Datalog-Logic As Database Language-Lecture Slides, Slides of Database Programming

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Datalog

Rules

Programs

Negation

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Review of Logical If-Then Rules

h(X,…) :- a(Y,…) & b(Z,…) & …

head

body

subgoals

“The head is true if all the subgoals are true.”

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Semantics

Predicates represent relations.

An atom is true for given values of its variables iff the arguments form a tupleof the relation.

Whenever an assignment of values to all variables makes all subgoals true,the rule asserts that the resulting headis also true.

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Example

We shall develop rules that describe what is necessary to “make” a file.

The predicates/relations:

Š

source(F)

=

F

is a “source” file.

Š

includes(F,G)

=

F

#includes

G.

Š

create(F,P,G)

=

F

is created by

applying process

P

to file

G.

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Why Not Just Use SQL?

Recursion is much easier to express inDatalog.

‹

Viz. last rule for

req

.

Rules express things that go on in bothFROM and WHERE clauses, and let usstate some general principles (e.g.,containment of rules) that are almostimpossible to state correctly in SQL.

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IDB/EDB

A predicate representing a stored relation is called

EDB

(extensional database).

A predicate representing a “view,” i.e., a defined relation that does not exist in thedatabase is called

IDB

(intesional

database).

Head is always IDB; subgoals may be IDB or EDB.

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Extensions

Negated subgoals.

Constants as arguments.

Arithmetic subgoals.

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Negated Subgoals

NOT in front of a subgoal means that an assignment of values to variablesmust make it false in order for the bodyto be true.

Example:

cycle(F) :- req(F,F) & NOT source(F)

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13

Arithmetic Subgoals

Comparisons like < may be thought of as infinite, binary relations.

Š

Here, the set of all tuples (x,y) such that x<y.

Use infix notation for these predicates.

Example:

composite(A)

divides(B,A)

B

B

A

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Evaluating Datalog Programs

Nonrecursive programs.

Naïve evaluation of recursiveprograms without IDB negation.

Seminaïve evaluation of recursiveprograms without IDB negation.

‹

Eliminates some redundant computation.

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Examples: Nonsafety

p(X)

q(Y)

bachelor(X)

NOT

married(X,Y)

bachelor(X)

person(X)

NOT

married(X,Y)

X is the problem

Both X and Yare problems

Y is still a problem

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Nonrecursive Evaluation

If (and only if!) a Datalog program is not recursive, then we can order theIDB predicates so that in any rule for

p

(i.e.,

p

is the head predicate), the only

IDB predicates in the body precede

p.

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Applying Rules

To evaluate an IDB predicate

p :

Apply

each rule for

p

to the current

relations corresponding to its subgoals. ‹

“Apply” = If an assignment of values tovariables makes the body true, insert thetuple that the head becomes into the relationfor

p

(no duplicates).

Take the union of the result for each

p-

rule.

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Example

p(X,Y)

q(X,Z)

r(Z,Y)

Y<

Q = {(1,2), (3,4)};R = {(2,5), (4,9), (4,10), (6,7)}

Assignments making the body true:

(X,Y,Z) = (1,5,2), (3,9,4)

So P = {(1,5), (3,9)}.

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