Problem 5: Let Mstate be a denotational semantic mapping that takes a syntax rule and a state and produces a state. Define the Mstate mapping for the following three syntax rules assuming we allow side effects, that is, assuming expressions and conditions can change the values of variables. = if then statement? else while condition> Assume we have the following mappings defined: Malue takes a syntax rule and a state and produces a numeric value (or an error condition) Mboolean takes a syntax rule and a state and produces a true / false value (or an error condition). Mname takes a syntax rule and produces a name (or an error condition). Add takes a name, a value, and a state and produces a state that adds the pair (name, value) to the state. Remove takes a name and a state and produces a state that removes any pair that contains the name as the first element. You may assume the Add and Remove mappings do not produce errors. Problem 5: Let Mstate be a denotational semantic mapping that takes a syntax rule and a state and produces a state. Define the Mstate mapping for the following three syntax rules assuming we allow side effects, that is, assuming expressions and conditions can change the values of variables. = if then statement? else while condition> Assume we have the following mappings defined: Malue takes a syntax rule and a state and produces a numeric value (or an error condition) Mboolean takes a syntax rule and a state and produces a true / false value (or an error condition). Mname takes a syntax rule and produces a name (or an error condition). Add takes a name, a value, and a state and produces a state that adds the pair (name, value) to the state. Remove takes a name and a state and produces a state that removes any pair that contains the name as the first element. You may assume the Add and Remove mappings do not produce errors