1. Integrity Prof. Yin-Fu Huang CSIE, NYUST Chapter 9

2. Advanced Database SystemYin-Fu Huang An integrity constraint is a boolean expression that is associated with some database and is required to evaluate at all times to TRUE. e.g. Constraint SC1 Is_Empty (S Where Status 100); Drop Constraint SC1; 9.1Introduction

3. Advanced Database SystemYin-Fu Huang The fact that a given variable is of some given type represents an a prior constraint on the variable in question. Tutorial D examples: 1. Constraint SC2 Forall SX (If SX.City = ‘London’ Then SX.Status = 20 End If); 2. Constraint PC3 If Exists PX (True) Then Exists PX (PX.Color = Color(‘Blue’)) End If; 9.2A Closer Look

4. Advanced Database SystemYin-Fu Huang 3. Constraint SC4 Forall SX Forall SY (If SX.S# = SY.S# Then SX.Sname = SY.Sname And SX.Status = SY.Status And SX.City = SY.City End If); 4. Constraint SSP5 Forall SPX Exists SX (Sx.S# = SPX.S#) 5. Constraint SSP6 Forall SX Forall SPX (If Sx.S# = SPX.S# Then SX.Status  20 Or SPX.Qty  500 End If); 9.2A Closer Look (Cont.)

5. Advanced Database SystemYin-Fu Huang 9.3Predicates and Propositions A constraint as formally stated is a predicate. When that constraint is checked, arguments are substituted for the parameters and the predicate is thereby reduced to a proposition – and that proposition is then required to evaluated to TRUE.

6. Advanced Database SystemYin-Fu Huang 9.4Relvar Predicates and Database Predicates The relvar predicate for R is the logical And or conjunction of all of the constraints that apply to relvar R. The Golden Rule No update operation must ever assign to any relvar a value that causes its relvar predicate to evaluate to FALSE. The database predicate for D is the conjunction of all of those relvar predicates. The Golden Rule No update operation must ever assign to any database a value that causes its database predicate to evaluate to FALSE.

7. Advanced Database SystemYin-Fu Huang 9.5Checking the Constraints The sequence of events: 1. Insert the new tuple. 2. Check the constraint. 3. Undo the update (because the check fails). But this is absurd! All constraint checking is immediate? Most of the literature argues that “the unit of integrity” is the transaction and that at least some checking has to be deferred until end-of-transaction (i.e., COMMIT time).

8. Advanced Database SystemYin-Fu Huang 9.6 Internal vs. External Predicates a formal construct vs. an informal construct. what the data means to the system vs. what the data means to the users. A given internal predicate is the system’s approximation to the corresponding external predicate. If (s  S) = TRUE Then XPS(s) = TRUE If (s  S) = FALSE Then XPS(s) = FALSE  s  S  XPS(s)

9. Advanced Database SystemYin-Fu Huang 9.7Correctness vs. Consistency Views too are subject to constraints, and they have relvar predicates, both internal and external. e.g., There exists some city City such that supplier S# is under contract, is named Sname, has status Status, and is located in City. 9.8 Integrity and Views The system cannot enforce truth, only consistency.  If the database contains only true propositions, then it is consistency, but the converse is not necessarily so.  If the database is inconsistency, then it contains at least one false proposition, but the converse is not necessarily so.

10. Advanced Database SystemYin-Fu Huang 9.9A Constraint Classification Scheme Four broad categories: database, relvar, attribute, and type constraints Type constraints e.g., Type Weight Possrep { D Decimal (5, 1) Constraint D > 0.0 And D < 5000.0 };  Type constraints are always checked immediately. Attribute constraints e.g., Var S Base Relation { S#S#, SnameName, StatusInteger, CityChar } … ;

11. Advanced Database SystemYin-Fu Huang 9.9A Constraint Classification Scheme (Cont.) Relvar and database constraints  A transition constraint is a constraint on the legal transitions that a given variable-in particular, a given relvar or a given database- can make from one value to another. e.g. Constraint TRC1 Forall SX’ Forall SX ( SX’.S#  SX.S# Or SX’.Status  SX.Status ); Constraint TRC2 Forall PX Sum ( SPX’ Where SPX’.P# = PX.P#, Qty )  Sum ( SPX Where SPX.P# = PX.P#, Qty );  The concept of transition constraints does not apply to type or attribute constraints.

12. Advanced Database SystemYin-Fu Huang Keys 9.10Keys Candidate Keys  Properties: 1. Uniqueness 2. Irreducibility  Key { }  Tuple-level addressing mechanism Primary Keys and Alternative Keys  Exactly one of candidate keys the primary key  The others alternative keys

13. Advanced Database SystemYin-Fu Huang Keys (Cont.) 9.10Keys (Cont.) Foreign Keys  A foreign key in R2 is a set of attributes of R2, say FK, such that: 1.There exists a relvar R1 (R1 and R2 not necessarily distinct) with a candidate key CK. 2.It is possible to rename some subset of the attributes of FK, such that FK becomes FK’ (say) and FK’ and CK are of the same (tuple) type. 3.For all time, each value of FK in the current value of R2 yields a value for FK’ that is identical to the value of CK in some tuple in the current value of R1.

14. Advanced Database SystemYin-Fu Huang Keys (Cont.) 9.10Keys (Cont.)  Points arising: 1.It will rarely be necessary in practice to perform any actual renaming. 2.While every value of FK must appear as a value of CK, the converse is not a requirement. 3.Simple or composite 4.Referencing relvar vs. referenced relvar 5.Referential diagrams S# P# S ← SP → P 6.A given relvar can be both referenced and referencing. R3 → R2 → R1

15. Advanced Database SystemYin-Fu Huang Keys (Cont.) 9.10Keys (Cont.) 7.Relvars R1 and R2 in the foreign key definition are not necessarily distinct. Var Emp Base Relation {Emp# Emp#,..., Mgr_emp# Emp#,...} Key {Emp#} Foreign Key {Rename Mgr_emp# As Emp#} References Emp; 8.Referential cycles 9.Such matches represent certain relationships. 10.Referential integrity The database must not contain any unmatched foreign key values.

16. Advanced Database SystemYin-Fu Huang Keys (Cont.) 9.10Keys (Cont.) Referential Actions  Foreign Key {... } References On Delete On Update ;  Cascade Restrict No Action

17. Advanced Database SystemYin-Fu Huang Triggers (A Digression) 9.11Triggers (A Digression) A triggered procedure is a precompiled procedure that is stored along with the database and invoked automatically whenever some specified event occurs. e.g., Create Trigger London_Supplier_Insert Instead Of Insert On London_Supplier Referencing New Row As R For Each Row Insert Into S ( S#, Sname, Status, City ) Values ( R.S#, R.Sname, R.Status, ‘London’) ;  The event  The condition  The action

18. Advanced Database SystemYin-Fu Huang 9.12SQL Facilities SQL does not support type constraints at all. SQL does support attribute constraints. SQL does not support relvar constraints as such.  base table constraints SQL does not support database constraints as such.  general constraints (“assertions”)

19. Advanced Database SystemYin-Fu Huang 9.12SQL Facilities (Cont.) Base Table Constraints 1. Candidate keys Primary Key ( ) at most one Unique ( ) any number 2. Foreign keys Foreign key ( ) References [( )] [On Delete ] [On Update ] Action: No Action, Restrict, Cascade, Set Default, Set Null

20. Advanced Database SystemYin-Fu Huang 3. Check constraints Check ( ) e.g., Create Table Sp (S# S# Not Null, P# P# Not Null, Qty Qty Not Null, Primary Key (S#, P#), Foreign Key(S#) References S On Delete Cascade On Update Cascade, Foreign Key(P#) References P On Delete Cascade On Update Cascade, Check (Qty  Qty(0) And Qty  Qty(5000))); 9.12SQL Facilities (Cont.)

21. Advanced Database SystemYin-Fu Huang 9.12SQL Facilities (Cont.) Assertions Create Assertion Check ( ); Drop Assertion ; e.g., Create Assertion SC1 Check (Not Exists (Select* From S WhereS.Status < 0 OrS.Status > 100)); Deferred Checking  In SQL, constraints can be defined to be Deferrable or Not Deferrable.

22. Advanced Database SystemYin-Fu Huang 9.12SQL Facilities (Cont.)  Deferrable constraints can be dynamically switched on and off by means of the statement Set Constraints ; option: Immediate, Deferred Triggers Create Trigger On [ Referencing ] [ For Each ] [ When ( ) ] ; Drop Trigger ;

23. Advanced Database SystemYin-Fu Huang The End.