On 4/8/23 08:19, Emanuel Berg wrote:
Tom Dial wrote:
Look at the use of parentheses in Lisp [...]
I have thought about that - is Lisp possible without them?
But how do you then know priority? I'm sure someone tried
to get rid of them, but how?
Its quite a few years since I had anything to do with Lisp,
and even more since I wrote my Symbolic Logic final using
parenthesis-free Polish notation (i.e., Reversed RPN).
Yes, you mean instead of
(* 1 2 (+ 1 2 3) 3)
How would that look?
1 2
1 2 3 +
3 *
?
Following Lukaciewicz,
* * * 1 2 + + 1 2 3 3
Evaluation:
* * * 1 2 + + 1 2 3 3 =>
* * * 1 2 + 3 3 3 =>
* * * 1 2 6 3 =>
* * 2 6 3 =>
* 12 3 =>
36
or
* * * 1 2 + + 1 2 3 3 =>
* * 2 + + 1 2 3 3 =>
* * 2 + 3 3 3 =>
* * 2 6 3 =>
* 12 3 =>
36
With RPN:
1 2 1 2 3 + + 3 * * *
Evaluation:
1 2 1 2 3 + + 3 * * * =>
=> 1 2 1 5 + 3 * * * =>
=> 1 2 6 3 * * * =>
=> 1 2 18 * * =>
=> 1 36 * =>
=> 36
'*' and '+' are binary operations. The simplified version '1 2 1 2 3 + 3 *' is
ambiguous without the sort of stop rules that parentheses provide in Lisp. It is
less than obvious how to provide for N-ary operations with N > 2. One, maybe
the simplest, is shown above.
Regards,
Tom
