Abstract Specification Theory Andrzej Tarlecki Institute of - - PowerPoint PPT Presentation

Abstract Specification Theory

Andrzej Tarlecki

Institute of Informatics, Warsaw University

and Institute of Computer Science, Polish Academy of Sciences

Warsaw, Poland

• ffice: 4750

tarlecki@mimuw.edu.pl phone: (48)(22)(55)44475 http://www.mimuw.edu.pl/~tarlecki This course: http://www.mimuw.edu.pl/~tarlecki/teaching/ast/

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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Long-term goal

A formal basis for systematic development

• f correct programs

from requirements specifications by verified refinement steps.

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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Overall plan

• Underlying logical framework: basic algebraic framework; first-order logic;

institutions plus: category theory

• Specifications: basic and structured specifications; proof systems for specifications
• Program development: simple refinements; constructor refinements; local

constructions in global refinement steps; architectural specifications

• Observational approach: observational/behavioural interpretation of

specifications, refinements, and architectural specifications; local correctness and stability

• Heterogeneous specifications: maps between institutions; focused heterogeneous

specifications; distributed heterogeneous specifications

• All propped up by examples? Conclusions?

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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My proposal

Let’s read together through: D.T. Sannella, A. Tarlecki Foundations of Algebraic Specifications and Formal Program Development Springer, forthcoming.

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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Contents

• Chap. 0: Introduction
• Chap. 1: Universal algebra
• Chap. 2: Simple equational specifications
• Chap. 3: Category theory
• Chap. 4: Working within an arbitrary logical system
• Chap. 5: Structured specifications
• Chap. 6: Parameterisation
• Chap. 7: Formal program development
• Chap. 8: Behavioural specifications
• Chap. 9: Proofs for specifications
• Chap. 10: Working with multiple logical systems

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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Literature

A rudimentary knowledge of basic concepts of universal algebra and category theory is expected. Plenty of standard textbooks But this will be roughly based on:

• D.T. Sannella, A. Tarlecki. Foundations of Algebraic Specifications and Formal

Program Development. Springer, forthcoming. − Chap. 1: Universal algebra − Chap. 2: Simple equational specifications − Chap. 3: Category theory

• D. Sannella, A. Tarlecki. Algebraic preliminaries. In: Algebraic Foundations of

System Specification, E. Astesiano, H.-J. Kreowski, B. Krieg-Br¨ uckner, eds., 13–30, Springer Verlag 1999.

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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The lectures will loosely follow the ideas presented in the following papers, which therefore should make a good background reading:

• A. Tarlecki. Abstract specification theory: an overview. In: Models, Algebras,

and Logics of Engineering Software, M. Broy, M. Pizka, eds., NATO Science Series - Computer and Systems Sciences, Vol. 191, 43–79, IOS Press, 2003.

• D. Sannella, A. Tarlecki. Essential concepts of algebraic specification and

program development. Formal Aspects of Computing 9(1997) 229–269.

• M. Bidoit, D. Sannella, A. Tarlecki. Architectural specifications in CASL. Formal

Aspects of Computing, 13 (2002), 252–273.

• M. Bidoit, D. Sannella, A. Tarlecki. Global development via local observational

construction steps. Proc. MFCS’02, Springer LNCS 2420, 1–24, Springer-Verlag 2002.

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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CoFI pages, http://www.cofi.info/, provide all the material on Casl and relate

• work. The following are not to be missed:
• M. Bidoit, P.D. Mosses. Casl User Manual. Springer LNCS 2900 (IFIP Series),
• 2004. With chapters by T. Mossakowski, D. Sannella, and A. Tarlecki.
• CoFI (The Common Framework Initiative). Casl Reference Manual. Springer

LNCS 2960 (IFIP Series), 2004.

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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Institutions have been introduced in:

• J. Goguen, R. Burstall. Institutions: abstract model theory for specification and
• programming. Journal of the Assoc. for Computing Machinery 39(1):95–146,

1992. The following book chapter provides an introduction to, motivation for, and some concepts and results built around this notion:

• A. Tarlecki. Institutions: an abstract framework for formal specifications. In:

Algebraic Foundations of System Specification, E. Astesiano, H.-J. Kreowski,

• B. Krieg-Br¨

uckner, eds., 105–130, Springer-Verlag 1999. See also http://www.mimuw.edu.pl/~tarlecki/marktoberdorf/.

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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Universal algebra and category theory: basic ideas, notions and some results

• Algebras, homomorphisms, equations: basic definitions and results
• Categories; examples and simple cateogrical definitions
• Limits and colimits
• Functors and natural transformations
• Adjunctions

BUT: Tell me what you want to learn!

Andrzej Tarlecki: Abstract Specificiation Theory, 2008

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One motivation

Software systems (modules, programs, databases. . . ): sets of data with operations on them

• Disregarding: code, efficiency, robustness, reliability, . . .
• Focusing on: CORRECTNESS

Universal algebra from rough analogy

module interface ❀ signature module ❀ algebra module specification ❀ class of algebras

Category theory

A language to further abstract away from the standard notions of univer- sal algebra, to deal with their numer-

• us variants needed in foundations of

computer science.

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