Database Query Languages Embedded in the Typed Lambda Calculus
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Tuple Relational Calculus Formula Defines Relation
COS 425: Database and Information Management Systems Relational model: Relational calculus Tuple Relational Calculus Queries are formulae, which define sets using: 1. Constants 2. Predicates (like select of algebra ) 3. BooleanE and, or, not 4.A there exists 5. for all • Variables range over tuples • Attributes of a tuple T can be referred to in predicates using T.attribute_name Example: { T | T ε tp and T.rank > 100 } |__formula, T free ______| tp: (name, rank); base relation of database Formula defines relation • Free variables in a formula take on the values of tuples •A tuple is in the defined relation if and only if when substituted for a free variable, it satisfies (makes true) the formula Free variable: A E x, x bind x – truth or falsehood no longer depends on a specific value of x If x is not bound it is free 1 Quantifiers There exists: E x (f(x)) for formula f with free variable x • Is true if there is some tuple which when substituted for x makes f true For all: A x (f(x)) for formula f with free variable x • Is true if any tuple substituted for x makes f true i.e. all tuples when substituted for x make f true Example E {T | E A B (A ε tp and B ε tp and A.name = T.name and A.rank = T.rank and B.rank =T.rank and T.name2= B.name ) } • T not constrained to be element of a named relation • T has attributes defined by naming them in the formula: T.name, T.rank, T.name2 – so schema for T is (name, rank, name2) unordered • Tuples T in result have values for (name, rank, name2) that satisfy the formula • What is the resulting relation? Formal definition: formula • A tuple relational calculus formula is – An atomic formula (uses predicate and constants): •T ε R where – T is a variable ranging over tuples – R is a named relation in the database – a base relation •T.a op W.b where – a and b are names of attributes of T and W, respectively, – op is one of < > = ≠≤≥ •T.a op constant • constant op T.a 2 Formal definition: formula cont. -
Tuple Relational Calculus Formula Defines Relation Quantifiers Example
COS 597A: Tuple Relational Calculus Principles of Queries are formulae, which define sets using: Database and Information Systems 1. Constants 2. Predicates (like select of algebra ) 3. Boolean and, or, not Relational model: 4. ∃ there exists 5. ∀ for all Relational calculus Variables range over tuples Value of an attribute of a tuple T can be referred to in predicates using T[attribute_name] Example: { T | T ε Winners and T[year] > 2006 } |__formula, T free ______| Winners: (name, tournament, year); base relation of database Formula defines relation Quantifiers • Free variables in a formula take on the values of There exists: ∃x (f(x)) for formula f with free tuples variable x • A tuple is in the defined relation if and only if • Is true if there is some tuple which when substituted when substituted for a free variable, it satisfies for x makes f true (makes true) the formula For all: ∀x (f(x)) for formula f with free variable x Free variable: • Is true if any tuple substituted for x makes f true i.e. all tuples when substituted for x make f true ∃x, ∀x bind x – truth or falsehood no longer depends on a specific value of x If x is not bound it is free Example Formal definition: formula • A tuple relational calculus formula is {T |∃A ∃B (A ε Winners and B ε Winners and – An atomic formula (uses predicate and constants): A[name] = T[name] and A[tournament] = T[tournament] and • T ε R where B[tournament] =T[tournament] and T[name2] = B[name] ) } – T is a variable ranging over tuples – R is a named relation in the database – a base relation • T not constrained to be element of a named relation • T[a] op W[b] where • Result has attributes defined by naming them in the formula: – a and b are names of attributes of T and W, respectively, T[name], T[tournament], T[name2] – op is one of < > = ≠ ≤ ≥ – so schema for result: (name, tournament, name2) • T[a] op constant unordered • constant op T[a] • Tuples T in result have values for (name, tournament, name2) that satisfy the formula • What is the resulting relation? 1 Formal definition: formula cont. -
Regulations & Syllabi for AMIETE Examination (Computer Science
Regulations & Syllabi For AMIETE Examination (Computer Science & Engineering) Published under the authority of the Governing Council of The Institution of Electronics and Telecommunication Engineers 2, Institutional Area, Lodi Road, New Delhi – 110 003 (India) (2013 Edition) Website : http://www.iete.org Toll Free No : 18001025488 Tel. : (011) 43538800-99 Fax : (011) 24649429 Email : [email protected] [email protected] Prospectus Containing Regulations & Syllabi For AMIETE Examination (Computer Science & Engineering) Published under the authority of the Governing Council of The Institution of Electronics and Telecommunication Engineers 2, Institutional Area, Lodi Road, New Delhi – 110 003 (India) (2013 Edition) Website : http://www.iete.org Toll Free No : 18001025488 Tel. : (011) 43538800-99 Fax : (011) 24649429 Email : [email protected] [email protected] CONTENTS 1. ABOUT THE INSTITUTION 1 2. ELIGIBILITY 4 3. ENROLMENT 5 4. AMIETE EXAMINATION 6 5. ELIGIBILITY FOR VARIOUS SUBJECTS 6 6. EXEMPTIONS 7 7. CGPA SYSTEM 8 8. EXAMINATION APPLICATION 8 9. EXAMINATION FEE 9 10. LAST DATE FOR RECEIPT OF EXAMINATION APPLICATION 9 11. EXAMINATION CENTRES 10 12. USE OF UNFAIR MEANS 10 13. RECOUNTING 11 14. IMPROVEMENT OF GRADES 11 15. COURSE CURRICULUM (Computer Science) (CS) (Appendix-‘A’) 13 16. OUTLINE SYLLABUS (CS) (Appendix-‘B’) 16 17. COURSE CURRICULUM (Information Technology) (IT) (Appendix-‘C”) 24 18. OUTLINE SYLLABUS (IT) (Appendix-‘D’) 27 19. COURSE CURRICULUM (Electronics & Telecommunication) (ET) 35 (Appendix-‘E’) 20. OUTLINE SYLLABUS (ET) (Appendix-‘F’) 38 21. DETAILED SYLLABUS (CS) (Appendix-’G’) 45 22. RECOGNITIONS GRANTED TO THE AMIETE EXAMINATION BY STATE 113 GOVERNMENTS / UNIVERSITIES / INSTITUTIONS (Appendix-‘I’) 23. RECOGNITIONS GRANTED TO THE AMIETE EXAMINATION BY 117 GOVERNMENT OF INDIA / OTHER AUTHORITIES ( Annexure I - V) 24. -
Session 5 – Main Theme
Database Systems Session 5 – Main Theme Relational Algebra, Relational Calculus, and SQL Dr. Jean-Claude Franchitti New York University Computer Science Department Courant Institute of Mathematical Sciences Presentation material partially based on textbook slides Fundamentals of Database Systems (6th Edition) by Ramez Elmasri and Shamkant Navathe Slides copyright © 2011 and on slides produced by Zvi Kedem copyight © 2014 1 Agenda 1 Session Overview 2 Relational Algebra and Relational Calculus 3 Relational Algebra Using SQL Syntax 5 Summary and Conclusion 2 Session Agenda . Session Overview . Relational Algebra and Relational Calculus . Relational Algebra Using SQL Syntax . Summary & Conclusion 3 What is the class about? . Course description and syllabus: » http://www.nyu.edu/classes/jcf/CSCI-GA.2433-001 » http://cs.nyu.edu/courses/fall11/CSCI-GA.2433-001/ . Textbooks: » Fundamentals of Database Systems (6th Edition) Ramez Elmasri and Shamkant Navathe Addition Wesley ISBN-10: 0-1360-8620-9, ISBN-13: 978-0136086208 6th Edition (04/10) 4 Icons / Metaphors Information Common Realization Knowledge/Competency Pattern Governance Alignment Solution Approach 55 Agenda 1 Session Overview 2 Relational Algebra and Relational Calculus 3 Relational Algebra Using SQL Syntax 5 Summary and Conclusion 6 Agenda . Unary Relational Operations: SELECT and PROJECT . Relational Algebra Operations from Set Theory . Binary Relational Operations: JOIN and DIVISION . Additional Relational Operations . Examples of Queries in Relational Algebra . The Tuple Relational Calculus . The Domain Relational Calculus 7 The Relational Algebra and Relational Calculus . Relational algebra . Basic set of operations for the relational model . Relational algebra expression . Sequence of relational algebra operations . Relational calculus . Higher-level declarative language for specifying relational queries 8 Unary Relational Operations: SELECT and PROJECT (1/3) . -
Ch06-The Relational Algebra and Calculus.Pdf
Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 1 Chapter 6 The Relational Algebra and Calculus Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Chapter Outline Relational Algebra Unary Relational Operations Relational Algebra Operations From Set Theory Binary Relational Operations Additional Relational Operations Examples of Queries in Relational Algebra Relational Calculus Tuple Relational Calculus Domain Relational Calculus Example Database Application (COMPANY) Overview of the QBE language (appendix D) Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 3 Relational Algebra Overview Relational algebra is the basic set of operations for the relational model These operations enable a user to specify basic retrieval requests (or queries) The result of an operation is a new relation, which may have been formed from one or more input relations This property makes the algebra “closed” (all objects in relational algebra are relations) Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 4 Relational Algebra Overview (continued) The algebra operations thus produce new relations These can be further manipulated using operations of the same algebra A sequence of relational algebra operations forms a relational algebra expression The result of a relational algebra expression is also a relation that represents the result of a database query (or retrieval request) Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 5 Brief History of Origins of Algebra Muhammad ibn Musa al-Khwarizmi (800-847 CE) wrote a book titled al-jabr about arithmetic of variables Book was translated into Latin. Its title (al-jabr) gave Algebra its name. Al-Khwarizmi called variables “shay” “Shay” is Arabic for “thing”. -
Relational Algebra & Relational Calculus
Relational Algebra & Relational Calculus Lecture 4 Kathleen Durant Northeastern University 1 Relational Query Languages • Query languages: Allow manipulation and retrieval of data from a database. • Relational model supports simple, powerful QLs: • Strong formal foundation based on logic. • Allows for optimization. • Query Languages != programming languages • QLs not expected to be “Turing complete”. • QLs not intended to be used for complex calculations. • QLs support easy, efficient access to large data sets. 2 Relational Query Languages • Two mathematical Query Languages form the basis for “real” query languages (e.g. SQL), and for implementation: • Relational Algebra: More operational, very useful for representing execution plans. • Basis for SEQUEL • Relational Calculus: Let’s users describe WHAT they want, rather than HOW to compute it. (Non-operational, declarative.) • Basis for QUEL 3 4 Cartesian Product Example • A = {small, medium, large} • B = {shirt, pants} A X B Shirt Pants Small (Small, Shirt) (Small, Pants) Medium (Medium, Shirt) (Medium, Pants) Large (Large, Shirt) (Large, Pants) • A x B = {(small, shirt), (small, pants), (medium, shirt), (medium, pants), (large, shirt), (large, pants)} • Set notation 5 Example: Cartesian Product • What is the Cartesian Product of AxB ? • A = {perl, ruby, java} • B = {necklace, ring, bracelet} • What is BxA? A x B Necklace Ring Bracelet Perl (Perl,Necklace) (Perl, Ring) (Perl,Bracelet) Ruby (Ruby, Necklace) (Ruby,Ring) (Ruby,Bracelet) Java (Java, Necklace) (Java, Ring) (Java, Bracelet) 6 Mathematical Foundations: Relations • The domain of a variable is the set of its possible values • A relation on a set of variables is a subset of the Cartesian product of the domains of the variables. • Example: let x and y be variables that both have the set of non- negative integers as their domain • {(2,5),(3,10),(13,2),(6,10)} is one relation on (x, y) • A table is a subset of the Cartesian product of the domains of the attributes. -
An E Cient and General Implementation of Futures on Large
An Ecient and General Implementation of Futures on Large Scale SharedMemory Multipro cessors A Dissertation Presented to The Faculty of the Graduate School of Arts and Sciences Brandeis University Department of Computer Science James S Miller advisor In Partial Fulllment of the Requirements of the Degree of Doctor of Philosophy by Marc Feeley April This dissertation directed and approved by the candidates committee has b een ac cepted and approved by the Graduate Faculty of Brandeis University in partial fulll ment of the requirements for the degree of DOCTOR OF PHILOSOPHY Dean Graduate School of Arts and Sciences Dissertation Committee Dr James S Miller chair Digital Equipment Corp oration Prof Harry Mairson Prof Timothy Hickey Prof David Waltz Dr Rob ert H Halstead Jr Digital Equipment Corp oration Copyright by Marc Feeley Abstract An Ecient and General Implementation of Futures on Large Scale SharedMemory Multipro cessors A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University Waltham Massachusetts by Marc Feeley This thesis describ es a highp erformance implementation technique for Multilisps future parallelism construct This metho d addresses the nonuniform memory access NUMA problem inherent in large scale sharedmemory multiprocessors The technique is based on lazy task creation LTC a dynamic task partitioning mechanism that dramatically reduces the cost of task creation and consequently makes it p ossible to exploit ne grain parallelism In LTC idle pro cessors get work to do -
The Complexity of Flow Analysis in Higher-Order Languages
The Complexity of Flow Analysis in Higher-Order Languages David Van Horn arXiv:1311.4733v1 [cs.PL] 19 Nov 2013 The Complexity of Flow Analysis in Higher-Order Languages A Dissertation Presented to The Faculty of the Graduate School of Arts and Sciences Brandeis University Mitchom School of Computer Science In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy by David Van Horn August, 2009 This dissertation, directed and approved by David Van Horn’s committee, has been accepted and approved by the Graduate Faculty of Brandeis University in partial fulfillment of the requirements for the degree of: DOCTOR OF PHILOSOPHY Adam B. Jaffe, Dean of Arts and Sciences Dissertation Committee: Harry G. Mairson, Brandeis University, Chair Olivier Danvy, University of Aarhus Timothy J. Hickey, Brandeis University Olin Shivers, Northeastern University c David Van Horn, 2009 Licensed under the Academic Free License version 3.0. in memory of William Gordon Mercer July 22, 1927–October 8, 2007 Acknowledgments Harry taught me so much, not the least of which was a compelling kind of science. It is fairly obvious that I am not uninfluenced by Olivier Danvy and Olin Shivers and that I do not regret their influence upon me. My family provided their own weird kind of emotional support and humor. I gratefully acknowledge the support of the following people, groups, and institu- tions, in no particular order: Matthew Goldfield. Jan Midtgaard. Fritz Henglein. Matthew Might. Ugo Dal Lago. Chung-chieh Shan. Kazushige Terui. Christian Skalka. Shriram Krishnamurthi. Michael Sperber. David McAllester. Mitchell Wand. Damien Sereni. Jean-Jacques Levy.´ Julia Lawall. -
Fundamentals of Type Inference Systems
Fundamentals of type inference systems Fritz Henglein DIKU, University of Copenhagen [email protected] February 1, 1991; revised January 31, 1994; updated August 9, 2009 1 Introduction These notes give a compact overview of established core type systems and of their fundamental properties. We emphasize the use and application of type systems in programming languages, but also mention their role in logic. Proofs are omitted, but references to relevant sources in the literature are usually given. 1.1 What is a \type"? There are many examples of types in programming languages: • Primitive types: int, float, bool • Compound types: products (records), sums (disjoint unions), lists, arrays • Recursively definable types, such as tree data types • Function types, e.g. int !int • Parametric polymorphic types • Abstract types, e.g. Java interfaces Loosely speaking a type is a description of a collection of related values. • A type has syntax (\description"): It denotes a collection. • A type has elements (\collection"): It makes sense to talk about ele- ments of a type; in particular, it may have zero, one or many elements 1 • A type's elements have common properties (\related"): Users of a type can rely on each element having some common properties|an interface| without having to know the identity of particular elements. Types incorporate multiple aspects: • Type as a set of values: This view focuses on how values are con- structed to be elements of a type; e.g. constructing the natural num- bers from 0 and the successor function; • Type as a an interface: This view focuses on how values can be used (\deconstructed") by a client; e.g. -
On the Resolution Semiring
Aix-Marseille Université École doctorale 184 UFR sciences Institut de Mathématiques de Marseille Thèse présentée pour obtenir le grade universitaire de docteur Spécialité: Mathématiques On the Resolution Semiring Marc Bagnol Jury: Pierre-Louis Curien Université Paris Diderot Jean-Yves Girard Aix-Marseille Université (directeur) Ugo dal Lago Università di Bologna (rapporteur) Paul-André Melliès Université Paris Diderot Myriam Quatrini Aix-Marseille Université Ulrich Schöpp LMU München Philip Scott University of Ottawa (rapporteur) Kazushige Terui Kyoto University Soutenue le 4/12/2014 à Marseille. This thesis is licensed under a Attribution-NonCommercial-ShareAlike 4.0 International licence. Résumé On étudie dans cette thèse une structure de semi-anneau dont le produit est basé sur la règle de résolution de la programmation logique. Cet objet mathématique a été initialement introduit dans le but de modéliser la procédure d’élimination des coupures de la logique linéaire, dans le cadre du programme de géométrie de l’interaction. Il fournit un cadre algébrique et abstrait, tout en étant présenté sous une forme syntaxique et concrète, dans lequel mener une étude théorique du calcul. On reviendra dans un premier temps sur l’interprétation interactive de la théorie de la démonstration dans ce semi-anneau, via l’axiomatisation catégorique de l’approche de la géométrie de l’interaction. Cette interprétation établit une traduction des programmes fonctionnels vers une forme très simple de programmes logiques. Dans un deuxième temps, on abordera des problématiques de théorie de la complexité: bien que le problème de la nilpotence dans le semi-anneau étudié soit indécidable en général, on fera apparaître des restrictions qui permettent de caractériser le calcul en espace logarithmique (déterministe et non-déterministe) et en temps polynomial (déterministe). -
RELATIONAL DATABASE PRINCIPLES © Donald Ravey 2008
RELATIONAL DATABASE PRINCIPLES © Donald Ravey 2008 DATABASE DEFINITION In a loose sense, almost anything that stores data can be called a database. So a spreadsheet, or a simple text file, or the cards in a Rolodex, or even a handwritten list, can be called a database. However, we are concerned here with computer software that manages the addition, modification, deletion and retrieval of data from specially formatted computer files. Such software is often called a Relational Database Management System (RDBMS) and that will be the subject of the remainder of this tutorial. RELATIONAL DATABASE HISTORY The structure of a relational database is quite specific. Data is contained in one or more tables (the purists call them relations). A table consists of rows (also known as tuples or records), each of which contains columns (also called attributes or fields). Within any one table, all rows must contain the same columns; that is, every table has a uniform structure; if any row contains a Zipcode column, every row will contain a Zipcode column. In the late 1960’s, a mathematician and computer scientist at IBM, Dr. E. F. (Ted) Codd, developed the principles of what we now call relational databases, based on mathematical set theory. He constructed a consistent logical framework and a sort of calculus that would insure the integrity of stored data. In other words, he effectively said, If you structure data in accordance with these rules, and if you operate on the data within these constraints, your data will be guaranteed to remain consistent and certain operations will always work. -
Scientific Calculator Operation Guide
SSCIENTIFICCIENTIFIC CCALCULATORALCULATOR OOPERATIONPERATION GGUIDEUIDE < EL-W535TG/W516T > CONTENTS CIENTIFIC SSCIENTIFIC HOW TO OPERATE Read Before Using Arc trigonometric functions 38 Key layout 4 Hyperbolic functions 39-42 Reset switch/Display pattern 5 CALCULATORALCULATOR Coordinate conversion 43 C Display format and decimal setting function 5-6 Binary, pental, octal, decimal, and Exponent display 6 hexadecimal operations (N-base) 44 Angular unit 7 Differentiation calculation d/dx x 45-46 PERATION UIDE dx x OPERATION GUIDE Integration calculation 47-49 O G Functions and Key Operations ON/OFF, entry correction keys 8 Simultaneous calculation 50-52 Data entry keys 9 Polynomial equation 53-56 < EL-W535TG/W516T > Random key 10 Complex calculation i 57-58 DATA INS-D STAT Modify key 11 Statistics functions 59 Basic arithmetic keys, parentheses 12 Data input for 1-variable statistics 59 Percent 13 “ANS” keys for 1-variable statistics 60-61 Inverse, square, cube, xth power of y, Data correction 62 square root, cube root, xth root 14 Data input for 2-variable statistics 63 Power and radical root 15-17 “ANS” keys for 2-variable statistics 64-66 1 0 to the power of x, common logarithm, Matrix calculation 67-68 logarithm of x to base a 18 Exponential, logarithmic 19-21 e to the power of x, natural logarithm 22 Factorials 23 Permutations, combinations 24-26 Time calculation 27 Fractional calculations 28 Memory calculations ~ 29 Last answer memory 30 User-defined functions ~ 31 Absolute value 32 Trigonometric functions 33-37 2 CONTENTS HOW TO