Lecture 4: Handling Heterogeneity with Information Resource Dictionary Systems Nick Rossiter, Computing Science, Newcastle University, England

Introduction Looking at multi-level architecture for information systems Need to handle higher levels than intension Take object work two levels higher Example with dates Composition of functors and natural transformations

Approach Principles of Information Resource Dictionary System (IRDS) Benefits in General Assistance for Cross-Platform Operation Search for Sound Theoretical Basis

IRDS/Reference Model Based on ISO/IEC Standards Information Res. Dict. Sys.(IRDS) Reference Model IRDS - System Interfaces; SQL

Extract IRDS Standard Framework

Outline IRDS Introduces concept of meta-meta data Four-level approach

Example of Dates IRDDS concepts is some measure of time IRDD is constructs available -- light years, years since various events, months, days, carbon dates, etc IRD is formats available -- yyyy, mm/dd/yyyy, dd/mm/yyyy, etc APP is values , 05/30/1967, 30/05/1967

Relating Extension to Intension levelexample Application data Supplier(1,’Smith’) extension -direct addressing Schema dataSupplier (supp_no, name) intension - addressing by name level pair:

Relating Intension to Constructs Schema dataSupplier (supp_no, name) intension - addressing by name Meta dataTable(supplier) data dictionary - addressing by concepts, constructs.

Relating Constructs to Abstractions Meta dataTable(Supplier) data dictionary - addressing by concepts, constructs. Meta meta data Aggregation(Table) real-world abstractions - addressing by abstractions

Level-pairs are the Critical Dictionary Entries Meta is: mapping from schema names (intension) to constructs available as 2-tuple: e.g., table> MetaMeta is: mapping from construct available to abstraction as 2-tuple: e.g.

Examples of Levels and Level- pairs: Intension/Extension Extension (APP): Student Intension (IRD): Student APP IRD by: Name: Student Student

Examples of Levels and Level- pairs: Constructs/Intension Intension (IRD): Student Constructs (IRDD): Table IRD IRDD by Meta: Student Table

Examples of Levels and Level- pairs: Abstractions/Constructs Constructs (IRDD): Table Abstractions (IRDDS): Aggregation IRDD IRDDS by MetaMeta: Table Aggregation

Interpretation of IRDS in Schematic form concepts mission MetaMeta Policy constructs management Meta Organize intension enterprise Name Data extension information Information Resource Dictionary Definition Schema (IRDDS) Information Resource Dictionary Definition (IRDD) Information Resource Dictionary (IRD) Information Resource Data (APP)

Overall Mappings Can write: System = MetaMeta o Meta o Name (APP) to represent composition. System(APP) = IRDDS Also the dual: Model = Data o Organize o Policy

IRDS Enables Heterogeneous Systems to be Related Only one IRDDS in principle but extensible IRDDS covers all paradigms For relational database, can use mapping: System : APPIRDDS Comparison of System for each paradigm enables in principle:  completely different approaches to be related  heterogeneous systems to be run in integrated fashion

Formalization of IRDS Approach Quality enhanced by formalization Can know more confidently the limits and behaviour of a system Which formalism is best-suited?

Category Theory? Need relations to represent level-pairs Multi-level construction (higher-order) Category theory seems appropriate: - categories for basic structures - functors relate categories - natural transformations relate functors

IRDS Levels in Functorial Terms MetaMeta IRDDSIRDD S ystem Policy Model Meta DataOrganize APPIRD Name

Dates Revisited Concept (IRDDS)date Policy MetaMeta Constructs (IRDD)giga yearsdays,months,years (years days, months, years (years AD) Muslim) Organize Universe AmericanEuroopean Muslim Meta Format (IRD)g.f x 10 9 mm/dd/yyyydd/mm/yyyydd/mm/yyyy Data Name Values4.205/19/200019/05/200014/03/1350 (APP)

Connections between levels are Adjunctions For two categories A and B, an adjunction between them involves two functors: –a free functor F: A B adding structure to A –an underlying functor G: BA forgetting structure in B Organize: IRDD IRD and Meta: IRD IRDD are a pair of adjunctions

Date Comparison as Natural Transformation Take composition of adjuntions: Model_US: date 05/19/00 Model_Eur: date 19/05/00 Then have natural transformation: Amer_Eur_Date_Compare: Model_USModel_Eur

Further Reading Information technology - Information Resource Dictionary System (IRDS) framework, Standard ISO/IEC (1990); (1993). Constructing Standards for Cross-Platform Operation, Heather, M A, & Rossiter, B N, Constructing Standards for Cross-Platform Operation, Software Quality Management VI, British Computer Society, Amsterdam, April 1998, (1998).

Concluding Remarks Lecture 1 -- Interoperability -- showed problems of handling heterogeneous data Lecture 2 -- Introduction to Category Theory -- described categories as a basis for thinking about information systems Lecture 3 -- Objects as Categories -- described how the intension/extension could be represented by categories, functors and natural transformations

Finale Lecture 4 -- IRDS -- showed how all four levels of an information system can be described formally with categories, perhaps giving a better understanding of problems.