Platoclast on Data

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		PLATOCLAST ON DATA A New Approach to Relational Data Base Adrian Larner


		Dedication
		To the memory of A H G Palmer Headmaster of Great Yarmouth Grammar School A fine mathematician

		Acknowledgments
		I am indebted, especially for what understanding I have of usability and simplicity, to John Kay, who showed me how to design software, and to William Reynolds, who showed me how to do systems analysis. This book has its genesis in my design of the IBM Query.DL/I program product, a user-friendly front-end to DL/I (hierarchical) data bases. I am indebted to my former manager, Ian Nussey, without whose commitment and zeal the product would never have seen the light of day; to John Knapman, who originally conceived it, and who kindly criticised the unpublished paper that was the distant predecessor of these lectures; to Chris Corfield, who checked the formal definitions in that paper; to John Dawkins, who originated the concept that I have called “many-dimensioned data”; to my colleagues on the Query.DL/I project. especially Peter Hayes, Michael Fabianski, and Mike Rigby, who managed against all the odds to implement the product; and to Leo Wu and Olov Pettersson, who worked so hard to get Query.DL/I accepted and enhanced. As the approach to data base theory in this book was the eventual outcome of my sleeplessness, Olov is now forgiven for inadvertently committing me to creating an SQL-Iike front-end to Query.DL/I overnight. My thanks go also to Hugh Darwen and Chris Date for many valuable discussions and criticisms of the ideas in this book, both face-to-face and by correspondence. Except in exposition of his theory I am not, in general, to be taken as speaking in propria persona through the mouth of Professor Platoclast, but his words are indeed mine when he begins by saying that “Dr Codd’s achievement is very great indeed”, and concludes: “I would be proud for my theory to be considered an extension (even merely an extension) to one of the greatest advances in the history of DP.” I would like to thank the many faculty members of the departments of Computer Science and Philosophy at the University of Warwick who made me welcome and stimulated my ideas during my sabbatical there in 1986/87, the only extended period that I have had for careful, calm deliberation of many of the ideas in these lectures. And I am most grateful to my employers, IBM United Kingdom Ltd, both for granting me that sabbatical and for filling my long career with the practical challenges in software design that have driven me to the theory propounded here.
		Adrian Lamer March 1993


	Contents
	Editor’s Introduction Platoclast’s Objective Platoclast’s Argument *Platoclast’s Permission to Publish* *Platoclast’s Introduction* Lecture I – Data Structure The Definition of Formatted Data Vagueness and Criteria of Application Ambiguity and Criteria of identity Fields Records Records are Essential Other Data Structures are Inessential No Duplicate Records Records are Unordered Tables Columns and Rows Polynormal Records Normal Records Tables of Uniform Format Are Tables Essential? Lecture II – Data Formalised Using a Logic Primitives, Definitions, and Postulates The First Order Logic Records, Parts, and Aggregates Record Types Record Values Base Records *Implication* Lecture III – The Interpretation of Relations Domains Relations Predicates and Propositions Speaking of Sets Speaking of Relations Set Theory Relations Are Not Sets Lecture IV – Data Manipulaton The Theory of Two-Dimensional Data Data Manipulations Aggregation of Records Interpretation Natural Join Selection Cartesian Product Intersection Extension Projection An Exercise in Interpretation Other Operations Lecture V – Predicates and Names Identity Natural Composition Names as Values Names and Implication Intensional Predicates “Shakespearean” Predicates Self-Interpretation The Join Trap Proper Names *The FOPC and Identity* Lecture VI – Entities and Identities The “Entity” Interpretation What Are Entities? Discovering Entities in the “Real World” Objections to “Entities” Entity and Identity Identity Absolute Identity Relative Identity Systemic Identity A Persistent Identity *Does Each Record Represent an Entity?* Lecture VII – The Same Again Economy of Means Relative Identity Naming Counting Trying to Count under Absolute Identity Concrete (Non-additional) Types Systemic Identity Neither Absolute Nor Persistent Relative Identity Persistent Abstract (Additional) Types (Sets) Abstraction and Cardinality Impossibility of Counting under Absolute Identity Sets as Interpretations Appeal to Simplicity Lecture VIII – New Interpretations Column Definitions and Criteria of Identity Narrowness and Completion of Criteria of Identity Proper and Common Names Existential Interpretation Special Cases Restriction Joins Projection Cryptic Data Proper Values *Are Records Assertions?* Lecture IX – Tables Are Not Essential The Classical Interpretation Reconsidered Can Abstract Types Be Saved? Tables Table Names Are Table Names Essential? Record Identifiers and Table Names Two Levels of Record Table Uniformity and a Language Question Connection Between Record Levels Lecture X – Handling Non-normal Records Typed and Untyped Quantification Polynormal Records The Postulate of Two-Dimensionality Restriction Conditions and the Quantifying Operators Restrictions on Present and Absent Fields Completed Identities and Cryptic and Esoteric Data SQL Introduced Lecture XI – Nulls Non-Uniform Tables Operations Nulls Missing Information Modalities What is the Problem of Nulls? Nulls and Joins Semantic Nulls Improper Values Proper Semantic Nulls Improper Semantic Non-Nulls *Semantic Nulls* Which Semantic Null? Lecture XII – Integrity, Domains, Defaults Entity Integrity Referential Integrity Domains and Nulls Default Values Operations Modalities Relatively Proper Values Padding Proper Semantic Nulls Improper Semantic Non-Nulls *Afterthoughts on Nulls* Lecture XIII – Conjunction Operations Reinterpretation Conjunction Varieties of Conjunction Data Manipulation Languages Domain Calculus Relational Algebra Tuple Calculus Union Lecture XIV – The Combination Operation Outer Join Varieties of Outer Join Loss of Information on Outer Join Intractability of Outer Join Conjoin Combination Lecture XV – Quantification Combination as a Primitive Operator Non-Uniform Tables and Language Issues Relational Union Quantification Accumulation and Collection Interpretation Lecture XVI – Data Types Data Representation Independence Data Encapsulation Token Processing Handling Nulls and Absent Values Accumulation by Reduction of Collections *On Some Fallacies* Lecture XVII – Collection and Negation Token Identity Identities of Multidimensional Data Modality as a Data Dimension Collections Differentiation Collections as Joins Difference *A Clarification* Lecture XVIII – Recapitulation Tables and Records Data Manipulations Fields Handling Data Outside the Data Manipulation Language Token Handling First Order Logic Subset Data Manipulation Language The “Closed Data Base” Assumption Outer Join Defined *A Remark on Object Orientation* *A Remark on Polymorphic Types* Lecture XIX – Data Independence Access Independence Data Organisation Program Data is Structured Program Structure Data Structured Programming A Common Program Structure Parallel Processing Closure *Afterword on Program Structures* Encapsulation of Structure Lecture XX – More Data Manipulations Hierarchies Level Breaks Headlining Empty-Headlining Constraints of Uniform Format Grouping Nested Queries Relaxing the Uniform Format Constraint “Ideal” Query Scheme Recapitulation Lecture XXI – Views Queries and Views View Facilities Schematic Queries User Views Program Queries and Views “Ideal” Definition of Views Updating Through Views Views Enhanced with Record Identifiers Relational Data Base Design Physical Design Stored Records *Views of What?* Lecture XXII – Some Data Base Problems Cryptic Identifiers Ordered Records Physical Views Limits of First Order Logic The Problem of the Ancestral Bills of Material What is “Logically Basic”? Lecture XXIII – Bills of Material A Solution in the Theory of Two-Dimensional Data A Solution Using a Schematic Query Logically Basic Records Primitive Predicates Postulates Updating Through Views Non-Updatable Views Lecture XXIV – Keys Primary Keys Identifiers and Keys Candidate Keys Keys in Optimisation Keys in Data Base Design The Join Trap Origins of Functional Determination *Duplicate Rows* “Duplicate” Needs Definition Interpretation of Duplicate Rows A Case for Duplicate Rows Arbitrary Choice Among Duplicates Duplicate Rows in SQL Lecture XXV – Integrity and Design Referential Integrity Existence Dependence and Simple Dependence Normal and Non-Normal Records Integrity Constraints on Views Dependence and Functional Determination Independent Entities Columns as Classifications of Entities Existence Dependence and Classification Independence and Existential Interpretations Lecture XXVI – More on Design Four Levels of Data Design Problems of Design Analysing “Part” Entities Composition Deletion Query Results Affected by Functional Determination Assertions A Miscellany of Problems Design of One-One Relationships Counts and Tallies Nested Queries A Problem with Normal Records Lecture XXVII – First Normal Form Polynormality Non-Normality Limits of Complexity Deviations from Normality Composite Columns Compound Values Encapsulated Data Structures Adequacy of Normal Records Non-Normal Relations Data Structure Dependence Structured Output Simplicity and Power *Character Strings* An Informal Symposium Tables and Views Table Types and Instances Views Adding Columns to Tables Cartesian Product v. Natural Join The Identity of Queries User Front-End with Natural Join Handling Very Large Tables Nested Queries Unnesting Queries Nesting as a Syntactic Variation The Importance of Syntax Non-Uniform Format Needed for Meta-Data A Philosophical Objection The End of the Conversation *On Nested Relations* Lecture XXIX – The Reckoning Platoclast‘s Theory Records Tables Interpretation Data Manipulations Nulls Multi-level Analysis Schematic Queries Negative Achievements Evaluation Extendability Upward Compatibility Lecture XXX – Retrospect and Prospect Challenges to Relational Theory The Use of Relative Identity Formalisation Non-Uniform Format Looking to the Future Duplicate Records Once Again Farewell Index

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Platoclast on Data: Editor’s Introduction
Copyright © 1993, 2001 Adrian Larner. The author asserts all moral rights.

Dedication

Acknowledgments

Contents