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Understanding logical query processing phases and the unique aspects of SQL is important to get into the special mind set required to program in SQL. By being familiar with those aspects of the language, you can produce ef cient solutions and explain your choices. Remember, the idea is to master the basics.
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Set Theory and Predicate Logic
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This chapter contains a brief introduction to two cornerstones of mathematics: set theory and predicate logic, which are intimately connected to the world of databases. Database tables represent sets of facts, and database queries produce result sets based on query predicates. The objects of study in logic are propositions statements of fact that are either true or false and propositional functions, which are open statements with one or more unspeci ed values. Database tables hold representations of statements of fact, and query predicates are propositional functions. Later in this book, you ll use logical set-based thinking to write a T-SQL SELECT query to return the following result set: all customers for whom every employee from the USA has handled at least one order. Your query won t tell the Microsoft SQL Server engine how to produce the desired result; instead, it will simply describe the result, in sharp contrast to how you d use a procedural programming language, such as C# or Fortran, to produce the same result. The more you understand about set theory and logic, the easier SQL will be for you.
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I ll begin this chapter by describing all customers for whom every employee from the USA has handled at least one order not in SQL, as you will see in 6, Subqueries, Table Expressions, and Ranking Functions, but in the mathematical language of set theory. Turning English into mathematics, by the way, is much harder than doing mathematics or speaking English, and this example will highlight some of the mathematical ideas that are particularly useful to SQL programmers. Some of the set theory notation in this section will be de ned later. Don t worry if it s unfamiliar. First of all, let s give the result set we re after a name.
De nition of the set S (in English)
Let S be the set of all customers for whom every employee from the USA has handled at least one order.
Inside Microsoft SQL Server 2008: T-SQL Querying
By naming this set of customers (even by referring to it as a set, so that we can talk about having named it!), we ve made an implicit assumption that the description has a clear meaning it describes something unambiguously. The de nition mentions customers, employees, and orders, and to talk about these categories of things mathematically, we should think of them as sets and name them: Let Customers, Employees, and Orders be the sets of customers, employees, and orders, respectively. To describe S mathematically, we don t have to understand what these terms mean; we only have to name them. One meaningful term in the description doesn t represent a kind of thing: handled. Again, we don t need to know what it means from a business point of view for an employee to handle an order for a customer, but we do need to understand that, given appropriate details, has handled is either true or false. We also have to be clear what details it s true or false about. If we dissect how handled is used in the description, we see that it has to do with three details: an employee, an order, and a customer. It s especially useful to be able to write down the handled fact in a particular case. Given a particular employee e, a particular order o, and a particular customer c, this fact (employee e handled order o for customer c) is either true or false. In other words, it s a predicate. Using function notation, write handled(e,o,c) to represent the truth value of employee e handled order o for customer c. Depending on the values of e, o, and c, handled(e,o,c) has a truth value: it s true or it s false.
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