SQL: Queries, Programming, Triggers

1
Database Systems II Query Compiler
2
Introduction

• The Query Compiler translates an SQL query into a
  physical query plan, which can be executed, in
  three steps
• The query is parsed and represented as a parse
  tree.
• The parse tree is converted into a relational
  algebra expression tree (logical query plan).
• The logical query plan is refined into a physical
  query plan, which also specifies the algorithms
  used in each step and the way in which data is
  obtained.

3
Introduction
SQL query
parse
parse tree
convert
answer
logical query plan
execute
query rewrite
Pi
improved l.q.p
pick best
estimate result sizes
(P1,C1),(P2,C2)...
l.q.p. sizes
estimate costs
consider physical plans
P1,P2,..
4
Introduction

• Example
• SELECT B,D
• FROM R,S
• WHERE R.A c ? S.E 2 ? R.CS.C
• Conceptual evaluation strategy
• Perform cartesian product,
• Apply selection, and
• Project to specified attributes.
• Use as starting point for optimization.

5
Introduction
?B,D sR.Ac? S.E2 ? R.C S.C (RXS)
6
Introduction
Example ?B,D sR.A c sS.E
2 R S
natural join

• This logical query plan is equivalent.
• It is more efficient, since it reduces the sizes
  of the intermediate tables.

7
Introduction

• Example
• Needs to be refined into physical query plan.
• E.g., use R.A and S.C indexes as follows
• (1) Use R.A index to select R tuples with
  R.A c
• (2) For each R.C value found, use S.C index
  to find matching tuples (3)
  Eliminate S tuples S.E ? 2
• (4) Join matching R,S tuples, project
• B,D attributes and place in result

8
Parsing

• Parse Trees
• Nodes correspond to either atoms (terminal
  symbols) or syntactic categories
  (non-terminal symbols).
• An atom is a lexical element such as a keyord,
  name of an attribute or relation, constant,
  operator, parenthesis.
• A syntactic category denotes a family of query
  subparts that all play the same role within a
  query, e.g. Condition.
• Syntactic categories are enclosed in triangular
  brackets, e.g. ltConditiongt.

9
Parsing

• Example
• SELECT title
• FROM StarsIn
• WHERE starName IN (SELECT name
• FROM MovieStar
• WHERE birthdate LIKE 1960)

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Parsing
ltQuerygt
ltSFWgt
SELECT ltSelListgt FROM ltFromListgt
WHERE ltConditiongt
ltAttributegt ltRelNamegt
ltTuplegt IN ltQuerygt
title StarsIn
ltAttributegt ( ltQuerygt )
starName ltSFWgt
SELECT ltSelListgt FROM ltFromListgt
WHERE ltConditiongt
ltAttributegt ltRelNamegt
ltAttributegt LIKE ltPatterngt
name MovieStar
birthDate 1960
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Parsing

• Grammar for SQL
• The following grammar describes a simple subset
  of SQL.
• Queries ltQuerygt SELECT ltSelListgt FROM
  ltFromListgt WHERE ltConditiongt
• Selection lists ltSelListgt ltAttributegt,
  ltSelListgt ltSelListgt ltAttributegt
• From lists ltFromListgt ltRelationgt,
  ltFromListgt ltFromListgt ltRelationgt

12
Parsing

• Grammar for SQL
• Conditions ltConditiongt ltConditiongt AND
  ltConditiongt ltConditiongt ltAttributegt IN
  (ltQuerygt) ltConditiongt ltAttributegt
  ltAttributegt ltConditiongt ltAttributegt LIKE
  ltPatterngt
• Syntactic categories Relation and Attribute are
  not defined by grammar rules, but by the
  database schema.
• Syntactic category Pattern defined as some
  regular expression.

13
Conversion to Query Plan

• How to convert a parse tree into a logical query
  plan, i.e. a relational algebra expression?
• Queries with conditions without subqueries are
  easy
• Form Cartesian product of all relations in
  ltFromListgt.
• Apply a selection sc where C is given by
  ltConditiongt.
• Finally apply a projection pL where L is the
  list of attributes in ltSelListgt.
• Queries involving subqueries are more difficult.
• Remove subqueries from conditions and represent
  them by a two-argument selection in the
  logical query plan.
• See the textbook for details.

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Algebraic Laws for Query Plans

• Introduction
• Algebraic laws allow us to transform a
  Relational Algebra (RA) expression into an
  equivalent one.
• Two RA expressions are equivalent if, for all
  database instances, they produce the same answer.
• The resulting expression may have a more
  efficient physical query plan.
• Algebraic laws are used in the query rewrite
  phase.

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Algebraic Laws for Query Plans

• Introduction
• Commutative law Order of arguments does
  not matter. x y y x
• Associative law May group two uses of the
  operator either from the left or the right.
  (x y) z x (y z)
• Operators that are commutative and associative
  can be grouped and ordered arbitrarily.

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Algebraic Laws for Query Plans
Natural Join, Cartesian Product and Union
R S S R (R S) T R (S T)
R x S S x R (R x S) x T R x (S x T) R U S
S U R R U (S U T) (R U S) U T
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Algebraic Laws for Query Plans
Natural Join, Cartesian Product and Union

• R S S R
• To prove this law, need to show that any tuple
  resulting from the left side expression is also
  produced by the right side expression, and vice
  versa.
• Suppose tuple t is in R S.
• There must be tuples r in R and s in S that agree
  with t on all shared attributes.
• If we evaluate S R, tuples s and r will
  againresult in t.

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Algebraic Laws for Query Plans
Natural Join, Cartesian Product and Union

• R S S R
• Note that the order of attributes within a tuple
  doesnot matter (carry attribute names along).
• Relation as bag of tuplesAccording to the same
  reasoning, the number of copies of t must be
  identical on both sides.
• The other direction of the proof is essentially
  the same, given the symmetry of S and R.

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Algebraic Laws for Query Plans
Selection
sp1?p2(R) sp1vp2(R)
sp1 sp2 (R) sp1 (R) U sp2 (R)
sp1 sp2 (R) sp2 sp1 (R)

• Simple conditions p1 or p2 may be pushed down
  further than the complex condition.

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Algebraic Laws for Query Plans
Bag Union

• What about the union of relations with
  duplicates (bags)?
• R a,a,b,b,b,c
• S b,b,c,c,d
• R U S ?
• Number of occurrences either SUM or MAX of
  occurrences in the imput relations.
• SUM R U S a,a,b,b,b,b,b,c,c,c,d
• MAX R U S a,a,b,b,b,c,c,d

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Algebraic Laws for Query Plans
Selection

• s p1vp2 (R) sp1(R) U sp2(R)
• MAX implementation of union makes rule work.
• Ra,a,b,b,b,c
• p1 satisfied by a,b, p2 satisfied by b,c
• sp1vp2 (R) a,a,b,b,b,c sp1(R)
  a,a,b,b,b sp2(R) b,b,b,c sp1 (R) U
  sp2 (R) a,a,b,b,b,c

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Algebraic Laws for Query Plans
Selection

• s p1vp2 (R) sp1(R) U sp2(R)
• SUM implementation of union makes more sense.
• Senators () Reps ()
• T1 p yr,state Senators, T2 p yr,state
  Reps
• T1 Yr State T2 Yr State
• 97 CA 99 CA
• 99 CA 99 CA
• 98 AZ 98 CA
• Use SUM implementation, but then some laws do
  not hold.

Union?
23
Algebraic Laws for Query Plans
Selection and Set Operations
sp(R U S) sp(R) U sp(S) sp(R - S) sp(R) - S
sp(R) - sp(S)
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Algebraic Laws for Query Plans
Selection and Join

• p predicate with only R attributes
• q predicate with only S attributes
• m predicate with attributes from R and S
• sp (R S)
• sq (R S)

sp (R) S R sq (S)
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Algebraic Laws for Query Plans
Selection and Join
sp?q (R S) sp (R) sq (S) sp?q?m
(R S) sm (sp R) (sq S) spvq (R
S) (sp R) S U R (sq S)
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Algebraic Laws for Query Plans
Selection and Join
sp?q (R S) sp sq (R S) sp R
sq (S) sp (R) sq (S)
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Algebraic Laws for Query Plans
Projection

• X set of attributes
• Y set of attributes
• XY X U Y
• pxy (R)
• May introduce projection anywhere in an
  expression tree as long as it eliminates no
  attributes needed by an operator above and no
  attributes that are in result

px py (R)
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Algebraic Laws for Query Plans
Projection and Selection

• X subset of R attributes
• Z attributes in predicate P (subset of R
  attributes)
• px (spR)
• Need to keep attributes for the selection and
  for the result

sp px (R)
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Algebraic Laws for Query Plans
Projection, Selection and Join
pxy sp (R S)
pxy sp pxz (R) pyz (S) Y subset of
S attributes z subset of R attributes used
in P z subset of S attributes used in P
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Improving Logical Query Plans

• Introduction
• How to apply the algebraic laws to improve a
  logical query plan?
• Goal minimize the size (number of tuples,
  number of attributes) of intermediate results.
• Push selections down in the expression tree
  as far as possible.
• Push down projections, or add new projections
  where applicable.

31
Improving Logical Query Plans

• Pushing Selections
• Replace the left side of one of these (and
  similar) rules by the right side
• Can greatly reduce the number of tuples of
  intermediate results.

sp1?p2 (R) ? sp1 sp2 (R) sp (R S) ? sp
(R) S
32
Improving Logical Query Plans

• Pushing Projections
• Replace the left side of one of this (and
  similar) rules by the right side
• Reduces the number of attributes of
  intermediate results and possibly also the
  number of tuples.

px sp (R) ? px sp pxz (R)
33
Improving Logical Query Plans

• Pushing Projections
• Consider the following example
• R(A,B,C,D,E) P (A3) ? (Bcat)
• Compare
• pE sp (R) vs. pE sppABE(R)

34
Improving Logical Query Plans

• Pushing Projections
• What if we have indexes on A and B?
• B cat A3
• Intersect pointers to get pointers to matching
  tuples
• Efficiency of logical query plan may depend on
  choices made during refinement to physical plan.
• No transformation is always good!

35
Improving Logical Query Plans

• Grouping Associative / Commutative Operators
• For operators which are commutative and
  associative, we can order and group their
  arguments arbitrarily.
• In particular natural join, union,
  intersection.
• As the last step to produce the final logical
  query plan, group nodes with the same
  (associative and commutative) operator into
  one n-ary node.
• Best grouping and ordering determined during
  the generation of physical query plan.

36
Improving Logical Query Plans
Grouping Associative / Commutative Operators
?
U
C
D
E
U
C
D
E
A
B
A
B
37
From Logical to Physical Plans

• So far, we have parsed and transformed an SQL
  query into an optimized logical query plan.
• In order to refine the logical query plan into
  a physical query plan, we
• consider alternative physical plans,
• estimate their cost, and
• pick the plan with the least (estimated) cost.
• We have to estimate the cost of a plan without
  executing it. And we have to do that efficiently!

38
From Logical to Physical Plans

• When creating a physical query plan, we have
  to decide on the following issues.
• order and grouping of operations that are
  associative and commutative,
• algorithm for each operator in the logical plan,
• additional operators which are not represented
  in the logical plan, e.g. sorting,
• the way in which intermediate results are
  passed from one operator to the next, e.g. by
  storing on disk or passing one tuple at a time.

39
Estimating the Cost of Operations

• Intermediate relations are the output of some
  relational operator and the input of another one.
• The size of intermediate relations has a major
  impact on the cost of a physical query plan.
• It impacts in particular - the choice of an
  implementation for the various operators
  and - the grouping and order of commutative
  / associative operators.

40
Estimating the Cost of Operations

• A method for estimating the size of an
  intermediate relation should be
• reasonably accurate,- efficiently computable,-
  not depend on how that relation is computed.
• We want to rank alternative query plans w.r.t.
  their estimated costs.
• Accuracy of the absolute values of the
  estimates not as important as the accuracy of
  their ranks.

41
Estimating the Cost of Operations

• Size estimates make use of the following
  statistics for relation R
• T(R) tuples in R
• S(R) of bytes in each R tuple
• B(R) of blocks to hold all R tuples
• V(R, A) distinct values for attribute A in
  R.
• MIN(R,A) minimum value of attribute A in R.
• MAX(R,A) maximum value of attribute A in
  R.HIST(R,A) histogram for attribute A in R.
• Statistics need to be maintained up-to-dateunder
  database modifications!

42
Estimating the Cost of Operations
R A 20 byte string B 4 byte
integer C 8 byte date D 5 byte
string
T(R) 5 S(R) 37 V(R,A) 3 V(R,C)
5 V(R,B) 1 V(R,D) 4
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Estimating the Cost of Operations

• Size estimate for W R1 x R2
• T(W) T(R1) ? T(R2)
• S(W) S(R1) S(R2)
• Size estimate for W sAa (R)
• Assumption values of A are uniformly distributed
  over the attribute domain
• T(W) T(R)/V(R,A) S(W) S(R)

44
Estimating the Cost of Operations

• Size estimate for W s z ? val (R)
• Solution 1 on average, half of the tuples will
  satisfy an inequality condition
• T(W) T(R)/2
• Solution 2 more selective queries are more
  frequent, e.g. professors who earn more than
  200000 (rather than less than 200000)
• T(W) T(R)/3

45
Estimating the Cost of Operations

• Solution 3 estimate the number of
  attributevalues in query range
• Use minimum and maximum value to define range of
  the attribute domain.
• Assume uniform distribution of valuesover the
  attribute domain.
• Estimate is the fraction of the domain thatfalls
  into the query range.

46
Estimating the Cost of Operations
R
Z
MIN(R,Z)1 V(R,Z)10 W sz ? 15
(R) MAX(R,Z)20
f 20-151 6 (fraction of range)
20-11 20 T(W) f ? T(R)
47
Estimating the Cost of Operations

• Size estimate for W R1 R2
• Consider only natural join of R1(X,Y) and
  R2(Y,Z).
• We do not know how the Y values in R1 and R2
  relate- disjoint, i.e. T(R1 R2) 0,- Y
  may be a foreign key of R1 and the primary
  key of R2, i.e. T(R1 R2) T(R1),- all
  the R1 and all the R2 tuples have the same Y
  value, i.e. T(R1 R2) T(R1) ?T(R2).

48
Estimating the Cost of Operations

• Make several simplifying assumptions.
• Containment of value sets V(R1,Y) ? V(R2,Y) ?
  every Y value in R1 is in R2
• V(R2,Y) ? V(R1,Y) ? every Y value in
  R2 is in R1
• This assumption is satisfied when Y is foreign
  key in R1 and primary key in R2.
• Is also approximately true in many other cases.

49
Estimating the Cost of Operations

• Preservation of value setsIf A is an attribute
  of R1 but not of R2, thenV(R1 R2,A)
  V(R1,A).
• Again, holds if the join attribute Y is foreign
  key in R1 and primary key in R2.
• Can only be violated if there are dangling
  tuples in R1, i.e. R1 tuples that have no
  matching partner in R2.

50
Estimating the Cost of Operations

• Uniform distribution of attribute values the
  values of attribute A are uniformly distributed
  over their domain, i.e. P(Aa1) P(Aa2) . . .
  P(Aak).
• This assumption is necessary to make cost
  estimation tractable.
• It is often violated, but nevertheless allows
  reasonably accurate ranking of query plans.

51
Estimating the Cost of Operations

• Independence of attributes the values of
  attributes A and B are independent from each
  other, i.e. P(AaBb) P(Aa) and P(BbAa)
  P(Bb) .
• This assumption is necessary to make cost
  estimation tractable.
• Again, often violated, but nevertheless allows
  reasonably accurate ranking of query plans.

52
Estimating the Cost of Operations

• Suppose that t1 is some tuple in R1, t2 some
  tuple in R2.
• What is the probability that t1 and t2 agree on
  the join attribute Y?
• If V(R1,Y) ? V(R2,Y), then the Y value of t1
  appears in R2, because of the containment of
  value sets.
• Assuming uniform distribution of the Y values in
  R2 over their domain, the probability of t2
  having the same Y value as t1 is 1/V(R2,Y).

53
Estimating the Cost of Operations

• If V(R2,Y) ? V(R1,Y), then the Y value of t2
  appears in R1, and the probability of t1 having
  the same Y value as t2 is 1 / V(R1,Y).
• T(W) number of pairs of tuples from R1 and R2
  times the probability that an arbitrary pair
  agrees on Y.
• T(R1 R2) T(R1) T(R2) /
  max(V(R1,Y), V(R2,Y)).

54
Estimating the Cost of Operations

• For complex query expressions, need to estimate
  T,S,V results for intermediate results.
• For example, W sAa (R1) R2
• treat as relation U
• T(U) T(R1)/V(R1,A) S(U) S(R1)
• Also need V (U, ) for all attributes of U(R1)!

55
Estimating the Cost of Operations
R 1 V(R1,A)3 V(R1,B)1 V(R1,C)5
V(R1,D)3
U sAa (R1)
V(U,A) 1 V(U,B) 1 V(U,C) T(R1)/ V(R1,A)
V(U,D) ... somewhere in between
56
Estimating the Cost of Operations

• R1(A,B), R2(A,C).
• Consider join U R1 R2.
• Estimate V results for U.
• V(U,A) min V(R1, A), V(R2, A) Holds due to
  containment of value sets.
• V(U,B) V(R1, B)
• V(U,C) V(R2, C) Holds due to
  preservation of value sets.

57
Estimating the Cost of Operations

• Consider the following example
• Z R1(A,B) R2(B,C) R3(C,D)
• T(R1) 1000 V(R1,A)50 V(R1,B)100
• T(R2) 2000 V(R2,B)200 V(R2,C)300
• T(R3) 3000 V(R3,C)90 V(R3,D)500
• Group and order as (R1 R2) R3

58
Estimating the Cost of Operations

• Partial result U R1 R2
• T(U) 1000?2000 / 200
• V(U,A) 50
• V(U,B) 100
• V(U,C) 300

59
Estimating the Cost of Operations

• Final result Z U R3
• T(Z) 1000?2000?3000 / (200 ? 300)
• V(Z,A) 50
• V(Z,B) 100
• V(Z,C) 90
• V(Z,D) 500