2 [1.5 marks] Recall in lambda calculus, logic connectives NOT and OR can be defined as: where T (Ary | x) and F (Ary | y). y (or in some textbooks. x y or x-> y) In logic, that "x implies y" is written x Denote this function by IMP (a) Give a lambda expression that defines IMP, i.e., write what is missing at the right hand side of the vertical bar below IMP = (Ary ! ) Make sure that your answer is a normal form, 1.e., t cannot contain still reducible. expressions that are Hint: In logic, we know x y V y. (b) Using your definition, for each expression below, reduce it to a normal form. Here, the order of reduction is unimportant. 2 [1.5 marks] Recall in lambda calculus, logic connectives NOT and OR can be defined as: where T (Ary | x) and F (Ary | y). y (or in some textbooks. x y or x-> y) In logic, that "x implies y" is written x Denote this function by IMP (a) Give a lambda expression that defines IMP, i.e., write what is missing at the right hand side of the vertical bar below IMP = (Ary ! ) Make sure that your answer is a normal form, 1.e., t cannot contain still reducible. expressions that are Hint: In logic, we know x y V y. (b) Using your definition, for each expression below, reduce it to a normal form. Here, the order of reduction is unimportant