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Object Identities

This presentation by Corey Anderson delves into the concept of object identities as first-class citizens within a formal framework inspired by Abiteboul and Kanellakis. It highlights the lack of a uniform formalism in object-oriented databases and proposes A&K's formalism as a solution. Key topics include unique identifiers (oids), schema definitions, the Identity Query Language (IQL), and examples of querying relations and instances. The presentation emphasizes the importance of oids in representing objects and demonstrates the expressive power of IQL in database transformations.

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Object Identities

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  1. Object Identities A presentation by Corey Anderson Inspired by Abiteboul and Kanellakis

  2. The big idea • Object-orientation in a database is good • But no one uniform formalism exists yet • So let’s use A&K’s formalism • Object identities as First Class Citizens

  3. Object Identity • A unique identity for each object oid o-value adam [ name: “Adam”, spouse: eve, children: {cain, abel, seth, …} ]

  4. Formalisms – basics • oid • An identifier • o-value • An oid, a constant, or a tuple of o-values • Schema v. Instance

  5. Formalisms – classes • Classes P = { P1, P2, … } • P = { 1st-gen, 2nd-gen } • (P) : P {oids} • (1st-gen) = { adam, eve }

  6. Formalisms – relations • Relations R = { R1, R2, … } • R = { ancestor-of-celebrity, founded-lineage } • (R) : R  {o-values} • (ancestor-of-celebrity) = {[seth, noah], …}

  7. Formalisms – typing • Everything has a type  •  = {} | constant | class | tuple | {} |  |  • Given , each type has an interpretation [](i.e., the set of things that are of that type) • [P] = (P) • [[1, 2]] = {[v1,v2] | v1  [1], v2  [2]}

  8. Formalisms – the last one! • A schema S is a triple (R,P,T) • Relations R, classes P, type mapping T : RP types(P) • An instance I is a triple (, , ) • o-value assignment , oid-assignment , oid-to-o-value partial function 

  9. An Example Schema • P = { 1st-gen, 2nd-gen } • R = { ancestor-of-celebrity, founded-lineage } • T(1st-gen) = [name: string, spouse: 1st-gen, children: {2nd-gen}] • T(2nd-gen) = [name: string, occupations: { string }] • T(ancestor-of-celebrity) = 2nd-gen • T(founded-lineage) = [anc: 2nd-gen, desc: (string or [spouse: string])]

  10. An Example Instance • (1st-gen) = { adam, eve } • (2nd-gen) = { seth, cain, abel, other } • (founded-lineage) = {cain, seth, other } • (ancestor-of-celebrity) = {[anc: seth, desc: noah], [anc: cain, desc: [spouse: “Ada”]] } • (adam) = [name: “Adam”, spouse: eve, children: {cain, abel, seth, other}] • (abel) = [name: “Abel”, occupations: {“shepherd”}] • (other) is undefined • …

  11. Posing Queries – IQL • The Identity Query Language • Rule-based, like Datalog • Formally, (S, Sin, Sout) • Sin, Sout are projections of S • Convert an instance of input schema Sin to an instance of output schema Sout • Typed

  12. Simple IQL example • Farmers who founded lineage • farmer-founders(x) 2nd-gen(x), founded-lineage(x), x = [n, o], o = “farmer”

  13. Less simple IQL example • Make a class of all the occupations S = { R, P {occupation}, T {T(occupation) = [name: string]} SinSSin from earlier SoutSSout = {{}, {occupation}, …} • What’s (S, Sin, Sout)?

  14. The query T(R1) = string T(R2) = [string, occupation] R1(o)  2nd-gen(x), x = [n,o] R2(o,z) R1(o) ;; Creates the oid z and ;; automagically sets ;; (occupation) = z R2(o,z) ;; Define z’s o-value

  15. Another example – nesting R = {R2, R3} T(R2) = [D, D] T(R3) = [D, {D}] R4(x) R2(x,y) R5(x,z) R4(x) ;; A new oid! (y) R5(x,z), R2(x,y) ;; z is set-valued R3(x, ) R5(x,z) G1 G2

  16. Why the authors like IQL • IQL can express (almost) all possible database transformations • oid invention was necessary here • IQL contains other cool query languages as sublanguages • Datalog, Datalog with negation, COL, …

  17. Type inheritance • Augment definition of schema to include type hierarchy • Schema S is a quadruple (R, P, T, ) where  is a partial order on P • Augment definition of instance to account for oids being a subclass object • (P) =  { (P’) | P’ P, P’ P }

  18. Take home messages • oids are unique identifiers for objects • oids and their use are formally defined • IQL is a language with which to query OODBs

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