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From the Calculus to the Structured Query Language Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems September 22, 2005 Some slide content courtesy of Susan Davidson & Raghu Ramakrishnan

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2 Administrivia Homework 1 due Tuesday Homework 2 will also be handed out Will involve writing SQL Oracle set up on eniac.seas.upenn.edu (also eniac-l.seas.upenn.edu) Go to: www.seas.upenn.edu/~zives/cis550/oracle-faq.html Click on “create Oracle account” link Enter your login info so you’ll get an Oracle account www.seas.upenn.edu/~zives/cis550/oracle-faq.html

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3 Tuple Relational Calculus (in More Detail) Queries of form: {T | p} Predicate: boolean expression over T x attribs Expressions: T x RT X.a op T Y.b T X.a op constconst op T X.a T.a = T x.a where op is , , , , , T x,… are tuple variables, T x.a, … are attributes Complex expressions: e 1 e 2, e 1 e 2, e, and e 1 e 2 Universal and existential quantifiers predicate

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4 Domain Relational Calculus to Tuple Relational Calculus { | 9 cid, sem, cid, sid ( 2 COURSE Æ 2 Takes} { | 9 s1, s2 ( 2 COURSE Æ 9 cid2, s3, s4 ( 2 COURSE Æ (cid > cid2)))}

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5 Mini-Quiz on the Relational Calculus How do you write: DRC: Which students have taken more than one course from the same professor? TRC: Which faculty teach every course?

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6 Algebra vs. Calculus We’ve claimed that the calculus (when safe) and the algebra are equivalent Thus (core) SQL => calculus algebra makes sense Let’s look more closely at this… SELECT * FROM STUDENT, Takes, COURSE WHERE STUDENT.sid = Takes.sID AND Takes.cID = cid STUDENT Takes COURSE Calculus

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7 Translating from RA to DRC Core of relational algebra: , , , x, - We need to work our way through the structure of an RA expression, translating each possible form. Let TR[e] be the translation of RA expression e into DRC. Relation names: For the RA expression R, the DRC expression is { | R}

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8 Selection: TR[ R] Suppose we have (e’), where e’ is another RA expression that translates as: TR[e’]= { | p} Then the translation of c (e’) is { | p ’} where ’ is obtained from by replacing each attribute with the corresponding variable Example: TR[ #1=#2 #4>2.5 R] (if R has arity 4) is { | R x 1 =x 2 x 4 >2.5}

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9 Projection: TR[ i 1,…,i m (e)] If TR[e]= { | p} then TR[ i 1,i 2,…,i m (e)]= { | x j 1,x j 2, …, x j k.p}, where x j 1,x j 2, …, x j k are variables in x 1,x 2, …, x n that are not in x i 1,x i 2, …, x i m Example: With R as before, #1,#3 (R)={ | x 2,x 4. R}

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10 Union: TR[R 1 R 2 ] R 1 and R 2 must have the same arity For e 1 e 2, where e 1, e 2 are algebra expressions TR[e 1 ]={ |p} and TR[e 2 ]={ |q} Relabel the variables in the second: TR[e 2 ]={ |q’} This may involve relabeling bound variables in q to avoid clashes TR[e 1 e 2 ]={ |p q’}. Example: TR[R 1 R 2 ] = { | R 1 R 2

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11 Other Binary Operators Difference: The same conditions hold as for union If TR[e 1 ]={ |p} and TR[e 2 ]={ |q} Then TR[e 1 - e 2 ]= { |p q} Product: If TR[e 1 ]={ |p} and TR[e 2 ]={ |q} Then TR[e 1 e 2 ]= { | p q} Example: TR[R S]= { | R S }

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12 Relational Algebra vs. Calculus Can translate relational algebra into relational calculus Given syntactic restrictions that guarantee safety of calculus query, can translate back to relational algebra These are the principles behind initial development of relational databases SQL is close to calculus; query plan is close to algebra But SQL can do other things (recursion, aggregation that RA/RC can’t) Great example of theory leading to practice!

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13 Basic SQL: A Friendly Face Over the Tuple Relational Calculus SELECT [DISTINCT] {T 1.attrib, …, T 2.attrib} FROM {relation} T 1, {relation} T 2, … WHERE {predicates} Let’s do some examples, which will leverage your knowledge of the relational calculus… Faculty ids Course IDs for courses with students expecting a “C” Courses taken by Jill select-list from-list qualification

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14 Our Example Data Instance sidname 1Jill 2Qun 3Nitin fidname 1Ives 2Saul 8Martin sidexp-gradecid 1A550-0105 1A700-1005 3C501-0105 cidsubjsem 550-0105DBF05 700-1005AIS05 501-0105ArchF05 fidcid 1550-0105 2700-1005 8501-0105 STUDENT Takes COURSE PROFESSOR Teaches

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15 Some Nice Features SELECT * All STUDENTs AS As a “range variable” (tuple variable): optional As an attribute rename operator Example: Which students (names) have taken more than one course from the same professor?

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16 Expressions in SQL Can do computation over scalars (int, real or string) in the select-list or the qualification Show all student IDs decremented by 1 Strings: Fixed (CHAR(x)) or variable length (VARCHAR(x)) Use single quotes: ’A string’ Special comparison operator: LIKE Not equal: <> Typecasting: CAST(S.sid AS VARCHAR(255))

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17 Set Operations Set operations default to set semantics, not bag semantics: (SELECT … FROM … WHERE …) {op} (SELECT … FROM … WHERE …) Where op is one of: UNION INTERSECT, MINUS/EXCEPT (many DBs don’t support these last ones!) Bag semantics: ALL

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18 Exercise Find all students who have taken DB but not AI Hint: use EXCEPT

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19 Nested Queries in SQL Simplest: IN/NOT IN Example: Students who have taken subjects that have (at any point) been taught by Martin

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20 Correlated Subqueries Most common: EXISTS/NOT EXISTS Find all students who have taken DB but not AI

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21 Universal and Existential Quantification Generally used with subqueries: {op} ANY, {op} ALL Find the students with the best expected grades

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22 Table Expressions Can substitute a subquery for any relation in the FROM clause: SELECT S.sid FROM (SELECT sid FROM STUDENT WHERE sid = 5) S WHERE S.sid = 4 Notice that we can actually simplify this query! What is this equivalent to?

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23 Aggregation GROUP BY SELECT {group-attribs}, {aggregate-operator}(attrib) FROM {relation} T 1, {relation} T 2, … WHERE {predicates} GROUP BY {group-list} Aggregate operators AVG, COUNT, SUM, MAX, MIN DISTINCT keyword for AVG, COUNT, SUM

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24 Some Examples Number of students in each course offering Number of different grades expected for each course offering Number of (distinct) students taking AI courses

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25 What If You Want to Only Show Some Groups? The HAVING clause lets you do a selection based on an aggregate (there must be 1 value per group): SELECT C.subj, COUNT(S.sid) FROM STUDENT S, Takes T, COURSE C WHERE S.sid = T.sid AND T.cid = C.cid GROUP BY subj HAVING COUNT(S.sid) > 5 Exercise: For each subject taught by at least two professors, list the minimum expected grade

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26 Aggregation and Table Expressions Sometimes need to compute results over the results of a previous aggregation: SELECT subj, AVG(size) FROM ( SELECT C.cid AS id, C.subj AS subj, COUNT(S.sid) AS size FROM STUDENT S, Takes T, COURSE C WHERE S.sid = T.sid AND T.cid = C.cid GROUP BY cid, subj) GROUP BY subj

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27 Something to Ponder Tables are great, but… Not everyone is uniform – I may have a cell phone but not a fax We may simply be missing certain information We may be unsure about values How do we handle these things?

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Relational Algebra & Calculus Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems September 16, 2004 Some slide content.

Relational Algebra & Calculus Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems September 16, 2004 Some slide content.

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