Transcript No Slide Title

Lecture 4: Handling
Heterogeneity with Information
Resource Dictionary Systems
Nick Rossiter, Computing Science,
Newcastle University, England
[email protected]
http://www.cs.ncl.ac.uk/people/b.n.rossiter/
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
• 10027
1990
• 10032
• 10728
1993
1993
• 9075
1992
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 -- 195, 05/30/1967,
30/05/1967
Relating Extension to Intension
level
• Application data
extension -direct
addressing
example
Supplier(1,’Smith’)
• Schema data
Supplier (supp_no, name)
intension - addressing
by name
level pair:
Relating Intension to Constructs
• Schema data
Supplier (supp_no,
name)
intension - addressing
by name
• Meta data
Table(supplier)
data dictionary - addressing
by concepts, constructs.
Relating Constructs to
Abstractions
• Meta data
Table(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: <intension_entry, construction>
e.g. <student<id,name>, table>
• MetaMeta is: mapping from construct
available to abstraction as 2-tuple:
<construction, abstraction>
e.g. <table, aggregation>
Examples of Levels and Levelpairs: Intension/Extension
• Extension (APP): Student<1234, ‘John
James’, ‘15 Montford Road’>
• Intension (IRD): Student<id, name,
address>
• APP
IRD by:
Name: Student<1234, ‘John James’, ‘15
Montford Road’>
Student<id, name, address>
Examples of Levels and Levelpairs: Constructs/Intension
• Intension (IRD): Student<id, name,
address>
• Constructs (IRDD): Table
• IRD
IRDD by
Meta: Student<id, name, address>
Table
Examples of Levels and Levelpairs: Abstractions/Constructs
• Constructs (IRDD): Table
• Abstractions (IRDDS): Aggregation
• IRDD IRDDS by
MetaMeta: Table
Aggregation
Interpretation of IRDS in
Schematic form
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•
concepts
MetaMeta
Meta
Name
extension
management
Organize
Information Resource
Dictionary (IRD)
intension
mission
Policy
Information Resource
Dictionary Definition
(IRDD)
constructs
•
•
Information Resource
Dictionary Definition
Schema (IRDDS)
Information Resource
Data (APP)
enterprise
Data
information
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 : APP
IRDDS
• 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
• IRDDS
System
IRDD
Policy
Model
Meta
Data
• APP
Organize
IRD
Name
Dates Revisited
Concept (IRDDS)
date
Policy
Constructs (IRDD)
Organize
Format (IRD)
MetaMeta
giga years
Universe
g.f x 109
days,months,years (years
AD)
American
Euroopean
days, months, years (years
Muslim)
Muslim
mm/dd/yyyy dd/mm/yyyy dd/mm/yyyy
Data
Values
(APP)
Meta
Name
4.2
05/19/2000
19/05/2000
14/03/1350
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: B
A
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_US
Model_Eur
Further Reading
• Information technology - Information Resource Dictionary
System (IRDS) framework, Standard ISO/IEC 10027
(1990); 10728 (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,
218-229 (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.