book

SQL and Relational Theory, 3rd Edition

by C.J. Date

November 2015

Intermediate to advanced

582 pages

16h 19m

English

O'Reilly Media, Inc.

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The relational model is much misunderstoodSome remarks on terminologyPrinciples not productsA review of the original modelModel vs. implementationProperties of relationsBase vs. derived relationsRelations vs. relvarsValues vs. variablesConcluding remarksExercisesAnswers

Types and relationsEquality comparisonsData value atomicityWhat’s a type?Scalar vs. nonscalar typesScalar types in SQLType checking and coercion in SQLCollations in SQLRow and table types in SQLConcluding remarksExercisesAnswers
What’s a tuple?Rows in SQLWhat’s a relation?Relations and their bodiesRelations are n-dimensionalRelational comparisonsTABLE_DUM and TABLE_DEETables in SQLColumn naming in SQLConcluding remarksExercisesAnswers
What’s wrong with duplicates?Duplicates: further issuesAvoiding duplicates in SQLWhat’s wrong with nulls?Avoiding nulls in SQLA remark on outer joinConcluding remarksExercisesAnswers
Updating is set levelRelational assignmentMore on candidate keysMore on foreign keysRelvars and predicatesRelations vs. typesExercisesAnswers
Some preliminariesMore on closureRestrictionProjectionJoinUnion, intersection, and differenceWhich operators are primitive?Formulating expressions one step at a timeWhat do relational expressions mean?Evaluating SQL table expressionsExpression transformationThe reliance on attribute namesExercisesAnswers
Exclusive unionSemijoin and semidifferenceExtendImage relationsDivideAggregate operatorsImage relations revisitedSummarizationSummarization revisitedGroup, ungroup, and relation valued attributes“What if” queriesA note on recursionWhat about ORDER BY?ExercisesAnswers
Type constraintsType constraints in SQLDatabase constraintsDatabase constraints in SQLTransactionsWhy database constraint checking must be immediateBut doesn’t some checking have to be deferred?Constraints and predicatesMiscellaneous issuesExercisesAnswers
Views are relvarsViews and predicatesRetrieval operationsViews and constraintsUpdate operationsWhat are views for?Views and snapshotsExercisesAnswers
Why do we need logic?Simple and compound propositionsSimple and compound predicatesQuantificationRelational calculusMore on quantificationSome equivalencesConcluding remarksExercisesAnswers
Some transformation lawsExample 1: Logical implicationExample 2: Universal quantificationExample 3: Implication and universal quantificationExample 4: Correlated subqueriesExample 5: Naming subexpressionsExample 6: More on naming subexpressionsExample 7: Dealing with ambiguityExample 8: Using COUNTExample 9: Another variationExample 10: UNIQUE quantificationExample 11: ALL or ANY comparisonsExample 12: GROUP BY and HAVINGExercisesAnswers
SELECT *Explicit tablesDot qualificationRange variablesSubqueries“Possibly nondeterministic” expressionsEmpty setsA simplified BNF grammarExercisesAnswers
The relational model vs. othersThe significance of theoryThe relational model definedDatabase variablesObjectives of the relational modelSome database principlesWhat remains to be done?
Vertical decompositionHorizontal decompositionWhat do the shaded entries mean?ConstraintsQueriesMore on predicatesExercisesAnswers
Functional segmentationShardingEventual consistencyThe Fernandez interview

Content preview from SQL and Relational Theory, 3rd Edition

Chapter 10

SQL and Logic

Logic takes care of itself;all we have to do is look and see how it does it.

—Ludwig Wittgenstein: Tractatus Logico-Philosophicus (1922)

As I mentioned in Chapter 1, there’s an alternative to the relational algebra called the relational calculus. What this means is that queries, constraints, view definitions, and so forth can all be formulated in calculus terms as well as algebraic ones; sometimes, in fact, it’s easier to come up with a calculus formulation than an algebraic one, though the opposite can also be true.

What is the relational calculus? Essentially, it’s an applied form of predicate calculus (also known as predicate logic), tailored to the needs of relational databases. So the aims of this chapter are to introduce the relevant features of predicate logic (hereinafter abbreviated to just logic); to show how those features are realized in concrete form in the relational calculus; and, of course, to consider the relevant features of SQL as we go.

Incidentally, it follows from the above that a relational language can be based on either the algebra or the calculus. For example, Tutorial D is based on the algebra (which is why there aren’t many references to Tutorial D in this chapter), and Query-By-Example and QUEL (see Appendix G) are both based on the calculus. So which is SQL based on? The answer, regrettably, is partly both and partly neither ... When it was first designed, SQL was specifically intended to be different from both the algebra ...