NOTE3-

Problem 2 [12pt] Consider the simply typed -calculus and its typing rules defined in Note 3, Suppose we want to add a new operation , which performs the xor" operation on two booleans. We can define the syntax of this new language as follows: terms where the dots represents the terms defined in note 3. The syntax of types remains unchanged a) (4pt) Follow the notations in Note 3, write down a typing rule (call it TXor) for the new term el C2. b) (8pt) What is the type of the terrn ((Az : bool. (z (true Afalse))) true) ? Justify your answer by writing down the proof tree for this term. Problem 2 [12pt] Consider the simply typed -calculus and its typing rules defined in Note 3, Suppose we want to add a new operation , which performs the xor" operation on two booleans. We can define the syntax of this new language as follows: terms where the dots represents the terms defined in note 3. The syntax of types remains unchanged a) (4pt) Follow the notations in Note 3, write down a typing rule (call it TXor) for the new term el C2. b) (8pt) What is the type of the terrn ((Az : bool. (z (true Afalse))) true) ? Justify your answer by writing down the proof tree for this term