Many simple languages, including most data languages, avoid the subtleties of grammar design by not introducing operators. Operators such as “+” and “-” bring up the question of whether
11 + 5 * 2
should equal 32 or 21. Different languages, notably Smalltalk and Java, have different answers to this question, depending on the precedence of operators. Another question that arithmetic encounters is whether
25 – 16 - 9
equals 0 or 18. Here the answer depends on the associativity of the “-” operator, which determines whether the rightmost or leftmost operator applies first. The grammar for your language determines the associativity and precedence of operators in your language.
In addition to establishing ...