K.Subieta. SBA and SBQL, appendix, slide 1 Sept Appendix: how the ENVS and QRES stacks work (M0 example) Presentation prepared for OMG Object Database Technology Working Group OMG TECHNICAL MEETING, Anaheim, CA USA September 25-29, 2006 by Prof. Kazimierz Subieta Polish-Japanese Institute of Information Technology, Warsaw, Poland SBA/SBQL pages:

K.Subieta. SBA and SBQL, appendix, slide 2 Sept Query addressing a tiny database Query: For each department get its reference and the average sal of its employees. SBQL: Dept join avg((employs.Emp).sal) Tiny database: Expected result: bag{ struct{i 17, 2500}, struct{i 22, 1450} }

K.Subieta. SBA and SBQL, appendix, slide 3 Sept Query syntax tree and execution scenario Dept join avg( ( employs. Emp ). sal ) join Deptavg..sal employsEmp 2 nd dot 1 st dot join1 st dot2 nd dot avg 1 st Dept 2 nd Dept 1 st employs 2 nd employs 1 st Emp 2 nd Emp 3 rd Emp3 rd employs

K.Subieta. SBA and SBQL, appendix, slide 4 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES empty Start

K.Subieta. SBA and SBQL, appendix, slide 5 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } After binding Dept

K.Subieta. SBA and SBQL, appendix, slide 6 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } join starts 1 st loop of the iteration over top of QRES dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) nested

K.Subieta. SBA and SBQL, appendix, slide 7 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) After binding employs i 21

K.Subieta. SBA and SBQL, appendix, slide 8 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) i 21 dot starts iteration on top of QRES Emp(i 1 ) nested

K.Subieta. SBA and SBQL, appendix, slide 9 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) i 21 Emp(i 1 ) After binding Emp i1i1

K.Subieta. SBA and SBQL, appendix, slide 10 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) Closing the iteration by the first dot i1i1

K.Subieta. SBA and SBQL, appendix, slide 11 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) i1i1 Second dot starts iteration over top of QRES name(i 2 ) sal(i 3 ) worksIn(i 4 ) nested

K.Subieta. SBA and SBQL, appendix, slide 12 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) i1i1 name(i 2 ) sal(i 3 ) worksIn(i 4 ) After binding sal i3i3

K.Subieta. SBA and SBQL, appendix, slide 13 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) i3i3 Closing the iteration by the second dot

K.Subieta. SBA and SBQL, appendix, slide 14 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) 2500 After performing avg on top of QRES

K.Subieta. SBA and SBQL, appendix, slide 15 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 18 ) loc(i 19 ) loc(i 20 ) employs(i 21 ) 2500 join forms the first partial result struct{ i 17, 2500 }Partial result of join:

K.Subieta. SBA and SBQL, appendix, slide 16 Sept After ending the 1 st loop by join 12 Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } struct{ i 17, 2500 }Partial result of join:

K.Subieta. SBA and SBQL, appendix, slide 17 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } join starts 2 nd loop of the iteration over top of QRES dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) nested struct{ i 17, 2500 }Partial result of join:

K.Subieta. SBA and SBQL, appendix, slide 18 Sept After binding employs 14 Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 25, i 26 } struct{ i 17, 2500 }Partial result of join:

K.Subieta. SBA and SBQL, appendix, slide 19 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 25, i 26 } First dot starts 1 st loop of iteration on top of QRES nested Emp(i 5 ) struct{ i 17, 2500 }Partial result of join:

K.Subieta. SBA and SBQL, appendix, slide 20 Sept After binding Emp 16 Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 25, i 26 } Emp(i 5 ) struct{ i 17, 2500 }Partial result of join: i5i5

K.Subieta. SBA and SBQL, appendix, slide 21 Sept Forming 1 st partial result of the first dot 17 Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 25, i 26 } struct{ i 17, 2500 }Partial result of join: i5i5 Partial result of dot:

K.Subieta. SBA and SBQL, appendix, slide 22 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 25, i 26 } struct{ i 17, 2500 }Partial result of join: i5i5 Partial result of dot: First dot starts 2 nd loop of iteration on top of QRES nested Emp(i 9 )

K.Subieta. SBA and SBQL, appendix, slide 23 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 25, i 26 } struct{ i 17, 2500 }Partial result of join: i5i5 Partial result of dot: Emp(i 9 ) After binding Emp i9i9

K.Subieta. SBA and SBQL, appendix, slide 24 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 25, i 26 } struct{ i 17, 2500 }Partial result of join: i5i5 Partial results of dot: i9i9 Forming 2 nd partial result of the first dot

K.Subieta. SBA and SBQL, appendix, slide 25 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 5, i 9 } struct{ i 17, 2500 }Partial result of join: Closing iteration by the first dot, forming its result

K.Subieta. SBA and SBQL, appendix, slide 26 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 5, i 9 } struct{ i 17, 2500 }Partial result of join: Second dot starts 1 st loop of iteration on top of QRES nested name(i 6 ) sal(i 7 ) worksIn(i 8 )

K.Subieta. SBA and SBQL, appendix, slide 27 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 5, i 9 } struct{ i 17, 2500 }Partial result of join: name(i 6 ) sal(i 7 ) worksIn(i 8 ) After binding sal i7i7

K.Subieta. SBA and SBQL, appendix, slide 28 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 5, i 9 } struct{ i 17, 2500 }Partial result of join: Forming 1 st partial result of the second dot i7i7 Partial result of dot:

K.Subieta. SBA and SBQL, appendix, slide 29 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 5, i 9 } struct{ i 17, 2500 }Partial result of join: i7i7 Partial result of dot: Second dot starts 2 nd loop of iteration on top of QRES nested name(i 10 ) sal(i 11 ) address(i 12 ) worksIn(i 16 )

K.Subieta. SBA and SBQL, appendix, slide 30 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 5, i 9 } struct{ i 17, 2500 }Partial result of join: i7i7 Partial result of dot: name(i 10 ) sal(i 11 ) address(i 12 ) worksIn(i 16 ) After binding sal i 11

K.Subieta. SBA and SBQL, appendix, slide 31 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 5, i 9 } struct{ i 17, 2500 }Partial result of join: i7i7 Partial result of dot: i 11 Forming 2 nd partial result of the second dot

K.Subieta. SBA and SBQL, appendix, slide 32 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) bag{ i 7, i 11 } struct{ i 17, 2500 }Partial result of join: Closing iteration by the second dot, forming its result

K.Subieta. SBA and SBQL, appendix, slide 33 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) 1450 struct{ i 17, 2500 }Partial result of join: After performing avg on top of QRES

K.Subieta. SBA and SBQL, appendix, slide 34 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ i 17, i 22 } dname(i 23 ) loc(i 24 ) employs(i 25 ) employs(i 26 ) 1450 struct{ i 17, 2500 }Partial results of join: join forms 2 nd partial result struct{ i 22, 1450 }

K.Subieta. SBA and SBQL, appendix, slide 35 Sept Dept join avg( ( employs. Emp ). sal ) Emp(i 1 ) Emp(i 5 ) Emp(i 9 ) Dept(i 17 ) Dept(i 22 ) ENVSQRES bag{ struct{ i 17, 2500}, struct{ i 22, 1450} } Closing the iteration by join, forming the final result

K.Subieta. SBA and SBQL, appendix, slide 36 Sept In closing … Please note that this evaluation scenario concerns the formal semantics executed by the abstract machine. –Our goal is clear, universal and free of ambiguities semantic specification rather than performance. In real implementation there are many obvious optimizations. The evaluation process is also the subject of many sophisticated optimizations (rewriting, indices, caching,…). The entire process is executed in the main memory, hence the computations are not critical. –Critical computations concern the access to external storage and network, and avoiding unnecessary (redundant) computations. –This is the subject of major SBA optimization methods.