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### Integrity

Keys

Candidate Keys

- K: a set of attributes of relvar R
- K is a candidate key for R iff
- Uniqueness
- No legal values of R contain two distinct tuples with the same value of K

- Irreducibility(minimality)
- No proper subset of k has the uniqueness

- Uniqueness
- Syntax
- Key {<attribute name commalist>}

Example of Candidate keys

- Ex)
VAR S BASE RELATION

{S# S#,

SNAME NAME,

STATUS INTEGER,

CITY CHAR}

KEY {S#};

VAR SP BASE RELATION

{S# S#,

P# P#,

QTY QTY}

KEY {S#, P#};

What are candidate keys for?

- The basic tuple-level addressing mechanism in a relational system
- Ex)
- S WHERE S# = S#(‘S3’)
at most one tuple

- S WHERE CITY = ‘Paris’
unpredictable number of tuples

- S WHERE S# = S#(‘S3’)

Superkey

- Superkey
- Uniqueness property
- Not necessarily irreducibility property

- If SK is a superkey for relvar R and A is an attribute of R
- Then the functional dependency SK A holds true in R
Ex) in relation S

- {S#}, {S#, SNAME}, {S#, CITY}, …., are superkeys

Primary keys, alternate keys

- Possible to have more than one candidate key
- Primary key
- Exactly one of candidate keys be chosen

- Alternate keys
- The remainder, if any

- The choice of which is to be primary
- arbitrary

Foreign keys

- In supplier-and-parts database
- A given value for S# of relation SP should be permitted to appear in the database
- only if that same value also appears as a value of the primary key S# of relation S

- Definition
- Let R2 be a relvar. Then foreign key in R2 is a subset of the set of attributes of R2, say FK, such that
- There exists a base relation R1 with a candidate key CK
- For all time each value of FK in the current value of R2 is identical to the value of CK in some tuple in the current value of R1

- Let R2 be a relvar. Then foreign key in R2 is a subset of the set of attributes of R2, say FK, such that

Foreign keys (cont.2)

- Points
- The definition requires every value of a given foreign key to appear as a value of the matching candidate key
- The converse of foreign key definition is not a requirements
- Ex) the supplier S5 appears in relvar S, but not in relvar SP

- Composite foreign key iff the candidate key it matched is composite too
- The same name and type as the corresponding component of the matching candidate key

- The definition requires every value of a given foreign key to appear as a value of the matching candidate key

Foreign Keys (cont.3)

- Terminology
- Referenced tuple(target tuple): candidate key value
- Referential integrity: valid foreign key value

- Referential diagram
- Represents referential constraint
- Ex) S <- SP -> P

Foreign keys(cont.4)

- Referential path
- A relation can be
- A referenced relation and
- A referencing relation

- Ex) R2 is the case
R3 -> R2 -> R1

- In general, there is a referential constraint from Rn to R(n-1), a referential constraint from R(n-1) to R(n-2) ,…, R2 to R1, we write
Rn -> R(n-1) -> …R2 -> R1

- A relation can be

Foreign keys(cont.5)

- Self-referencing
- A relation can
- reference itself

- Ex)
VAR EMP BASE RELATION

{EMP# EMP#,

………….

MGR_EMP# EMP#,

…………..}

PRIMARY KEY {EMP#}

FOREIGN KEY {RENAME MGR_EMP# AS EMP#} REFERENCES EMP;

- A relation can

Foreign keys(cont.6)

- Referential cycle
- If Rn includes a foreign key referring to R(n-1), and
- R(n-1) includes a foreign key referring to R(n-2), and
- ……
- If R1 includes a foreign key referring to Rn.
Rn -> R(n-1) ->……->R1 -> Rn

Foreign keys(cont.7)

- Caution
- The common attribute CITY in S and P does NOT have foreign key relationship
- CITY is not a candidate key of S and P!

Foreign keys(cont.8)

- Referential integrity rule
- The database must not contain any unmatched foreign key values
- If B references A, then A must exist
- ‘Foreign key’ and ‘referential integrity’ are defined in terms of each other

Referential actions for deletion

- What should happen on an attempt to delete the target of a foreign key reference?
- RESTRICTED
- Restricted to the case where there is no matching

- CASCADES
- Cascades to delete those matching also

- RESTRICTED

Referential actions for update

- What should happen on an attempt to update the target of a foreign key reference?
- RESTRICTED
- Restricted to the case where there is no matching

- CASCADES
- Cascades to update the foreign key in those matching also

- RESTRICTED

Referential action example

- For our Supplier and parts database
VAR SP BASE RELATION {…}…

FOREIGN KEY {S#} REFERENCES S

ON DELETE CASCADE;

Referential action for more than two relations

- Assume we have the following references
- R3->R2->R1 and
- Referential constraint is CASCADE

- Then
- Deleting tuple of R1 implies deleting certain tuple of R2
- Deleting tuple of R2 implies deleting certain tuple of R3
- If one of DELETEs fails, entire operation fails and database remains unchanged
- Atomic operation

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