Problem 5 [14pt] Consider the simply typed A-calculus and its typing rules defined in Note 4 (with type inference) a) (7pt) What constraints are generated for the term ( z. ( y)) if we use the type system defined in Note 4? Justify your answer by writing down the proof tree for this term. b) (7pt) Suppose that during type inference, a compiler generates the following constraints to be solved: Solve those constraints by the unification algorithm in Note 4. You need to write down the steps during constraint solving. Problem 5 [14pt] Consider the simply typed A-calculus and its typing rules defined in Note 4 (with type inference) a) (7pt) What constraints are generated for the term ( z. ( y)) if we use the type system defined in Note 4? Justify your answer by writing down the proof tree for this term. b) (7pt) Suppose that during type inference, a compiler generates the following constraints to be solved: Solve those constraints by the unification algorithm in Note 4. You need to write down the steps during constraint solving