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Abstract Specification Theory Andrzej Tarlecki Institute of Informatics, Warsaw University and Institute of Computer Science, Polish Academy of Sciences Warsaw, Poland office: 4750 phone: (48)(22)(55)44475 tarlecki@mimuw.edu.pl


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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.

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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.

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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

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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.

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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.

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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.

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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/.

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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!

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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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