Lecture 9: Trees and XML

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Slides : Recording

From the strict rectangles of structured data to the more generous triangles of semistructured data. This morning’s lecture gave an overview of what kind of data is seen as “semistructured”; the idea of trees as a mathematical model of data; the particular form of trees in the XPath data model; and their textual representation in XML — the Extensible Markup Language.

XML also has a large number of domain-specific variants. These are all valid XML, and use standardised sets of element types to give a custom language for representing data relevant to a particular field: from musical scores to financial trading.
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Tutorial Notes and Exercises

Tutor notes and solutions for Tutorial 2 are now on the tutorial page, together with next week’s exercises. Tutorial 3 is about formulating queries in tuple relational calculus and finding ways to compute them in relational algebra.

Have a look at the exercises now, and if you have questions about anything then ask on Piazza or after lectures.

Lecture 6: Tuple Relational Calculus

Title slideToday, another language for talking about databases. This one is the Tuple Relational Calculus for writing queries that describe information to be extracted from the linked tables of a relational database. There’s a separation of roles here: the tuple relational calculus is good for succinctly stating what we want to find out; while relational algebra from the last lecture describes how to combine and sift tables to extract that information from the data. We distinguish what information we want from how to compute it.
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Lecture 5: Relational Algebra

Title slideThis morning’s lecture presented a mathematical language for slicing and dicing the structured tables of the relational model: selection, projection, renaming; union, intersection, difference; cross product, join, equijoin and natural join. A key feature of this relational algebra is that just six of these operations are enough to capture an extremely wide range of queries and transformations of data. Database implementors work hard to build highly efficient engines to carry out these operations, which can then support many different kinds of user application.
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Lecture 4: From ER Diagrams to Relational Models

Title slideToday’s lecture reviewed the high-level conceptual language of ER diagrams and the more concrete structures of the relational model; followed by some recipes for translating from the first into the second. This isn’t always an exact match, and for any particular ER diagram we might go back to its original scenario description to decide how to best represent it as a relational model. Even so, this kind of step-by-step staging towards a fully formal representation is an effective route to capturing the subtleties of real-world systems.
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Lecture 3: The Relational Model

Title slideToday’s lecture expanded on last week’s material on Entity-Relationship modelling, and then set out the basic elements of the Relational Model for structured data. While ER diagrams provide a conceptual language for describing things as they are, and have applications outside databases for general organisation and management, the relational model is explicitly intended as a mathematically precise scheme for the computer-assisted creation and querying of large datasets.
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