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Database Theory: Lecture 1 Introduction and the Relational Model Background Database Models This Lecture Course

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Database Theory: Lecture 1 Introduction and the Relational Model Background Database Models This Lecture Course Background A database model contains the means for ¡ Specifying particular data structures ¡ Constraining the data sets Database Theory: Lecture 1 ¡ Manipulating the data Introduction and the relational model A DDL (Data Definition Language) provides the means to specify the structures and constraints. Dr G.M. Bierman A DML (Data Manipulation Language) provides the means to manipulate the data; specifically querying and updating. www.cl.cam.ac.uk/Teaching/2002/DBaseThy Database Theory 2003 1 c GMB/AD Database Theory 2003 2 c GMB/AD ¢ Database models This lecture course Database models are typically characterized by the prominent data structure, e.g. We will study some of these database models from a theoretical perspective. ¥ £ Graphs: Study closely the data model Network model – ¥ Study closely the associated query languages: – Semantic model – Choices of query languages – Object model – Relationships between them – XML (?) – Their characteristics (typically expressivity) £ Trees: Three database models considered in this course: – Hierarchical model 1. Relational £ Relations: 2. Object – Relational model 3. Semi-structured/XML Database Theory 2003 3 c GMB/AD Database Theory 2003 4 c GMB/AD ¦ ¤ Warning Books This is a brand new course! Recommended textbooks: There will be eight lectures, two examples classes, and two lecturers! ¨ Foundations of databases Abiteboul, Hull and Vianu. Addison Wesley, 1995 Schedule: ¨ Data on the web Abiteboul, Buneman and Suciu. Morgan Kaufmann, 2000. 1. GMB - (now!) relational model Also: Some useful information in any of the database books from the IB 2. AD - Relational calculus Databases course. 3. AD - Deductive databases 4. AD - Recursion and negation 5. AD - Expressivity and complexity 6. GMB - Complex values 7. GMB - Object model 8. GMB - Semistructured/XML model Database Theory 2003 5 c GMB/AD Database Theory 2003 6 c GMB/AD © § What is the relational model? Codd 70: – Data structure: flat relations – Simple algebra of queries The relational model – No constraints – No updates Codd 72-: – Same data structure – Second query language (based on FOL) – Proof of equivalence to algebra language – Integrity constraints - functional dependencies Database Theory 2003 7 c GMB/AD Database Theory 2003 8 c GMB/AD What is the relational model? cont. Basics Therafter a whole host of extensions. Thus the relational model means the class Fix a countably infinite set of attribute names, with a total order of database models that have relations as the core data structure and incorporate Fix a single countably infinite set : the underlying domain some of Codd's approach. Fix a countably infinite set of relation names Assume that there is a sort for each element of , i.e. a function ! . " # The arity of a relation $ is then defined %&' ( 01 & ( + + ) * ,.- / * , / A relation schema is just a relation name. We may write $ 3 to denote $ is 2 4 5 of sort 3 , and $ to denote it is of arity 265 4 A database schema is just a nonempty finite set of relation schema, e.g. 8 < < < 3 $ 3 $ 7 : : = = ; ; 4> 2 9 2 4 Database Theory 2003 9 c GMB/AD Database Theory 2003 10 c GMB/AD ? Example relations Choicepoint: names Q: Are the attribute names part of the explicit database schema or not? F H P AB CD E IJ A CK IQ ER A B I AU T C @ M M S M O O G L N L N L NV In SQL they are available, e.g. SELECT p.Name FROM Persons p Movies Title Director Actor Magnolia Anderson Moore Guide Title Cinema Time But are they compiled away by the system to just integers? Magnolia Anderson Cruise Rocky Warner 12:00 More theoretically: Spiderman Raimi Maguire Spiderman Picturehouse 19:00 X _ ]^ : A tuple over relation schema Y [ is a map from [ to Named Z \ Spiderman Raimi Dunst ... ... Spiderman Phoenix 19:00 X : A tuple over relation schema Y is a element of the cartesian Unnamed Z6` \ Rocky Avildsen Stallone Magnolia Picturehouse 22:00 _ba product ]^ RockyII Stalone Stallone The choice of model impacts on the query language. Location Cinema Address Tel Having assumed a total order on the attribute names provides us with a Picturehouse Cambridge 504444 correspondence between the two. Thus we'll flip between the two during this Phoenix Oxford 512526 course Warner Cambridge 560225 Database Theory 2003 11 c GMB/AD Database Theory 2003 12 c GMB/AD c W Database Database Theor Theor A (Simplest SPC y y quer 2003 2003 y quer © ª Ê possib is y « well-f ² © ª ¦ © ª d le Ar © ª ormed algebr © ª ity ¦ ¤ «  ² e ¶ ÃÄ Å µ e f Å ¥ ¦ h h h h h Å ³ » ¶ · ¦ Unnamed: judgements Ä § ¨ a ¤ « ® wr ¸ ¶ first) ¹ Æ g u n n d z ¦ © ² ij6k t « ¦ ¹ ¼ º o v o p o p a ² « ¹ ³ º ´ À schema ¦ ¾ w x lm q t x ½ Á d x ´ Á r r w d o y d Á s s ½ r d ´ s SPC Ë ¿ º f or 15 13 if Base Car Projection Select Select Singleton there © ª SPC © ª algebr tesian ª © relation « e ² (attr (constant) © ª xists À ² « © ª ¦ constant quer À È ² product ib ¦ a µ ute) Ì · ¶ ¬­ ® ¦ such ² Ç « ¿ ies ³ » ª © ¯° ¹ « ² « relation ¦ ® º that ± » É ² Ç ¦ « ¼ » ¹ Ë Í ´ ½ ¾ º Ê Î Ì . 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