An Introduction to Functional Programming Through Lambda Calculus

- 83 -will do so. However, for a non numeric argument, ISZERO (and thence the two IFs) will return a BOOL_ERRORinstead of a NUMB_ERROR.As definitions these seem satisfactory but they would be appallingly inefficient if used as the basis of animplementation because of repetitive type checking. Consider, for example(*):ADD 1 2First of all in:both:and:IF AND (ISNUMB 1) (ISNUMB 2)ISNUMB 1ISNUMB 2are checked and return booleans. Next:AND (ISNUMB 1) (ISNUMB 2)checks that both ISNUMBs return booleans and then itself returns a boolean. Then:IF AND (ISNUMB 1) (ISNUMB 2)checks that AND returns a boolean.Secondly, after ADD1 is called:calls:IF ISZERO 2ISZERO 2to check that 2 is a number and return a boolean. Next:IF ISZERO 2checks that ISZERO returns a boolean.Now, ADD1 is called recursively through:so:calls:ADD1 (SUCC 1) (PRED 2)IF ISZERO (PRED 2)________________________________________________(*) This example also highlights repetitive argument evaluation due to naive normal order evaluation. We will consider differentapproaches to argument evaluation in chapter 8.