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The Part/Subparts Example assembly(PART, SUBPART, QTY) CREATE RECURSIVE VIEW all_subparts(Major, Minor) AS SELECT PART SUBPART FROM assembly UNION SELECT all.Major assb.SUBPART FROM all_subparts AS all, assembly AS assb WHERE all.Minor= assb.PART This is called a recursive union. We have the union of an Exit Select and a Recursive Select This definition corresponds to left-linear recursive Datalog rules Materialization of the recursive view from the previous Example SELECT * FROM all_subparts
Citation preview
CS240A: Databases and Knowledge BasesRecursive Queries in SQL 2003
Carlo ZanioloDepartment of Computer ScienceUniversity of California, Los Angeles
Notes From Chapter 9 of Advanced Database Systems by Zaniolo, Ceri, Faloutsos, Snodgrass, Subrahmanian and ZicariMorgan Kaufmann, 1997
Datalog Patterns
assemby(PART, SUBPART) ..
%left-linear
all(Major, Minor) <- all (Major, Mid), assembly(Mid, Minor).
%right-linear
all(Major, Minor) <- assembly(Major, Mid), all(Mid, Minor).
The Part/Subparts Exampleassembly(PART, SUBPART, QTY)
CREATE RECURSIVE VIEW all_subparts(Major, Minor) AS SELECT PART SUBPART
FROM assembly
UNION
SELECT all.Major assb.SUBPARTFROM all_subparts AS all, assembly AS assbWHERE all.Minor= assb.PART
This is called a recursive union. We have the union of an Exit Select and a Recursive Select This definition corresponds to left-linear recursive Datalog rules Materialization of the recursive view from the previous Example
SELECT * FROM all_subparts
The WITH Construct
The WITH construct provides another way, and a more direct one to express recursion in SQL:1999
Query: Find the parts using top tubeWITH RECURSIVE all_super(Major, Minor) AS
(SELECT PART, SUBPART FROM assembly UNION ALL
SELECT assb.PART, all.Minor FROM assembly AS assb,
all_super AS all WHERE assb.SUBPART = all.Major )
SELECT * FROM all_subparts WHERE Minor = 'top_tube‘ this corresponds to a right-linear Datalog rule
Implementation
CREATE RECURSIVE VIEW all_subparts(Major, Minor) AS SELECT PART SUBPART
FROM assembly
UNION ALL
SELECT all.Major assb.SUBPARTFROM all_subparts AS all, assembly AS assbWHERE all.Minor= assb.PART
To implement the differential fixpoint improvement we replace the recursive relation all_subparts in the FROM clause by all_subparts, where all_subparts contains the new tuples generated in the previous iteration of differential fixpoint Algorithm. (But also eliminate duplicates as they are generated)
Find the parts using top tube (on Right Linear Recursion)
WITH RECURSIVE all_super(Major, Minor) AS (SELECT PART, SUBPART FROM assembly UNION ALL SELECT assb.PART, all.Minor FROM assembly AS assb, all_super AS all WHERE assb.SUBPART = all.Major) SELECT * FROM all_super WHERE Minor = 'top tube‘
Add Minor= 'top tube', to the WHERE clauses in exit select and the recursive select:WITH RECURSIVE all_super(Major, Minor) AS (SELECT PART, SUBPART FROM assembly
WHERE SUBPART = 'top tube' UNION ALL SELECT assb.PART, all.Minor FROM assembly AS assb, all_super AS all WHERE assb.SUBPART = all.Major AND all.Minor = 'top tube‘) SELECT * FROM all_super
Implementation left-recursion and right-recursion
SELECT * FROM_all subparts WHERE Minor = 'top tube'
Expressed against the virtual view of
CREATE RECURSIVE view all_subparts(Major, Minor) AS SELECT PART SUBPART FROM assembly UNION SELECT all.Major AS assb.SUBPART FROM all_subparts AS all, assembly AS assb WHERE all.Minor= assb.PART
The addition of the condition Minor = 'top tube' to the recursive select would not produce an equivalent query.
Thus, the compiler transforms the recursive select into its right linear equivalent , then adds Minor ='top tube' to the WHERE clause.
Example from Chamberlin’s book
WITH trips(destination, route, nsegs, totalcost) AS ((SELECT destination, CAST(destination AS Varchar(20)), 1, cost FROM flights WHERE origin = 'SFO') UNION ALL (SELECT f.destination, CAST(t.route || ', ' || f.destination AS Varchar(20)), t.nsegs + 1, t.totalcost + f.cost FROM trips t, flights f WHERE t.destination = f.origin AND f.destination <> 'SFO' AND f.origin <> 'JFK' AND t.nsegs < 3 )) SELECT route, totalcost FROM tripsWHERE destination = 'JFK'AND totalcost = (SELECT min(totalcost) FROM trips WHERE destination = 'JFK');
Limitations of Stratification
Aggregates are nonmonotonic They cannot be used inside recursion—
stratification condition for aggregates Without aggregates we cannot express optimal
graph-traversal algorithm Much research work in nonmonotonic reasoning. Naïve extensions do not work: e.g. Russell’s
paradox—who shaves the barber?
Recursive Rule Processing in SQL
• In general the compilation techniques usable for such transformations are basically those previously described for Datalog. Including the magic set transformation.
• Also stratification w.r.t. negation and aggregates* is required in SQL:1999
• Mutual recursion is supported and this where WITH becomes indispensable.
---------* Because aggregates are nonmonotonic!
Recursive Rule Processing in SQL
In general, the compilation techniques usable for such transformations are basically those previously described for Datalog---Including the magic set transformation
Also stratification w.r.t. `negation’ and aggregates is required by SQL:1999.
By negation, we mean NOT EXIST and EXCEPT because conditions such as NOT(A>B) become A<=B.
That means that you cannot express several graph algorithms in SQL:1999
Discussion
Datalog contributionsPower (beyond SQL-2)Rule-based programming paradigm very effective in
many applicationsSimple Formal semantics Novel Technology
Significant impact on SQL:1999 (SQL:2003 a clean up version of SQL:1999)Recursive queries now supported in commercial DBMSsLimited used in applications, because hard to write and
also restrictions imposed by stratification.
Discussion (cont.)
Recursion add expressive power to SQL but Complex objects not supported: (Deductive Object-
Oriented DBs—DOODs)... As opposed to OO-DB research that instead wants to unify DBs and object-oriented PL.
The Non-Monotonic conundrum: Not a new problem: naïve set theory (Russell’s) paradox,
AI Circumscription (J. Carthy) Stratification is not sufficient, in many cases to:
ensure termination, and Express classical graph algorithms (using extrema aggregates). Significant progress achieved in this area not part of SQL
standards.
Discussion (cont.)
Datalog remains a great framework for formal database research: E.g. Integration Information,Data Mining (Inductive Databases)Network routing algorithmsStatic program analysis.