333 would be 3/(3/3) = 3 which is not correct. division doesn't work as expected if T -> F | F * T | F / T, since the T after * or / will recurse until T -> F, and then the operation evaluates from the last F back, so 3/3/3 =.An exercise is to write out the grammar, and then devise the other methods of the grammar, as well as the constant tokenizer.

The constant is a parse of a lexeme which consists of (whitespace ignored) initial + or -, a string of numbers and/or decimal point occurring once. a factor is a parenthesised expression or a entity, and.a term is a factor, a factor multiplied by a term, or a factor divided by a term, and.The rest of the grammar is something like if the function expr is returning +, the first term call's return value is being held in a register and pushed on the cpu stack before the second call to term. This relies on the program stack to use recursion not only to provide the ordering for the grammar rules, but to do depth first processing so that intermediate results are stored on the stack in the callers' program stack frames.Į.g.

When parsing is complete, this array is traversed, and a third mutable array is used to process each token in order, pushing number tokens, and popping numbers for operations and pushing results.Ī third implementation could eliminate the use of a stack by having operations return numbers which are the result of applying operations or converting a number lexeme.

#import int main ( void ) Īnother implementation of plus, is that there is a second instance of a mutableArray that stores NSString tokens, and 'plus' simply pushes a '+' NSString token onto this second array.

Xcde simple writer