Consider the following grammar (yes, it is ambiguous but that is unimportant). The subscripts are used to distinguish otherwise identical non-terminals for the purpose of the questions below. → ; → → → int double = → → + + - | * : → → + → a legal name in the language → a base 10 representation of an integer → a base 10 representation of a floating point number Suppose our static semantic description has five attributes: type = { integer, double } typetable() = { integer, double, error } inittable() = { true, false, error } typebinding = (, { integer, double }) initialized = (, { true, false }) typetable maps each possible variable name to its declared type, and inittable maps each possible variable name to a boolean indicating whether the variable has been assigned a value. Initially, both typetable and inittable will map all possible variable names to error to indicate that the variables have not been declared in the program. typebinding maps a single variable name to its declared type, and initialized maps a single variable name to whether it has been assigned a value. For each subscripted non-terminal, provide a rule to calculate its type, table, inittable, typebindig, and ini- tialized attributes, if that non-terminal requires that attribute. Each attribute should either be inherited or synthesized, but not both. For example, here are two such rules: .type := integer .initialized := (, false) (Here I am using := to create a mapping so you can use = to mean only mathematical equality.)