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From elementary school to high school we learn to compute with one form ofdata: numbers. Our first use of numbers is to count real things, say, threeapples, five friends, twelve bagels. Later we use numbers without anyappeal to concrete objects, but we have learned that numbers representinformation in the real world.Computing with software is <#60269#>algebra for all kinds of data<#60269#>, not justnumbers. Nowadays, computer programs process representations of music,molecules, law cases, electrical diagrams, architectures of houses, andpoems. Fortunately, we have learned to represent information with otherforms of data than just numbers. Otherwise, computing and programming wouldbecome extremely tedious tasks.Above all, we shouldn't forget that computing means to manipulate datathrough proper basic operations. Some operations create new values. Othersextract values from values. Yet others modify values. Finally, there arealso basic operations for determining to which class a piece of databelongs. Built-in operations and functions are of course just another classof data. Definition is value creation, application is a form of valueextraction.When we define a function, we combine basic data operations. There are twofundamental mechanisms for combining functions: function composition andconditional expressions. The former means that the result of one functionbecomes the argument of another one. The latter represents a choice amongseveral possibilities. When we eventually apply a function, we trigger acomputation. In this book we have studied the laws of basic operations and the laws ofoperation combination. Using these laws we can understand, in principle,how any function processes its input data and how it produces its resultsand effects. Because the computer is extremely fast and good at using theselaws, it can perform such evaluations for more data and for larger programsthan we can do with paper and pencil.