test.p6

# https://en.wikipedia.org/wiki/Parsing_expression_grammar
grammar Arithmetic {
    rule TOP     { ^^ <Exp> $$ }
    rule Exp     { <Sum> }
    rule Sum     { <Product>+ % <[+-]> }
    rule Product { <Value>+   % <[*/]> }
    rule Value   { <ident>+ | '('<Exp>')' }
}

say Arithmetic.parse($_) for
'a',
'a+b',
'a*b',
'(a-b)*(a+b)',
;