Set I/O Architectures
Data diversity and storage access are dependent on how data is
physically represented on a computer.
Though data processing results are independent of computer representations,
the performance of processing operations vary dramatically.
on physical representations and organization of data.
An ideal storage management environment would support
many varieties of physical data representations.
Set I/O architectures are very different than
record I/O architectures.
Sets are mathematical objects.
Records are physical objects,
are formally defined abstract definitions that are independent
of any physical representation.
are arbitrarily defined concrete definitions that are dependent on
currently existing physical representations.
Systems processing data as mathematical objects
rely on the properties of the abstract definitions,
not on the current state of the physical representations.
requires knowledge of how data is physically represented in storage.
requires knowledge of how data is mathematically represented in storage.
Set I/O implementations were first introduced in
Though set accessing systems have been commercially available since
the performance advantages of set accessing I/O over record accessing I/O are little known.
The key I/O performance difference is that record accessing I/O
depends on physical representations of storage data,
while set accessing I/O depends on mathematical representations of storage data.
Storage independent representation of data is key to I/O performance.
Set I/O architectures use a formal foundation
for a mathematical representation
and manipulation of system data.
Changes to the physical representation
and organization of data can be made at any
time, as long as mathematical integrity is
In 1965 ARPA initiated research to
explore the feasibility of
a mathematical foundation for representing
data on a computer.[IFIP]
contained in data is independent of any representation,
and since mathematically well-defined objects
and operations on such objects
are also independent of representations,
ARPA directed the research to
provide applications with
machine-independent access to stored
All the properties of Classical set theory,
except one, fit the criteria for modeling computer data
as mathematical objects.
ARPA research focused on
extending Classical set theory to include the property of
giving birth to the concept of
Record I/O architectures specify physical
representations and organizations
of data that reflect specific
application processing requirements.
Set I/O architectures insulate applications from direct access
to storage by use of set operations.
Record I/O architectures bind applications to
storage by use of index structures.
Set I/O implementations have been commercially active since
Early implementations only supported data represented as labeled arrays.
XML documents became represented as extended sets in
By 2011 extended set theory
provided a mathematical foundation
capable of modeling any computer representation of
Set I/O architectures provide applications global access to data,
while local platforms focus on performance issues.
Developers can use
set I/O for universal data access
while allowing local implementations freedom to provide
Data Access: Data access is a process.
Mathematically well-defined process descriptions
seldom exist to assist system developers.
Data access is an exception.
All data access on a digital computer can be
in terms of XST.
is an assertion about the relationship
of certain items of interest.
This assertion (data content) can be faithfully
represented as a set in XST,
is a user-friendly representation of some
specific data content,
All application data representations can be faithfully
represented as a set in XST.
is a machine-friendly representation of
an application data representation.
All storage data representations can be faithfully
represented as a set in XST.
is a process of exchanging data content
between application data representations
and storage representations.
Given the proper suite of XSP operations,
any application can access any data,
anywhere at any time.
Data as XSP Sets:
Twelve RDM tables
R1 - R12 expressed by a single Labeled
set Ri, RDM.
A very simple XML-structure expressed as a labeled
Three extended relations expressed as labeled
Two complex extended relations expressed as labeled
The fundamental result of ARPA's research
exploring the feasibility of a
machine-independent data model was the discovery that
data could be represented as a mathematical object.
A formal modeling notation was developed to
represent and manipulate all computer data as
The evolution of this notation gave rise to XSP Technology.
The ability to represent and manipulate data as XSP sets is what
distinguishes Set I/O implementations from traditional
For those interested in the formal description of
XST operations, a summary is presented
For those interested in exploring the
formal modeling of systems behavior,
presents an XST representation of all 29 processes
available on a digital computer.
Data That Can't Be Accessed, Can't Be Processed.
If Data Can Be Accessed, It Has A Set Identity.
If Data Has A Set Identity, It Can Be Processed By Set Operations.
If Data Can Be Processed By Set Operations, Processes Are Limited Only By Imagination.
Though all XST operations are non-proprietary,
software and hardware
implementations of XST operations may be highly-proprietary.
The only criteria for a XST operation
implementation is that it has a well-defined XST definition.
All the necessary mathematical material for defining
any XST operation
is available below.
Feasibility of a Set-theoretic Data Structure:
IFIPS - 1968
Description of a Set-theoretic Data Structure:
AFIPS - 1968
CONCOMP Project Appendix D: Description of a Set-Theoretic Data Structure - 1970
Extended Set Theory:
A General Model For Very Large, Distributed, Backend Information Systems.
1984 VLDB Panel: Inexpensive Large Capacity Storage Will Revolutionize
The Design Of Database Management Systems.
XSP TECHNOLOGY: Theory & Practice Formal Modeling & Practical Implementation of XML & RDM Systems
The RDM works in spite of set theory, not because of it.
XML-Structures and operations on these structures are set-theoretically sound under XST.
In this paper the formal foundations of RDM and XML systems are examined in the light of XST to provide practical relevance of XSP Technology to the field of software systems development.
MICRO-STDS RDBMS 1971-1998
(First commercially available Set I/O architecture.)
Lawrence Livermore Lab.:
Set Theoretic Data Structures (STDS): a tutorial
Technical Report, 1977.
XSP: An Integration Technology for Systems Development and Evolution - 2001
Why Not Sets? All computer processing is set-theoretic
in nature. - 2010
A multiple storage XOP commutative diagram supporting:
For all x in A, ri(hi(gi(x))) = f(x).
Adaptive Data Restructuring Functions Death Of A Dream.
Pebble Piles & Index Structures
Piles of pebbles or parchment with numbers?
Data Access for User Productivity
Content-Container Data Access Strategies Content for Functionality - Containers for Performance - 2016
Since data represented for processing is not always ideal
for preservation, and since data represented for
preservation is not always ideal for processing,
accessing application-friendly data
from storage-friendly data
poses a genuine challenge.
Set Processing vs. Record Processing Performance:
Dynamic Data Restructuring vs. Prestructured Data Storage (1 page summary)
Record processing systems and set processing systems are very different.
This paper attempts to clarify the major differences and demonstrate
the performance advantages of set processing.
Sets, Data Models and Data Independence - 2010
XSP: Extended Set Processing:
Mathematically Managing Data Representations (1 page summary)
This paper presents a high level overview of why a mathematical model of
data representations is necessary, and how an extended set processing
model accomplishes the task.
---------- XST --------
Blass, A., Childs, D L:
Axioms and Models for an Extended Set Theory - 2011
Extended Set Theory: A Summary A clarification of extended set notation. - 2015
Functions As Set Behavior Essential Concepts: Conceptual &
Formal modeling foundations.
Processes, Functions, Applications & Composition
♦ Lambda application & category composition of processes.
XST Definitions, Operations, & Properties -Tuples, Graphs, Functions -
♦ CST operations subsumed under XST operations.
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INTEGRATED INFORMATION SYSTEMS
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