Here's a possible translation scheme:
\begin{align*} 1. & \quad \text{<assign-stmt>} \ ::= \ \text{<LHS> := <E>} \quad & \{ \text{postfix(LHS, E);} \} \\ 2. & \quad \text{<E>} \ ::= \ \text{<E> + <T> | <T>} \quad & \{ \text{postfix(E, T, "+");} \} \\ 3. & \quad \text{<T>} \ ::= \ \text{<T> * <V> | <V>} \quad & \{ \text{postfix(T, V, "*");} \} \\ 4. & \quad \text{<V>} \ ::= \ \text{id | (<E>)} \quad & \{ \text{postfix(V);} \} \\ 5. & \quad \text{(LHS)} \ ::= \ \text{id} \quad & \{ \} \\ \end{align*}
The translation scheme defines the following semantic actions:
-
Assignment Statement (<assign-stmt>
):
- Postfix the right-hand side expression (
E
), then append the assignment operation (:=
) with the appropriate type information.
-
Expression Addition (<E>
):
- Postfix the left-hand side expression (
E
), postfix the right-hand side term (T
), and append the addition operation (+
) with the appropriate type information.
-
Term Multiplication (<T>
):
- Postfix the left-hand side term (
T
), postfix the right-hand side variable (V
), and append the multiplication operation (*
) with the appropriate type information.
-
Variable (<V>
):
- If the production is
id
, postfix the identifier.
- If the production is
(<E>)
, postfix the expression inside the parentheses.
-
Left-Hand Side ((LHS)
):
- For a variable identifier (
id
), do nothing.
The type-specific operations ((+,i)
, (+,r)
, (*,i)
, (*,r)
, (:=,i)
, (:=,r)
) are determined based on the type information obtained from the give_type
function for each variable.
The translation scheme generates postfix expressions for expressions and assignments in the given language with type-specific operations.