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Parenthesized expressions over binary +, -, *, /, and ^ (^ with lower precedence than * and /)
The set of tokens of the language is
{+,-,*,/,^,(,),NUMBER}.
The token NUMBER represents unsigned integers, i.e., non-empty sequences
of digits. Examples of correct expressions are “9”,
“1+2^3/1”, “0^(0+0)/2-3”, “1/2^3”, whereas
“1+”, “/3”, “1 2”, “^6”, “5/4*3+”
are not. The generated AST must correspond to an interpretation of all
operators as left-associative, except exponentiation, which is
right-associative. The precedence is different than usual, with exponentiation
having less priority than products and divisions (but more than additions and
subtractions), the rest being as usual. As an example, for input
1+2*3^4/5-6
the resulting AST must be
-(+(1,^(*(2,3),/(4,5)),6),7)
i.e., as if the implicit parenthesization was
(1+((2*3)^(4/5))-6
Authors: Pau Fernández
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Documentation: