An Introduction to Functional Programming Through Lambda Calculus

- 14 -We have made a function from a formula by replacing an object with a name and identifying the name that we used.We have then evaluated the function by replacing the name in the formula with a new object and evaluating theresulting formula.Let us use abstraction again to generalise our example further. Suppose the cost of items goes up to 11 pence. Nowthe total cost of items is:REPLACE items IN 11*itemsSuppose the cost of items drops to 9 pence. Now the total cost of items is:REPLACE items IN 9*itemsBecause the cost changes, we could also introduce a name to stand for the cost in general, say cost:REPLACE cost INREPLACE items IN cost*itemsHere we have abstracted over two operands in the formula. To evaluate the abstraction we need to supply two values.For example, 12 items at 32 pence will have total cost:which is:which is:REPLACE cost WITH 32 INREPLACE items WITH 12 IN cost*itemsREPLACE items WITH 12 IN 32*items32*12For example, 25 items at 15 pence will have total cost:which is:which is:REPLACE cost WITH 15 INREPLACE items WITH 25 IN cost*itemsREPLACE items WITH 25 IN 15*items15*25Suppose we now want to solve a different problem. We are given the total cost and the number of items and we wantto find out how much each item costs. For example, if 12 items cost 144 pence then each item costs:144/12If 15 items cost 45 pence then each item costs:45/12In general, if items items cost cost pence then each item costs:REPLACE cost INREPLACE items IN cost/items