Use an LR syntactic grammar to parse the token stream given by the lexer. The goal symbol is either a single expression or nothing. Support the operations of addition, subtraction, multiplication, division, and exponentiation.
The terminal NUMBER in the syntactic grammar above refers to the nonterminal IntegerLiteral in the lexical grammar.
Implicit grouping (sometimes incorrectly called “associativity”) is left-to-right for all operations except for exponentiation, which is right-to-left.
"1 + 2 + 3" is implied as "(1 + 2) + 3"
"1 - 2 - 3" is implied as "(1 - 2) - 3"
"1 * 2 * 3" is implied as "(1 * 2) * 3"
"1 / 2 / 3" is implied as "(1 / 2) / 3"
"1 ^ 2 ^ 3" is implied as "1 ^ (2 ^ 3)"
Operator precedence, not including grouping symbols, is strongest for exponentiation, medium for multiplication/division, and weakest for addition/subtraction.
"1 + 2 - 3" is implied as "(1 + 2) - 3"
"1 - 2 + 3" is implied as "(1 - 2) + 3"
"1 * 2 / 3" is implied as "(1 * 2) / 3"
"1 / 2 * 3" is implied as "(1 / 2) * 3"
"1 + 2 * 3" is implied as "1 + (2 * 3)"
"1 - 2 * 3" is implied as "1 - (2 * 3)"
"1 + 2 / 3" is implied as "1 + (2 / 3)"
"1 - 2 / 3" is implied as "1 - (2 / 3)"
"1 + 2 ^ 3" is implied as "1 + (2 ^ 3)"
"1 - 2 ^ 3" is implied as "1 - (2 ^ 3)"
"1 * 2 ^ 3" is implied as "1 * (2 ^ 3)"
"1 / 2 ^ 3" is implied as "1 / (2 ^ 3)"
Use an LR syntactic grammar to parse the token stream given by the lexer. The goal symbol is either a single expression or nothing. Support the operations of addition, subtraction, multiplication, division, and exponentiation.
The terminal
NUMBERin the syntactic grammar above refers to the nonterminalIntegerLiteralin the lexical grammar.Implicit grouping (sometimes incorrectly called “associativity”) is left-to-right for all operations except for exponentiation, which is right-to-left.
Operator precedence, not including grouping symbols, is strongest for exponentiation, medium for multiplication/division, and weakest for addition/subtraction.