Calculate input with atoms, erlang - erlang

Question

I am trying to calculate this input:
evaluate({mul,{plus,{num,2},{num,3}},{num,4}}).
and get this as an answer:
20
But I cant get it working, here is my code:
evaluate(List) ->
[Res] = lists:foldl(fun evaluate/2, [], tuple_to_list(List)),
Res.
evaluate({num,X},Stack) -> [X|Stack];
evaluate(plus,[N1,N2|Stack])->[N1+N2|Stack];
evaluate(mul,[N1,N2|Stack])->[N1*N2|Stack];
evaluate([{Optr, Num1, Num2}],Stack) ->
evaluate(Num1,Stack),evaluate(Num2,Stack),evaluate(Optr,Stack).
Can you point out my mistakes and correct me, thank you.

Answer 1

First, define your syntax:
{num,Value} for a number,
{plus,Term1,Term2} for an addition,
{mul,Term1,Term2} for a multiplication,
and so on.
Second, solve individual cases:
evaluate({num,Value}) -> Value;
evaluate({plus,Term1,Term2}) -> evaluate(Term1) + evaluate(Term2);
evaluate({mul,Term1,Term2}) -> evaluate(Term1) * evaluate(Term2).
in the shell:
1> E = fun E({num,Value}) -> Value;
1> E({plus,Term1,Term2}) -> E(Term1) + E(Term2);
1> E({mul,Term1,Term2}) -> E(Term1) * E(Term2)
1> end.
#Fun<erl_eval.30.90072148>
2> E({mul,{plus,{num,2},{num,3}},{num,4}}).
20
3>
Although I used a lot the reverse polish notation, it does not apply in your example. The input should be (for your example) [ 2, 3, plus, 4, mul] and it can be solved like this:
evaluate(plus,[A,B|Rest]) -> [A+B|Rest];
% pop operands,perform the operation and push the result
evaluate(mul,[A,B|Rest]) -> [A*B|Rest];
evaluate(A,Acc) when is_number(A) -> [A|Acc]. % push operand on the stack
evaluate(Exp) -> [Res] = lists:foldl(evaluate/2,[],Exp), Res.
in the shell
22> E = fun E(plus,[A,B|Rest]) -> [A+B|Rest];
22> E(mul,[A,B|Rest]) -> [A*B|Rest];
22> E(A,Acc) -> [A|Acc]
22> end.
#Fun<erl_eval.36.90072148>
23> Eval = fun(Exp) -> [Res] = lists:foldl(E,[],Exp), Res end.
#Fun<erl_eval.6.90072148>
24> Eval([2,3,plus,4,mul]).
20