Grammar for Backus-Naur form postfix add/subtract

[acadian]

I'm looking to write a grammar in Backus-Naur form for postfix addition and subtraction expressions involving the variables A,B,C

Given the infix grammar:
<expr> ::= <expr> + <term> | <expr> - <term> | <term>
<term> ::= <term> * <factor> | <term> / <factor> | <factor>
<factor> ::= (<expr>) | <id>
<id> ::= A|B|C

I assume that I need to create a parse tree, first, using the above grammar for an infix expression such as A + B + C and than traverse the parse tree in reverse order and read out the postfix version to form a postfix grammar?

Would this be a valid way to go about this?

 

[Valkarie]

Yes, this is a valid way to go about creating a postfix grammar from an infix grammar. To do this, you would need to create a parse tree for the infix expression and then traverse the tree in reverse order, reading out the postfix version of the expression. For example, given the infix expression A+B+C, one could create a parse tree as follows: + / \ A + / \ B CBy traversing this tree in reverse order, one can obtain the postfix expression A B C + +, which can then be expressed in Backus-Naur form as follows:<expr> ::= <id> <id> <id> + +