An Introduction to Functional Programming Through Lambda Calculus

- 48 -def = We can now re-write all our definitions:def identity x = xdef self_apply s = s sdef apply func = λarg.(func arg)and hence:def apply func arg = func argdef select_first first = λsecond.firstand hence:def select_first first second = firstdef select_second first = λsecond.secondand hence:def select_second first second = seconddef make_pair e1 = λe2.λc.(c e1 e2)and hence:and hence:def make_pair e1 e2 = λc.(c e1 e2)def make_pair e1 e2 c = c e1 e2def cond e1 e2 c = c e1 e2def true first second = firstdef false first second = seconddef not x = x false truedef and x y = x y falsedef or x y = x true yFor some functions there are standard equivalent notations. Thus, it is usual to write:cond in an if ... then ... else ... form. We will use:if then else