An Introduction to Functional Programming Through Lambda Calculus

- 86 -For boolean functions, we will allow the use of the constants TRUE and FALSE in place of bound variables. Ingeneral, for:def =IF THEN ELSE we will now write:def TRUE = or FALSE = Thus, negation is defined by:NOT TRUE = FALSENOT FALSE = TRUEbut written as:def NOT X =IF XTHEN FALSEELSE TRUEWe will now write:def NOT TRUE = FALSEor NOT FALSE = TRUESimilarly, implication is defined by:IMPLIES TRUE Y = YIMPLIES FALSE Y = TRUEbut written as:def IMPLIES X Y =IF XTHEN YELSE TRUEWe will now write:def IMPLIES TRUE Y = Yor IMPLIES FALSE Y = TRUEFor numbers, we will allow the use of the constant 0 and bound variables qualified by nested SUCCs in place of boundvariables. In general, for:rec =IF ISZERO THEN ELSE we will now write: