working with computers even if it takes a bit of head wrapping for humans).
Postfix is interesting in forth. It makes the stack manipulations very easy to reason about, and the stack is very important there so this looks like a win. The cost is in coherently expressing complex functions, hence the advice to keep words simple. The forth programmers are doing register allocation interwoven with the domain logic.
Lisp makes semantics very easy to write down and obfuscates the memory management implied. No thought goes on register allocation but neither can you easily talk about it.
Discarding the lever of syntactic representation is helpful for communication and obstructive to cognition. See also macros.
3 _ 2 ^ p gives 0
_3 2 ^ p gives 9
3 2 ^ _ p gives 0
5 _ p gives 0
_5 p gives -5
~ % dc -v
dc 6.5.0
Copyright (c) 2018-2023 Gavin D. Howard and contributors
Report bugs at: https://git.gavinhoward.com/gavin/bc
This is free software with ABSOLUTELY NO WARRANTY.
~ % dc
3 _ 2 ^ p
9
_3 2 ^ p
9
3 2 ^ _ p
-9
5 _ p
-5
_5 p
-5
(control-D)
You are correct about its behavior.
See https://git.gavinhoward.com/gavin/bc/src/branch/master/manua... (scroll down to the underscore command).
dc -V
dc (GNU bc 1.07.1) 1.4.1
3 _ 2 ^ p
0My dc does have a few differences from the GNU dc. I added the extension of using _ as a negative sign.
That is why you are both seeing behavior differences.