Dhaka::Grammar

Abstract base class for grammar specifications.

The following is a grammar specification for simple arithmetic. Precedences are specified as in Yacc - in ascending order of binding strength, with equal-strength symbols on the same level. Production rules are specified for each symbol by specifying the name of the production (used when encoding the Evaluator) and the expansion for that particular production. For example, the production named addition expands the symbol 'E' to the list of symbols ['E', '+', 'E'].

class ArithmeticPrecedenceGrammar < Dhaka::Grammar
  precedences do
    left ['+', '-']
    left ['*', '/']
    nonassoc ['^']
  end

  for_symbol(Dhaka::START_SYMBOL_NAME) do
    expression ['E']
  end

  for_symbol('E') do
    addition ['E', '+', 'E']
    subtraction ['E', '-', 'E']
    multiplication ['E', '*', 'E']
    division ['E', '/', 'E']
    power ['E', '^', 'E']
    literal ['n']
    parenthetized_expression ['(', 'E', ')']
    negated_expression ['-', 'E'], :prec => '*'
  end
end

In the above grammar, the symbols + and - are declared as being left-associative, meaning that 1 + 2 + 3 is parsed as (1 + 2) + 3 as opposed to 1 + (2 + 3) (right-associativity). The symbol ^ is declared nonassoc which means that expressions such as 2 ^ 3 ^ 4 are not allowed (non-associative). + and - are listed before ^ which means that they bind lower, and an expression such as 2 + 3 ^ 5 will be always be parsed as 2 + (3 ^ 5) and not (2 + 3) ^ 5.