Synthesized Attributes

We want to decorate the parse trees we construct with annotations that give the value of certain attributes of the corresponding node of the tree. We will do the example of translating infix to postfix with 1+2/3-4*5. We use the following grammar, which follows the normal arithmetic terminology where one multiplies and divides factors to obtain terms, which in turn are added and subtracted to form expressions.

  expr   → expr + term | expr - term | term
  term   → term * factor | term / factor | factor
  factor → digit | ( expr )
  digit  → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

This grammar supports parentheses, although our example does not use them. On the right is a movie in which the parse tree is build from this example.

The attribute we will associate with the nodes is the postfix form of the string in the leaves below the node. In particular, the value of this attribute at the root is the postfix form of the entire source.

The book does a simpler grammar (no *, /, or parentheses) for a simpler example. You might find that one easier.