1. The Query Compiler Parses SQL query into parse tree Transforms parse tree into expression tree (logical query plan) Transforms logical query plan into physical query plan

2. {P1,P2,…..} {P1,C1>...} parse convert apply laws estimate result sizes consider physical plans estimate costs pick best execute Pi answer SQL query parse tree logical query plan “improved” l.q.p l.q.p. +sizes statistics

3. Grammar for simple SQL ::= ::= ( ) ::= SELECT FROM WHERE ::=, ::= ::=, ::= ::= AND ::= IN ::= = ::= LIKE ::= A toms(constants), (variable), ::= (can be expressed/defined as)

4. Query and parse tree StarsIn( title,year,starName ) MovieStar( name,address,gender,bdate ) Query: Give titles of movies that have at least one star born in 1960 SELECT title FROM StarsIn WHERE starName IN ( SELECT name FROM MovieStar WHERE birthdate LIKE '%1960%' );

5. Another query equivalent SELECT title FROM StarsIn, MovieStar WHERE starName = name AND birthdate LIKE '%1960%' ;

6. Parse Tree SELECT FROM WHERE, AND title StarsIn = LIKE starName name birthdate ‘%1960’ MovieStar

7. The Preprocessor (expand query & semantic checking) Checks against schema definition: –Relation uses –Attribute uses, resolve names ( A to R.A) –Use of types (strings, integers, dates, etc) and operators’ arguments type/arity  These preprocessing functions are called semantic checking If all tests are passed, then the parse tree is said to be valid

8. Algebraic laws for transforming logical query plans Commutative and associative laws: Above laws are applicable for both sets and bags

9. Theta-join Commutative: Not always associative: –On schema R(a,b), S(b,c), T(c,d) the first query can not be transformed into the second: (Why?) Because, we can’t join S and T using the condition a<d since a is an attribute of neither S nor T.

10. Laws Involving Selection (  ) Splitting laws Only if R is a set. The union is “set union” Order is flexible

11. Laws Involving Selection (  ) For intersection, the selection is required to be pushed to one argument. What about intersection?

12. If all attributes in the condition C are in R (for binary operators)

13. Example: Consider relation schemas R(A,B) and S(B,C) and the expression below:  (A=1 OR A=3) AND B < C (R  S) 1.Splitting AND  A=1 OR A=3 (  B < C (R  S)) 2.Push  to S  A=1 OR A=3 (R   B < C (S)) 3.Push  to R  A=1 OR A=3 (R)   B < C (S)

14. Some Trivial Laws Watch for some extreme cases: –an empty relation: e.g., R  S = S, if R =  –a selection or theta-join whose condition is always satisfied e.g.,  C (R) = R, if C = true –a projection on all attributes is “better” not to be done at all!!

15. Pushing selections Usually selections are pushed down the expression tree. The following example shows that it is sometimes useful to pull selection up in the tree. StarsIn(title,year,starName) Movie(title,year,length,studioName) CREATE VIEW MoviesOf1996 AS SELECT * FROM MOVIE WHERE year=1996; Query: Which stars worked for which studios in 1996? SELECT starName,studioName FROM MoviesOf1996 NATURAL JOIN StarsIN;

16. pull selection up then push down

17. Laws for (bag) Projection A simple law: Project out attributes that are not needed later. I.e. keep only the input attr. and join attr. Projections cannot be pushed below  S, or either set/bag versions of  and – Example: Consider R(A,B) and S(A,C). Supp. R = {(1,2)} and S = {(1,3)}.   A (R  S) =  A (  ) but  A (R)   A (S) = {(1)}

18. Example Schema : StarsIn(title,year,starName) Query: SELECT starName FROM StarsIn WHERE year = 1996; Should we can transform to   starName  year=1996 StarsIn  starName  year=1996 StarsIn  starName,year