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.

Read now

Unlock full access

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 11

Using Logic to Formulate SQL Expressions

There is science, logic, reason; there is thought verified by experience. And then there is California.¹

—Edward Abbey: A Voice Crying in the Wilderness (1989)

In Chapter 6, I described the process of expression transformation as it applied to expressions of the relational algebra; to be specific, I showed how one such expression could be transformed into another logically equivalent one, using various transformation laws. The laws I considered included such things as:

Restriction distributes over union, intersection, and difference
Projection distributes over union but not over intersection or difference

and several others. (As you might expect, analogous laws apply to expressions of the relational calculus also, though I didn’t say much about any such laws in Chapter 10.)

Now, the purpose of such transformations, as I discussed them earlier, was essentially optimization; the aim was to come up with an expression with the same semantics as the original one but better performance characteristics. But the concept of expression transformation—or query rewrite, as it’s sometimes (not very appropriately) known—has application in other areas, too. In particular, and very importantly, it can be used to transform precise logical expressions, representing queries and the like, into SQL equivalents. And that’s what this chapter is all about: It shows how to take the logical (i.e., relational calculus) formulation of, e.g., some query ...