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Integrity Constraints Review Three things managed by a DBMS 1. Data organization E/R Model Relational Model 2. Data Retrieval Relational Algebra Relational Calculus SQL 3. Data Integrity and Database Design Integrity Constraints Functional Dependencies Normalization Integrity Constraints Purpose: prevent semantic inconsistencies in data e.g.: e.g.: cname John cname Jones Turner Smith svngs 100 bname Kenmore Main St Union 4 kinds of IC’s: 1. Key Constraints 2. Attribute Constraints 3. Referential Integrity Constraints 4. Global Constraints check 200 total 250 bname Main St Union Union bcity Boston NY NY No entry for Kenmore... ??? IC’s What are they? predicates on the database must always be true (:, checked whenever db gets updated) There are the following 4 types of IC’s: Key constraints (1 table) e.g., 2 accts can’t share the same acct_no Attribute constraints (1 table) e.g., 2 accts must have nonnegative balance Referential Integrity constraints ( 2 tables) E.g. bnames associated w/ loans must be names of real branches Key Constraints Idea: specifies that a relation is a set, not a bag SQL examples: 1. Primary Key: CREATE TABLE branch( bname CHAR(15) PRIMARY KEY, bcity CHAR(20), assets INT); or CREATE TABLE depositor( cname CHAR(15), acct_no CHAR(5), PRIMARY KEY(cname, acct_no)); 2. Candidate Keys: CREATE TABLE customer ( ssn CHAR(9) PRIMARY KEY, cname CHAR(15), address CHAR(30), city CHAR(10), UNIQUE (cname, address, city); Key Constraints Effect of SQL Key declarations PRIMARY (A1, A2, .., An) or UNIQUE (A1, A2, ..., An) Insertions: check if any tuple has same values for A1, A2, .., An as any inserted tuple. If found, reject insertion Updates to any of A1, A2, ..., An: treat as insertion of entire tuple Primary vs Unique (candidate) 1. 1 primary key per table, several unique keys allowed. 2. Only primary key can be referenced by “foreign key” (ref integrity) 3. DBMS may treat primary key differently (e.g.: implicitly create an index on PK) 4. NULL values permitted in UNIQUE keys but not in PRIMARY KEY Attribute Constraints Idea: Attach constraints to values of attributes Enhances types system (e.g.: >= 0 rather than integer) In SQL: 1. NOT NULL e.g.: CREATE TABLE branch( bname CHAR(15) NOT NULL, .... ) Note: declaring bname as primary key also prevents null values 2. CHECK e.g.: CREATE TABLE depositor( .... balance int NOT NULL, CHECK( balance >= 0), .... ) affect insertions, update in affected columns CHECK constraint in Oracle CHECK cond where cond is: Boolean expression evaluated using the values in the row being inserted or updated, and Does not contain subqueries; sequences; the SQL functions SYSDATE, UID, USER, or USERENV; or the pseudocolumns LEVEL or ROWNUM Multiple CHECK constraints No limit on the number of CHECK constraints you can define on a column CREATE TABLE credit_card( .... balance int NOT NULL, CHECK( balance >= 0), CHECK (balance < limit), .... ) Referential Integrity Constraints Idea: prevent “dangling tuples” (e.g.: a loan with a bname of ‘Kenmore’ when no Kenmore tuple is not in branch table) Referencing Relation (e.g. loan) “foreign key” bname Referenced Relation (e.g. branch) primary key bname Ref Integrity: ensure that: foreign key value primary key value (note: need not to ensure , i.e., not all branches have to have loans) Referential Integrity Constraints bname child Referencing Relation (e.g. loan) x x bname x Referenced Relation (e.g. branch) In SQL: CREATE TABLE branch( bname CHAR(15) PRIMARY KEY ....) CREATE TABLE loan ( ......... FOREIGN KEY bname REFERENCES branch); Affects: 1) Insertions, updates of referencing relation 2) Deletions, updates of referenced relation parent Referential Integrity Constraints c ti x tj x c parent x child A B what happens when we try to delete this tuple? Ans: Oracle allows the following possibilities • No action • RESTRICT: reject deletion/ update • SET TO NULL: set ti [c], tj[c] = NULL • SET TO DEFAULT: set ti [c], tj[c] = default_val • CASCADE: propagate deletion/update DELETE: delete ti, tj UPDATE: set ti[c], tj[c] to updated values Referential Integrity Constraints c ti x tj x Emp c x Dept what happens when we try to delete this tuple? ALTER TABLE Dept ADD Primary Key (deptno); ALTER TABLE Emp ADD FOREIGN KEY (Deptno) REFERENCES Dept(Deptno) [ACTION]; Action: 1) ON DELETE NO ACTION left blank (deletion/update rejected) 2) ON DELETE SET NULL/ ON UPDATE SET NULL sets ti[c] = NULL, tj[c] = NULL 3) ON DELETE CASCADE deletes ti, tj ON UPDATE CASCADE sets ti[c], tj[c] to new key values Global Constraints Idea: two kinds 1) single relation (constraints spans multiple columns) E.g.: CHECK (total = svngs + check) declared in the CREATE TABLE Example: All Bkln branches must have assets > 5M CREATE TABLE branch ( .......... bcity CHAR(15), assets INT, CHECK (NOT(bcity = ‘Bkln’) OR assets > 5M)) Affects: insertions into branch updates of bcity or assets in branch 2) Multiple Relations: NOT supported in Oracle Need to be implemented as a Trigger Global Constraints (NOT in Oracle) SQL example: 2) Multiple relations: every loan has a borrower with a savings account CHECK (NOT EXISTS ( SELECT * FROM loan AS L WHERE NOT EXISTS( SELECT * FROM borrower B, depositor D, account A WHERE B.cname = D.cname AND D.acct_no = A.acct_no AND L.lno = B.lno))) Problem: Where to put this constraint? At depositor? Loan? .... Ans: None of the above: CREATE ASSERTION loan-constraint CHECK( ..... ) Checked with EVERY DB update! very expensive..... Global Constraints Issues: 1) How does one decide what global constraint to impose? 2) How does one minimize the cost of checking the global constraints? Ans: Functional dependencies. but before we go there Deferring the constraint checking SET ALL CONSTRAINTS DEFERRED; Defers all constraint checks till the end of the transaction Especially useful in enforcing Referential integrity Insert new rows into ‘Child’ table but referred key is not yet in Parent Insert corresponding row in ‘Parent’ table Constraint checking done at the end of the transaction Can also defer individual constraint checking by specifying the constraint name Finding the constraint information in Oracle SELECT * FROM USER_CONSTRAINTS; SELECT * FROM USER_CONS_COLS; Summary: Integrity Constraints Constraint Type Where declared Affects... In Oracle ? Key Constraints CREATE TABLE Insertions, Updates Yes (PRIMARY KEY, UNIQUE) CREATE TABLE Insertions, Updates Yes Attribute Constraints Referential Integrity CREATE DOMAIN (Not NULL, CHECK) Table Tag (FOREIGN KEY .... REFERENCES ....) 1.Insertions into referencing rel’n 2. Updates of referencing rel’n of relevant attrs 3. Deletions from referenced rel’n 4. Update of referenced rel’n Global Consraints Table Tag (CHECK) or outside table (CREATE ASSERTION) 1. For single rel’n constraint, with insertion, deletion of relevant attrs 2. For assesrtions w/ every db modification CREATE DOMAIN not supported in Oracle Yes Possible Actions: -- Update/delete no aciton -- delete CASCADE -- delete SET NULL, SET DEFAULT,… Assertions, domains not supported in Oracle. Review Three things managed by a DBMS 1. Data organization E/R Model Relational Model 2. Data Retrieval Relational Algebra Relational Calculus SQL 3. Data Integrity and Database Design Integrity Constraints Functional Dependencies Constraints that hold for legal instance of the database Example: Every customer should have a single credit card Normalization Functional Dependencies A a a a b b B C 1 1 5 3 3 D U V W W W ABC “ AB determines C” two tuples with the same values for A and B will also have the same value for C Constraints that will hold on all “legal” instances of the database for the specific business application. In most cases, specified by a database designer/business architect Functional Dependencies A a a a b b Shorthand: C BD B C 1 1 5 3 3 D U U W W W same as C B CD Be careful! AB C not the same as AC BC Not true Functional Dependencies Example: suppose R = { A, B, C, D, E, H} and we determine that: F = { A BC, B CE, A E, AC H, D B} Then we determine the ‘canonical cover’ of F: Fc = { A BH, B CE, D B} ensuring that F and Fc are equivalent Note: F requires 5 assertions Fc requires 3 assertions Canonical cover (or minimal cover) algorithm: In the book (not covered here). Functional Dependencies Equivalence of FD sets: FD sets F and G are equivalent if the imply the same set of FD’s e.g. A B and B C : implies A C equivalence usually expressed in terms of closures Closures: For any FD set, F, F+ is the set of all FD’s implied by F. can calculate in 2 ways: (1) Attribute Closure (2) Armstrong’s axioms Both techniques tedious-- will do only for toy examples F equivalent to G iff F+ = G+ Armstrong’s Axioms A. Fundamental Rules (W, X, Y, Z: sets of attributes) 1. Reflexivity If Y X then X Y 2. Augmentation If X Y then WX WY 3. Transitivity If X Y and Y Z then XZ B. Additional rules (can be proved from A) 4. UNION: If X Y and X Z then X YZ 5. Decomposition: If X YZ then X Y, X Z 6. Pseudotransitivity: If X Y and WY Z then WX Z 2 Proving 4.(sketch): X Y => XXXY =>XXY XYYZ For every step we used the rules from A. 3 => X YZ FD Closures Using Armstrong’s Axioms Given; F = { A BC, B CE, A E, AC H, D B} (1) (2) (3) (4) (5) Exhaustively apply Armstrong’s axioms to generate F+ F+ = F 1. 2. 3. 4. 5. { A B, A C}: decomposition on (1) { A CE}: transitivity to 1.1 and (2) { B C, B E}: decomp to (2) { A C, A E} decomp to 2 { A H} pseudotransitivity to 1.2 and (4) Attribute Closures Given; R = { A, B, C, D, E, H,I} and: F = { A BC, C D, CE, AH I} What is the closure of A (A+) ? Attribute closure A Iteration Result ----------------------------------0 A 1 ABC 2 AB CD 3 ABCDE Algorithm att-closure (X: set of Attributes) Result X repeat until stable for each FD in F, Y Z, do if Y Result then Result Result Z Better to determine if a set of attributes is a key Functional dependencies Our goal: given a set of FD set, F, find an alternative FD set, G that is: smaller equivalent Bad news: Testing F=G (F+ = G+) is computationally expensive Good news: Canonical Cover algorithm: given a set of FD, F, finds minimal FD set equivalent to F Minimal: can’t find another equivalent FD set w/ fewer FD’s FD so far... 1. Canonical Cover algorithm • result (Fc) guaranteed to be the minimal FD set equivalent to F 2. Closure Algorithms a. Armstrong’s Axioms: more common use: test for extraneous attributes in C.C. algorithm b. Attribute closure: more common use: test for superkeys 3. Purposes a. minimize the cost of global integrity constraints so far: min gic’s = |Fc| In fact.... Min gic’s = 0 (FD’s for “normalization”) Another use of FD’s: Schema Design Example: R= bname Downtown Downtown Mianus Downtown bcity Bkln Bkln Horse Bkln assets 9M 9M 1.7M 9M cname Jones Johnson Jones Hayes lno L-17 L-23 L-93 L-17 amt 1000 2000 500 1000 R: “Universal relation” tuple meaning: Jones has a loan (L-17) for $1000 taken out at the Downtown branch in Bkln which has assets of $9M Design: +: -: fast queries (no need for joins!) redudancy: update anomalies examples? deletion anomalies