1. The Challenge of Interoperability: the Grid, Semantic Web and Categories Nick Rossiter Seminar -- Northumbria University, 13th November 2002 http://computing.unn.ac.uk/staff/CGNR1/ nick.rossiter@unn.ac.uk

2. Interoperability 1 Interoperability: the ability to request and receive services between various systems and use their functionality. More than data exchange. Implies a close integration

3. Interoperability 2 Features: –exchange of messages and requests –use of each other’s functionality –client-server abilities –distribution –operate multiple systems as single unit –communication despite incompatibilities –extensibility and evolution

4. Motivations 1 Diversity of modelling techniques Distributed businesses may exercise local autonomy in platforms Data warehousing requires heterogeneous systems to be connected Data mining enables new dependencies to be derived from heterogeneous collections

5. Motivations 2 Pervasive Computing : networks supporting many diverse nodes to be driven by users specifying policy and function. –Policy: statements governing how a solution will be achieved. Statements are derived from requirements –Function: mechanism for achieving objectives. Mobile Computing: wireless networks

6. Motivations 3 E-Science –Distribution of functionality transparently across many different platforms Grid –Layered components available in network: –Computational, information and knowledge layers and probably more.

7. Motivations 4 Semantic Web –Correlating web resources –Use of Resource Description Framework (RDF) and XML –Ontologies (giving ‘meanings’ of terms)

8. Definition: Model (as it varies!) Model: a representation of policies in a structured form according to some perceived view of reality e.g. –Relational model – world is tabular –Hierarchical model – world is tree-like –Security model – world is task-based –Object model – world is based on o-o paradigm

9. Semantic Problems in Interoperability 1 People call different properties by different names People classify properties differently: –Different contexts e.g. colour is property in describing a car but a table to the paint shop. –Different normalization priorities e.g. many tables optimised for updates versus few tables optimised for searching.

10. Semantic Problems in Interoperability 2 People make use of facilities in different ways. For instance: –In SQL-92 can achieve uniqueness in tables by: Defining keys or Modifying table storage method on various properties or Defining a unique index –and in SQL-1999 we also have: object identifiers (oids) - So many legacy problems

11. Constraints and Types May differ between systems: –e.g. student ids may be held as: integers (leading zeros removed) 65275 integers (padded out with so many leading zeros) 0065275 strings (fixed length) ‘0065275’ –Ids may have checksum function or not

12. Semantic Problems in Interoperability 3 Structural problems are bad enough. But also: Functionality can be applied in many different ways: –Procedures or functions; –different module layout. Rules can be in: –Model structures, model coding, procedures or application programs.

13. Simple Problem in Interoperability 1 Two schemas in SQL-1999 AB author char(50)author_surname char(50) author_initials char(10) title varchar(300)title varchar(200) keyword set(char(30))keywd array(8) (char(30)) Note: homogeneous model -- both SQL-1999 -- but difficulties.

14. Different Standards For example -- Names: –Person(surname, first_name,..) –or Person(first_name, surname, …) –or Person(name, …) First two may easily be made equivalent but convention in third needs to be understood. Note also possibilities of A.N.Other, AN Other, A N Other.

15. Simple Problem in Interoperability 2 Homogeneous Models –the same information may be held as attribute name, relation name or a value in different databases –e.g. fines in library; could be held in a dedicated relation Fine(amount, borrowed_id) or as an attribute Loan(id, isbn, date_out, fine) or as a value Charge(1.25, ‘fine’)

16. Complex Problems in Interoperability Heterogeneous models Need to relate model constructions to one another, for example: – relate classes in object-oriented to user-defined types in object-relational All problems are magnified at this level.

17. Handling Naming, Classifying, Meta and MetaMeta Levels A Foundation for Heterogeneous Interoperability

18. Foundation Work Rather neglected in database area recently Moves by Date/Darwen/Codd to introduce ‘pure’ relational model handling objects in an orthogonal manner Open Database Group at UNN (now 8 members) looking at object-relational foundations Common objectives with work described here

19. Meta Data Meta means ‘about’ The basis of schema integration Sometimes treated as an object (MOF - Meta Object Facility) Better viewed as a relationship: –Name (data files) –Classify (database classes) –Meta (data dictionary) –MetaMeta (classify data dictionary )

20. Bottom Level -- Data Values (tuples) Student information: – Module Information: – Which students take which modules: –

21. Naming Data Values Student Name {, } Module Name {, } Modules_taken : Name {, } Name associates each value with a name

22. Relating Named Values to Types -- Classification Named application data: Schema data (types including constraints, rules) Student Name {, } Student ( id integer, name char(50), primary key id, constraint ‘id format’) Classify Classify associates each name with a type in the schema

23. Relating Types to Constructs - Data Dictionary Classified schema data (types): Constructions (e.g. table, column, function, key): Student ( id integer, name char(50), primary key id, constraint ‘id format’) {Table, Column, Function, Primary Key,...} Meta Meta associates each schema type with a construction e.g. Student to Table, id to Column, id to Primary Key

24. Relating Constructs to Abstractions Constructions (e.g. table) Abstractions (of real-world, open-ended, concepts) {Table, Column, Function, Foreign Key,..} {Aggregation, inheritance, association, …} MetaMeta MetaMeta associates each construction with an abstraction e.g. Table to Aggregation, Foreign Key to Association

25. Mappings are two-way MetaMeta Policy Meta Organize Classify Instantiate Concepts Constructs Schema Types Named Data Values Downward arrows are intension-extension pairs

26. Formalising the Architecture Requirements: –mappings within levels and across levels –bidirectional mappings –closure at top level –open-ended logic –relationships (product and coproduct) Candidate: category theory as used in mathematics as a workspace for relating different constructions

27. Choice: category theory Requirements: –mappings within levels and across levels arrows: function, functor, natural transformation –bidirectional mappings adjunctions –closure at top level four levels of arrow, closed by natural transformation –open-ended logic Heyting intuitionism –relationships (product and coproduct) Cartesian-closed categories (like 2NF): pullback and pushout

28. Categories Each level is represented by a category: –Named data values by DATA (DT) valuename –Schema types by SCHEMA (SM) –Constructions by CONSTRUCTS (CS) –Concepts by CONCEPTS (CC) Red font -- categories

29. Functors Relationships between categories at adjacent levels are given by a functor –For example: –Meta: SCHEMACONSTRUCTS –Meta is a functor Blue font -- functors

30. Levels in Functorial Terms MetaMeta CONCEPTS CONSTRUCTS S ystem Policy Model Meta InstantiateOrganize DATASCHEMA Classify Green font - composed functors: System = MetaMeta o Meta o Classify

31. Composition of Adjoint Functors Classify -- CMeta-- M MetaMeta -- A Policy -- POrganise -- O Instantiate -- I CCCSSMDT P OI AMC Composed adjunction

32. Adjunctions The adjointness between two functors is given by a 4-tuple e.g. for CCCS –  unit of adjunction measures change from initial cc to cc obtained by following P and A (1 CC AP(cc) ) –  counit of adjunction measures PA(cs)1 cs –Unit and counit give measure of creativity of arrows and preservation of style in mapping by functors. – If complete preservation of style (  =1) and no creativity (  =0) -- isomorphism. P A

33. Composed Adjunction for Four Levels Represents complex mappings across the levels of the system

34. Benefits of Approach Can represent relationships between levels, either: –abstractly with one relationship from top to bottom levels –in much more detail with all combinations of adjoints expressed.

35. Comparing one System with Another CCCSSMDT CCCS´SM´ DT´ POI P´P´ O ´I ´  , ,  are natural transformations (comparing functors) 

36. Godement Calculus Rules showing: –composition of functors and natural transformations is associative –natural transformations can be composed with each other For example: (I´O´)  = I´(O´  );  (OP) = (  O)P   = (  O) o (I´  );   =  P o (O´  )

37. Four Levels are Sufficient In category theory: –objects are identity arrows –categories are arrows from object to object –functors are arrows from category to category –natural transformations are arrows from functor to functor An arrow between natural transformations is a composition of natural transformations, not a new level

38. Analogous Levels for Interoperability

39. The Grid Use of distributed computer power Analogy with national power generation Processing performed where appropriate Requires local definitions to be used interoperably Early stage of development

40. Grid in Levels LevelIntension  Extension 1Grid Policy  Program Purpose  2Grid Organize  Program Standard  3Grid Implement  Program Spec  4Grid Operation  Program Execution

41. Databases on the Grid Nearly all data sources are not formal database files yet (Paul Watson, 2002) Data is in operating system files perhaps readable only by particular programs which understand the format So level achieved is really only 3, that is program specification (no organization or policy).

42. Semantic Web Levels: –data values to be marked up with tags –XML document -- data with XML tags –DTD -- document structure defining tags –RDF -- triples components are typically URIs, could also be literals, collections of URIs or another RDF –Semantic Web -- semantic interoperability between data sources using agents to explore RDFs and ontologies

43. Semantic Web as Formal Levels

44. Semantic Web is rather Flat Only handles two bottom levels of architecture Aims to achieve comparison of mappings (  ) through: –an agent exploring RDFs –each RDF relates one URI to another URI in the context of a predicate –ontologies are used to explain and synchronise meanings of terms An AI approach rather than a data-driven one

45. Discussion 1 Category theory shows that: –four levels are ideal for interoperability –more than four yields no benefits –less than four gives only local interoperability Categorical approach provides: –an architecture for universal interoperability –a calculus (Godement) for composing mappings at any level –adjunctions for evaluating two-way mappings

46. Discussion 2 In industry: –Approach seems to be getting flatter –In MOF (Meta-Object Facility) which is a four-level system (top-level ‘hard-wired’), drive to bypass top levels –IRDS (Information Resource Dictionary System) – four levels but one-way mapping – not used as much as expected –ISO though are trying a four-level approach for mapping modelling languages

47. Discussion 3 Lack of adequate foundations may explain some of the reticence Also some suppliers perhaps think that market dominance is the answer, making interoperability irrelevant. But legacies remain! Categorical framework provides a coherent basis for taking this area forward. Even if the framework is translated into a more familiar notation.

48. References 1 MOF –Bezivin, J, From Object Composition to Model Transformation with the MDA, 3rd International Conference on Enterprise Information Systems (ICEIS), Setubal, invited paper (2001). Plus OMG web pages. IRDS –Gradwell, D J L, The Arrival of IRDS Standards, 8th BNCOD, York 1990, Pitman 196-209 (1990). GRID –Watson, P, Databases and the Grid, Computing Science Technical Report no.755, University of Newcastle upon Tyne (2002), (16pp). SEMANTIC WEB: W3C web pages Our work (available from NR’s home page) –Heather, M A, & Rossiter, B N, The Anticipatory and Systemic Adjointness of E- Science Computation on the Grid, Computing Anticipatory Systems, Proceedings CASYS`01, Liège, Dubois, D M, (ed.), AIP Conference Proceedings 627 565-574 (2002). –Rossiter, B N, Heather, M A, & Nelson, D A, A Universal Technique for Relating Heterogeneous Data Models, 3rd International Conference on Enterprise Information Systems (ICEIS), Setúbal, I 96-103 (2001). –Heather, M A, & Rossiter, B N, Constructing Standards for Cross-Platform Operation, Software Quality Journal, 7(2) 131-140 (1998).

49. References 2 ISO modelling: –Study Report on the Feasibility of Mapping Modelling Languages for Analysis and Design Models.ISO/IEC JTC1/SC7 N2112, 1999/04/19, http://www.info.uqam.ca/Labo\_Recherche/Lrgl/sc7/N2101-N2150/07n2112.pdf (1999). Category Theory and Computing Science: –Barr, M, & Wells, C, Category Theory for Computing Science, Prentice-Hall (1990). –Mac Lane, S, Categories for the Working Mathematician, Springer, 2 nd ed (1998). Category Theory and Information Systems: some other workers –Zinovy Diskin (USA, formerly Latvia) –Boris Cadish (Latvia) –Robert Rosebrugh (Canada) –Michael Johnson (Australia) –Christopher Dampney (Australia) –Michael Heather (Northumbria) –David Nelson (Sunderland) –Arthur ter Hofstede (Australia, formerly Holland) Many other workers on category theory and program semantics