Question :

Suppose we have the following context-free grammar which accepts a list of variable

initializations.
Goal ::= single | Goal single
single ::= VAR "=" exp ";"
exp ::= VAR | INT | exp + exp

Here each V AR terminal can be matched to an arbitrary variable name (e.g., a, b, c), and each INT terminal can be matched to an arbitrary integer value (e.g., 5, 25).

1. Add translation schemes to evaluate the number of variables being initialized and the number of variables used to initialize other variables.

2. Add translation schemes to evaluate the value of each variable being initialized and report errors if a variable is used before being initialized. You can assume a global symbol table exists which can be used to store the value of each variable. You can invoke add var(name,val) to insert a (VAR,INT) pair to the symbol table and can invoke lookup var(name) to obtain the value of a varible name; a special value UNDEF is returned if the variable name does not exist in the global symbol table.

3. Modify your translation scheme for (2) to count the index of each variable being initialized; that is, for each variable being initialized, remember how many other variables have already been initialized before it, so that we can use an unique integer to identify each variable initialization; that is, the interface of add var becomes add var(index, name, val) in order to insert a new variable to the global symbol table.