Integrity Constraints

Review Three things managed by a DBMS Data organization Data Retrieval E/R Model Relational Model Data Retrieval Relational Algebra Relational Calculus SQL Data Integrity and Database Design Integrity Constraints Functional Dependencies Normalization

Integrity Constraints Purpose: prevent semantic inconsistencies in data e.g.: e.g.: 4 kinds of IC’s: 1. Key Constraints 2. Attribute Constraints 3. Referential Integrity Constraints 4. Global Constraints 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 primary key per table, several unique keys allowed. Only primary key can be referenced by “foreign key” (ref integrity) 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) Referenced Relation (e.g. branch) “foreign key” bname 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 bname x Referencing Relation (e.g. loan) parent Referenced Relation (e.g. branch) x x child 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

Referential Integrity Constraints x parent tj x x child what happens when we try to delete this tuple? A B 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 x tj x x what happens when we try to delete this tuple? Emp Dept 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( 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 (PRIMARY KEY, UNIQUE) Insertions, Updates Yes Attribute Constraints CREATE DOMAIN (Not NULL, CHECK) CREATE DOMAIN not supported in Oracle Referential Integrity 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 Possible Actions: -- Update/delete no aciton -- delete CASCADE -- delete SET NULL, SET DEFAULT,… 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 Assertions, domains not supported in Oracle.

Review Three things managed by a DBMS Data organization Data Retrieval E/R Model Relational Model Data Retrieval Relational Algebra Relational Calculus SQL 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 B  C “ 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 Shorthand: C  BD same as C  B C  D Be careful! AB  C not the same as AC BC 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 XZ 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 3 Proving 4.(sketch): X Y => XXXY =>XXY XYYZ => X YZ For every step we used the rules from A.

FD Closures Using Armstrong’s Axioms Given; F = { A  BC, (1) B  CE, (2) A  E, (3) AC  H, (4) D  B} (5) Exhaustively apply Armstrong’s axioms to generate F+ F+ = F  1. { A  B, A  C}: decomposition on (1) 2. { A  CE}: transitivity to 1.1 and (2) 3. { B  C, B  E}: decomp to (2) 4. { A  C, A  E} decomp to 2 5. { A  H} pseudotransitivity to 1.2 and (4)

Attribute Closures Given; Attribute closure A R = { A, B, C, D, E, H,I} and: F = { A  BC, C D, CE, AH  I} Attribute closure A Iteration Result ----------------------------------- 0 A 1 A B C 2 A B C D 3 A B C D E What is the closure of A (A+) ? 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 = 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