Advanced Views: XMLRelational Storage and Datalog

1
Advanced ViewsXML-Relational Storage and Datalog

• Zachary G. Ives
• University of Pennsylvania
• CIS 550 Database Information Systems
• November 7, 2007

Some slide content courtesy of Susan Davidson,
Dan Suciu, Raghu Ramakrishnan
2
Administrivia

• Homework 4 is now due Friday at 1159PM EST
• Project teams should be complete
• However, there are several teams of 3
• For a 3-person team, you may eliminate one data
  source and wrapper from your system
• By next Wednesday a brief email for each
  project group describing the expected division of
  labor
• Note the project has a demo presentation and a
  10 page report consider those as well!

3
Mapping Relational ? XML

• We know the following
• XML is a tree
• XML is SEMI-structured
• Theres some structured stuff
• There is some unstructured stuff
• Issues relate to describing XML structure,
  particularly parent/child in a relational
  encoding
• Relations are flat
• Tuples can be connected via foreign-key/primary-
  key links

4
The Simplest Way to Encode a Tree

• Suppose we hadlttree id0gt ltcontent id1gt
  ltsub-contentgtXYZ lt/sub-contentgt
  lti-contentgt14 lt/i-contentgt
  lt/contentgtlt/treegt
• If we have no IDs, we CREATE values

• BinaryLikeEdge(key, label, type, value, parent)

What are shortcomings here?
5
Florescu/Kossmann Improved Edge Approach

• Consider order, typing separate the values

• Vint(vid, value)
• Vstring(vid, value)

• Edge(parent, ordinal, label, flag, target)

6
How Do You Compute the XML?

• Assume we know the structure of the XML tree
  (well see how to avoid this later)
• We can compute an XML-like SQL relation using
  outer unions we first this technique in
  XPERANTO
• Idea if we take two non-union-compatible
  expressions, pad each with NULLs, we can UNION
  them together
• Lets see how this works

7
A Relation that Mirrors theXML Hierarchy

• Output relation would look like

8
A Relation that Mirrors theXML Hierarchy

• Output relation would look like

9
A Relation that Mirrors theXML Hierarchy

• Output relation would look like

Colors are representative of separate SQL queries
10
SQL for Outputting XML

• For each sub-portion we preserve the keys
  (target, ord) of the ancestors
• Root
• select E.label AS rLabel, E.target AS rid, E.ord
  AS rOrd, null AS cLabel, null AS cid, null AS
  cOrd, null AS subOrd, null AS sid, null AS str,
  null AS intfrom Edge Ewhere parent IS NULL
• First-level children
• select null AS rLabel, E.target AS rid, E.ord AS
  rOrd, E1.label AS cLabel, E1.target AS cid,
  E1.ord AS cOrd, null AS from Edge E, Edge
  E1where E.parent IS NULL AND E.target E1.parent

11
The Rest of the Queries

• Grandchild
• select null as rLabel, E.target AS rid, E.ord AS
  rOrd, null AS cLabel, E1.target AS cid, E1.ord AS
  cOrd, E2.label as sLabel, E2.target as sid,
  E2.ord AS sOrd, null as from Edge E, Edge E1,
  Edge E2where E.parent IS NULL AND E.target
  E1.parent AND E1.target E2.parent
• Strings
• select null as rLabel, E.target AS rid, E.ord AS
  rOrd, null AS cLabel, E1.target AS cid, E1.ord AS
  cOrd, null as sLabel, E2.target as sid, E2.ord AS
  sOrd, Vi.val AS str, null as intfrom Edge E,
  Edge E1, Edge E2, Vint Vi where E.parent IS NULL
  AND E.target E1.parent AND E1.target
  E2.parent AND Vi.vid E2.target
• How would we do integers?

12
Finally

• Union them all together
• ( select E.label as rLabel, E.target AS rid,
  E.ord AS rOrd, from Edge E where parent IS
  NULL)UNION ( select null as rLabel, E.target
  AS rid, E.ord AS rOrd, E1.label AS cLabel,
  E1.target AS cid, E1.ord AS cOrd, null as
  from Edge E, Edge E1 where E.parent IS NULL AND
  E.target E1.parent) UNION (
• .
• ) UNION ( .
• )
• Then another module will add the XML tags, and
  were done!

13
Inlining Techniques

• Folks at Wisconsin noted we can exploit the
  structured aspects of semi-structured XML
• If were given a DTD, often the DTD has a lot of
  required (and often singleton) child elements
• Book(title, author, publisher)
• Recall how normalization worked
• Decompose until we have everything in a relation
  determined by the keys
• But dont decompose any further than that
• Shanmugasundaram et al. try not to decompose XML
  beyond the point of singleton children

14
Inlining Techniques

• Start with DTD, build a graph representing
  structure

tree
?
_at_id

content
_at_id


i-content
sub-content

• The edges are annotated with ?, indicating
  repetition,optionality of children
• They simplify the DTD to figure this out

15
Building Schemas

• Now, they tried several alternatives that differ
  in how they handle elements w/multiple ancestors
• Can create a separate relation for each path
• Can create a single relation for each element
• Can try to inline these
• For tree examples, these are basically the same
• Combine non-set-valued things with parent
• Add separate relation for set-valued child
  elements
• Create new keys as needed

author
book
name
16
Schemas for Our Example

• TheRoot(rootID)
• Content(parentID, id, _at_id)
• Sub-content(parentID, varchar)
• I-content(parentID, int)
• If we suddenly changed DTD to lt!ELEMENT
  content(sub-content, i-content?) what would
  happen?

17
XQuery to SQL

• Inlining method needs external knowledge about
  the schema
• Needs to supply the tags and info not stored in
  the tables
• We can actually directly translate simple XQuery
  into SQL over the relations not simply
  reconstruct the XML

18
An Example

• for X in document(mydoc)/tree/contentwhere
  X/sub-content XYZreturn X
• The steps of the path expression are generally
  joins
• Except that some steps are eliminated by the
  fact weve inlined subelements
• Lets try it over the schema
• TheRoot(rootID)
• Content(parentID, id, _at_id)
• Sub-content(parentID, varchar)
• I-content(parentID, int)

19
XML Views of Relations

• Weve seen that views are useful things
• Allow us to store and refer to the results of a
  query
• Weve seen an example of a view that changes from
  XML to relations and weve even seen how such a
  view can be posed in XQuery and unfolded into
  SQL

20
An Important Set of Questions

• Views are incredibly powerful formalisms for
  describing how data relates fn rel ? ? rel ?
  rel
• Can I define a view recursively?
• Why might this be useful in the XML construction
  case? When should the recursion stop?
• Suppose we have two views, v1 and v2
• How do I know whether they represent the same
  data?
• If v1 is materialized, can we use it to compute
  v2?
• This is fundamental to query optimization and
  data integration, as well see later

21
Reasoning about Queries and Views

• SQL or XQuery are a bit too complex to reason
  about directly
• Some aspects of it make reasoning about SQL
  queries undecidable
• We need an elegant way of describing views (lets
  assume a relational model for now)
• Should be declarative
• Should be less complex than SQL
• Doesnt need to support all of SQL aggregation,
  for instance, may be more than we need

22
Lets Go Back a Few WeeksDomain Relational
Calculus

• Queries have form
• ltx1,x2, , xngt p
• Predicate boolean expression over x1,x2, , xn
• We have the following operations
• ltxi,xj,gt ? R xi op xj xi op const const op xi
• ?xi. p ?xj. p p?q, p?q ?p, p?q
• where op is ?, ?, ?, ?, ?, ? and
• xi,xj, are domain variables p,q are predicates
• Recall that this captures the same expressiveness
  as the relational algebra

domain variables
predicate
23
A Similar Logic-Based LanguageDatalog

• Borrows the flavor of the relational calculus but
  is a real query language
• Based on the Prolog logic-programming language
• A datalog program will be a series of if-then
  rules (Horn rules) that define relations from
  predicates
• Rules are generally of the form
• Rout(T1) ? R1(T2), R2(T3), , c(T2 Tn)
• where Rout is the relation representing the
  query result, Ri are predicates representing
  relations, c is an expression using
  arithmetic/boolean predicates over vars, and
  Ti are tuples of variables

24
Datalog Terminology

• An example datalog rule
• idb(x,y) ? r1(x,z), r2(z,y), z lt 10
• Irrelevant variables can be replaced by _
  (anonymous var)
• Extensional relations or database schemas (edbs)
  are relations only occurring in rules bodies
  these are base relations with ground facts
• Intensional relations (idbs) appear in the heads
  these are basically views
• Distinguished variables are the ones output in
  the head
• Ground facts only have constants, e.g., r1(abc,
  123)

body
head
subgoals
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Datalog in Action

• As in DRC, the output (head) consists of a tuple
  for each possible assignment of variables that
  satisfies the predicate
• We typically avoid 8 in Datalog queries
  variables in the body are existential, ranging
  over all possible values
• Multiple rules with the same relation in the head
  represent a union
• We often try to avoid disjunction (Ç) within
  rules
• Lets see some examples of datalog queries
  (which consist of 1 or more rules)
• Given Professor(fid, name), Teaches(fid, serno,
  sem), Courses(serno, cid, desc), Student(sid,
  name)
• Return course names other than CIS 550
• Return the names of the teachers of CIS 550
• Return the names of all people (professors or
  students)

26
Datalog is Relationally Complete

• We can map RA ? Datalog
• Selection ?p p becomes a datalog subgoal
• Projection ?A we drop projected-out variables
  from head
• Cross-product r ? s q(A,B,C,D) ? r(A,B),s(C,D)
• Join r ? s q(A,B,C,D) ? r(A,B),s(C,D),
  condition
• Union r U s q(A,B) ? r(A,B) q(C, D) - s(C,D)
• Difference r s q(A,B) ? r(A,B), s(A,B)
• (If you think about it, DRC ? Datalog is even
  easier)
• Great But then why do we care about Datalog?

27
A Query We CantAnswer in RA/TRC/DRC

• Recall our example of a binary relation for
  graphs or trees (similar to an XML Edge
  relation)
• edge(from, to)
• If we want to know what nodes are reachable
• reachable(F, T, 1) - edge(F, T) distance 1
• reachable(F, T, 2) - edge(F, X), edge(X,
  T) dist. 2
• reachable(F, T, 3) - reachable(F, X, 2), edge(X,
  T) dist. 3
• But how about all reachable paths? (Note this
  was easy in XPath over an XML representation --
  //edge)

(another way of writing ?)
28
Recursive Datalog Queries

• Define a recursive query in datalog
• reachable(F, T, 1) - edge(F, T) distance 1
• reachable(F, T, D 1) - reachable(F, X, D),
  edge(X, T) distance gt1
• What does this mean, exactly, in terms of logic?
• There are actually three different (equivalent)
  definitions of semantics
• All make a closed-world assumption facts
  should exist only if they can be proven true from
  the input i.e., assume the DB contains all of
  the truths out there!

29
Fixpoint Semantics

• One of the three Datalog models is based on a
  notion of fixpoint
• We start with an instance of data, then derive
  all immediate consequences
• We repeat as long as we derive new facts
• In the RA, this requires a while loop!
• However, that is too powerful and needs to be
  restricted
• Special case inflationary semantics (which
  terminates in time polynomial in the size of the
  database!)

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Our Query in RA while(inflationary semantics,
no negation)

• Datalog
• reachable(F, T, 1) - edge(F, T)
• reachable(F, T, D1) - reachable(F, X, D),
  edge(X, T)
• RA procedure with while
• reachable edge ? literal1
• while change
• reachable ?F, T, D(?F ! X(edge) ? ?T ! X,D !
  D0(reachable) ? add1)

Note literal1(F,1) and add1(D0,D) are actually
arithmetic and literal functions modeled here as
relations.
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Negation in Datalog

• Datalog allows for negation in rules
• Its essential for capturing RA set
  difference-style opsProfessor(name),
  Student(name)
• But negation can be tricky
• You may recall that in the DRC, we had a notion
  of unsafe queries, and they return here
• Single(X) ? Person(X), Married(X,Y)

32
Safe Rules/Queries

• Range restriction, which requires that every
  variable
• Occurs at least once in a positive relational
  predicate in the body,
• Or its constrained to equal a finite set of
  values by arithmetic predicates

Safeq(X) ? r(X,Y)q(X) ? X 5 q(X) ?
r(X,X), s(X)q(X) ? r(X) Ç (t(Y),u(X,Y))
Unsafeq(X) ? r(Y)q(X) ? r(X,X)q(X) ? r(X) Ç
t(Y)

• For recursion, use stratified semantics
• Allow negation only over edb predicates
• Then recursively compute values for the idb
  predicates that depend on the edbs (layered like
  strata)

33
A Special Type of Query Conjunctive Queries

• A single Datalog rule with no Ç, , 8 can
  express select, project, and join a conjunctive
  query
• Conjunctive queries are possible to reason about
  statically
• (Note that we can write CQs in other languages,
  e.g., SQL!)
• We know how to minimize conjunctive queries
• An important simplification that cant be done
  for general SQL
• We can test whether one conjunctive querys
  answers always contain another conjunctive
  querys answers (for ANY instance)
• Why might this be useful?

34
Example of Containment

• Suppose we have two queriesq1(S,C) -
  Student(S, N), Takes(S, C), Course(C, X),
  inCIS(C), Course(C, DB Info
  Systems)q2(S,C) - Student(S, N), Takes(S, C),
  Course(C, X)
• Intuitively, q1 must contain the same or fewer
  answers vs. q2
• It has all of the same conditions, except one
  extra conjunction (i.e., its more restricted)
• Theres no union or any other way it can add more
  data
• We can say that q2 contains q1 because this holds
  for any instance of our DB Student, Takes,
  Course

35
Wrapping up Datalog

• Weve seen a new language, Datalog
• Its basically a glorified DRC with a special
  feature, recursion
• Its much cleaner than SQL for reasoning about
• But negation (as in the DRC) poses some
  challenges
• Weve seen that a particular kind of query, the
  conjunctive query, is written naturally in
  Datalog
• Conjunctive queries are possible to reason about
• We can minimize them, or check containment
• Conjunctive queries are very commonly used in our
  next problem, data integration