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Parenthesized expressions over binary +, -, *, /, and ^ (^ with lowest precedence)
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 “1”,
“2+3^4/5”, “1^(1+0)/2-3”, “1/2^3”, whereas
“0+”, “/6”, “1 2”, “^1”, “1/2*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 in that
exponentiation have the lowest precedence. As an example, for input
1+2*3^4/5-6
the resulting AST must be
^(+(1,*(2,3)),-(/(4,5),6))
i.e., as if the implicit parenthesization was
(1+(2*3))^((4/5)-6)
Authors: Pau Fernández
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