Table Of ContentLogic and Algebra of Specification
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Series F: Computer and Systems Sciences Vol. 94
Logic and Algebra of Specification
Edited by
Friedrich L. Bauer
Wilfried Brauer
Institut fOr Informatik, Technische Universitat MOnchen
Arcisstr. 21,0-80333 MOnchen, Germany
Helmut Schwichtenberg
Mathematisches Institut
Ludwig-Maximilians-Universitat MOnchen
Theresienstr. 39,0-80333 MOnchen, Germany
Springer-Verlag Berlin Heidelberg GmbH
Proceedings of the NATO Advanced Study Institute on Logic and Algebra of
Specification, held in Marktoberdorf, Germany, July 23-August 4, 1991
CR Subject Classification (1991): 8.6, C.2, 0.1-3, F.3-4, 1.1-2
ISBN 978-3-642-63448-2 ISBN 978-3-642-58041-3 (eBook)
DOI 10.1007/978-3-642-58041-3
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© Springer-Verlag Berlin Heidelberg 1993
Originally published by Springer-Verlag Berlin Heidelberg New York in 1993
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Preface
The Marktoberdorf Summer School 1991 was held under the title Logic and Algebra of
Specification. It was the 11th of a series of Advanced Study Institutes under the spon
sorship of the NATO Scientific Affairs Division held at Marktoberdorf, and the second in
the new "blue" series with special emphasis on logic in Computer Science. This series is
intended to alternate in future with the traditional "red" series, whose subjects oscillate
more or less around Programming Methodology.
For some years, specification of software and hardware systems has not only been
influenced by algebraic methods (which has a long tradition) but also by new developments
in logic. These new developments in logic are partly based on the use of algorithmic
techniques in deduction and proving methods, but are also due to new theoretical advances,
to a great extent stimulated by computer science, which lead to new types of logics, new
logical calculi. The new techniques, methods and tools from logic combined with algebra
based ones offer very powerful and useful tools for the computer scientist, which already
in a near future might become practical even for industrial use. In particular for the
development of software for concurrent and distributed systems more powerful specification
tools are needed.
The Summer School 1991 aimed at giving a foundation for a combination of logic and
algebra for the purposes of specification under several aspects:
(1) Specification and Automated Deduction,
(2) Proving Techniques,
(3) Concurrency and Logic,
(4) Abstract Data Types and Operational Semantics,
(5) Constructive Methods.
We were lucky that a team of top level researchers had agreed to lecture on their most
recent research, and that we had a group of excellent participants selected from more
than twice as many applicants. This resulted in a stimulating atmosphere encouraging
a fruitful exchange of ideas, both by lively discussions and by numerous more or less
formal gatherings in smaller groups. An essential ingredient of such successful days was
the help of the experienced scientific staff from Munich and - last not least - the local
Marktoberdorf crew. Our thanks go to all of them.
Munich, April 1992 F.L. Bauer
W. Brauer
H. Schwichtenberg
Table of Contents
Distributed Action Systems .................................................... 1
Wilfried Brauer
Lectures on: Classical Proofs as Programs 31
Robert L. Constable
Linear Logic: A Survey 63
Jean-Yves Girard
Some Proof-Theoretic Aspects of Logic Programming... .... . ........ ....... . 113
Gerhard Jager
The Safety-Progress Classification ........................................... 143
Edward Chang, Zohar Manna, Amir Pnueli
The Polyadic 7r-Calculus: A Tutorial 203
Robin Milner
An Introduction to Action Semantics 247
Peter D. Mosses
Minimal Logic for Computable Functions .................................... 289
H. Schwichtenberg
Infinite Synchronous Concurrent Algorithms
The Algebraic Specification and Verification of a Hardware Stack 321
B. McConnell, J. V. Tucker
Four Lectures on Primitive Recursion.... ....... . ....... ....... .. . ..... .... .. 377
Stanley S. Wainer
Structured Specifications: Syntax, Semantics and Proof Calculus... . . .. ..... . 411
Martin Wirsing
Distributed Action Systems
From Sequential to Nonsequential Systems
or
From Transition Systems to Generalized Petri Nets
Wilfried Brauer, Technische Universitiit Miinchen
Abstract. Traditionally theoretical informatics is based on the notion of a sequential
machine for the stepwise computation of a function as a mechanization/abstraction of
the activity of a human calculator. Due to developments in hardware, applications and
theoretical informatics it is useful and possible to take a more general basis and consider
a group of interacting humans as a paradigm for basic notions in theoretical informatics.
Such a group can be constituted by the need of several people to have organized
access to common limited resources (this is the viewpoint taken in operating systems
theory since a long time) or a group brings together people who want to achieve common
goals by cooperation (this view was much used in artificial intelligence).
There are two basic ways of organizing the activities in the group: by central con
trol based on hierarchy and force (this is the traditional approach in informatics) or by
cooperative coordination using communication mechanisms for reaching consensus.
With these ideas in mind we can look at informatics in a new way, and we may
recognize, that we need many new concepts but also that quite a number of known
(traditional) concepts can well be interpreted in the new way and exhibit interesting
properties.
In the following we will see how the classical theory of (finite and pushdown) automata
and of (regular and context-free) formal languages and grammars can be built up from
the point of view of specification of (structure and semantics) of distributed systems of
actions (instead of considering them only from the viewpoint of a compiler writer). In the
second part we develop this idea further and introduce Petri nets as a basic general model
for distributed action systems and generalize them by including some sort of recursion.
Structure of the Paper
1. Introduction
2. Sequential Distributed Action Systems (SDASs)
3. Sequentially Cooperating SDASs
4. Nonsequential Distributed Action Systems (NDASs)
5. Cooperating NDASs
6. Concluding Remarks
7. References
2
1 Introduction:
Three Steps of Informatics Development
Three Phases of Informatics Development
Seen from a general, global and somewhat philosophical point of view the development of
informatics consists of 3 phases each of which I will briefly characterize by a paradigm, a
keyword and a sketchy description of the basic aspects of the use of computers. For more
details see [Bra91]
1.1 First Phase: The Age of Pioneers
Middle of 1930s to early 1960s
Turing-Zuse paradigm: The computing assistant
Keyword: Data processing
Computer simulates a single person in his activity of computing
Computer use: (formula evaluation)
"Empty" computer
Input: 1. Program (machine code)
2. Data
Activity: computation of function values
Output: Data
1.2 Second Phase: The Creation of Informatics
1960s - 1980s
Extended Turing-Zuse paradigm: A hierarchy of information processing specialists
Keyword: Information processing
Computer (system) - as part of an organisation - simulates a hierarchy of information
processors
Computer use: (information system)
"Non-empty" computer (contains operating system, compilers)
Input: 1. Program in a high-level language
2. Data
Activity: (different interpretations of inputs)
Computation of a function
1. program --+ program
2. data --+ data
Output: 1. Programs
2. Data
3
1.3 Third Phase: Informatics as a Fundamental Discipline
1990s -
The new paradigm [Petri, Dijkstra, Hewitt, Milner]:
A group of (autonomous, intelligent) individuals communicating with each other and
with the environment
Keyword: Knowledge processing
Computer use: Distributed, concurrent, interactive system (composed of men,
computers, machines, ... ) in communication with other systems
[concurrency ~ independence restricted by organisational means because of
• competition (traditional informatics)
• cooperation (AI)]
Computer contains:
• structured collection of data
• procedures for interpretation and processing of data
• rules for communication behaviour
Computer activity:
• reaction to queries
• control and manipulation
• learning
1.4 Some Implications
Computer: Not simply a tool, also medium for communication (Petri), partner for problem
solving (AI)
Design perspective for a system:
Which role will humans and computers have to play in the system?
Product-oriented versus process-oriented perspective (Ch. Floyd)
Control structure for systems:
Replace centralized control (force) and hierarchical organisation (subordination)
by
cooperation and self-organisation with decentralized (distributed) decision making by
means of communication.
Acceptance of systems can be enhanced
A wider, more comprehensive notion of informatics
Changes in informatics education necessary
• at school
4
• at university
• for adults
Teach system design and construction instead of programming only.
2 Sequential Distributed Action Systems (SDASs)
Our general metaphor for the kind of system we are dealing with in this chapter is a team
of actors working sequentially on a joint job - or a network of machines or of computers
through which objects are sent and manipulated sequentially. Not each of the actors need
to be involved in each sequential action sequence performed by the system.
The systems to be considered will be described in the following way. Firstly the
(static) structure is defined in a global way, then operations for constructing systems in a
modular way are given. Next the (dynamic) behaviour is described; firstly from the point
of view of possible observations (of an existing system) in terms of the actions performed,
then from the point of view of the specification (of the behaviour of a system yet to be
considered) in terms of the actions to be performed. For the specification we usually have
two options: to describe what is allowed or to state what is forbidden. Further topics are
related to the comparison of the behaviours and to the control of systems.
2.1 Plain SDASs
(a) Structure
There are different actors at different positions:
If an actor y can act only after an actor x has completed its work x and y are in the
precedence relation (x, y)
Repetitions are allowed
Certain actors may start the system's activities
others may stop them
