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Formal Methods

Jos Baeten, TU/e

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Formal methods

Is the mathematics of software engineering.

Modeling, calculation.

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Formal Methods

Research in Formal Methods is a systematic and scientific study of issues in computer science, based on solid mathematical principles.

Formal Methods apply to systems and constructions used in computer science. These constructions are described exactly in a formal syntax and are supplied with a formal semantics whenever appropriate.

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Formal Methods increase understanding of systems, increase clarity of description and help solve problems and remove errors. Use of Formal Methods increases dependability and usability of constructions and systems in computer science.

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Why Formal Methods?

Software (+ hardware) Engineering is craft, not science.

- Complex - No margin of error - Local action has global consequences - Discrete - (no intra-, extrapolation, some statistics possible)

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Process

Quality control

Product

Quality assurance safety + liveness

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Formal Methods

Specification - descriptive Verification - analysis

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Specification

Communication between designers.

Control and data.

“What” over “how”.

Reactive, parallel, distributed systems.

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Verification

Not pde but discrete math calculation.

Logic and deduction.

All behaviours. Parameters.

Hierarchy of abstraction.

Model needs to be validated against reality.

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Issues and choices

Selection: - Level of formality: 1. Math. argument 2. Formal spec. 3. Verif. system - Part of system, selected components - Selected properties - Part of lifecycle - Level of abstraction

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Specification: varieties

• Model-oriented: operational. Z.

• Property-oriented: logical. CTL/LTL.

• Concurrency. Process algebra.

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Verification: varieties.

• Consistency analysis and type checking • Validation: animation, challenges.

• Predicting behaviour and verifying refinement – State space exploration, model checking, language inclusion – Theorem proving, proof checking

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Certification of critical systems

Can never achieve failure rate of 10 -9 .

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User req. def.

Docs Verif.

Sw. req. def.

Arch.

design Detailed design Code Acceptance tests System tests Integration tests Unit tests

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Alexander theory EREA, PVS ADL RPA Docs Verif.

SDL, MSC, Spin, PVS, Z Invariants, PVS Spin, PVS, TTCN, TorX

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Advantages of FM

Precision engineering Complexity engineering Correctness engineering Automation engineering

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History

1956 Noam Chomsky models language 1957 John Backus defines Fortran syntax 1958 Haskel Curry and Robert Feys describe propositions-as-types analogy 1960 Peter Naur applies BNF to ALGOL60 1968 Adriaan van Wijngaarden defines ALGOL68, experiments with  , 2 l. grammar 1968 Donald Knuth invents attribute grammars

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History

1968 Dana Scott denotational sem. for  1969 Tony Hoare axiomatic semantics 1970 N.G. de Bruijn Automath 1972 IBM Vienna: FM for PL/I design 1974 Goguen Thatcher init. alg. sem. data types 1977 Joseph Stoy book denotational sem.

1978 Dines Bjørner, Cliff Jones VDM 1979 Philips Brussels CHILL design

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History

1980 Robin Milner CCS 1980 Jean-Raymond Abrial Z 1980-1990 Gerard Holzmann SPIN 1983 Jan Bergstra ACP 1985 Ed Brinksma LOTOS 1985-1995 ESPRIT: CIP, OBJ, PLUSS, ASL, Larch, SDL, ExSpect, ADJ, ASF, SDF, PSF, PVS, COLD, SPRINT, ERAE, CLEAR, …

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History

1993 VDM Europe becomes FME 1997 Intel establishes FM group after Pentium 1999 FM World Commercial firms offering FM (Verum, FDR) FMICS, IFM

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Ingredients

Syntax Logic Proof Data types Modularisation Type system Object orientation States Transitions Execution Communication Abstraction Timing Hybrid systems

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Semantics

Denotational De Bakker, Rozenberg Operational Axiomatic - assertional Kuiper, Jonkers, De Boer

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Varieties

Logic: thm proving PVS, COQ Hooman, Poll, Barendregt, Hesselink Temporele logica: CTL, LTL: Kuiper Game theory: v.d. Herik, De Bruin Categories, co-algebras: Rutten, Jacobs Multi-agent systems: Renardel

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Varieties

Equational:  -calculus Barendregt term rewriting Klop, v. Oostrom, Zantema type theory: Barendregt, Swierstra ASF+SDF: Klint Program derivation: Meertens Process algebra: Bergstra, Fokkink, Baeten, Groote, Brinksma

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Varieties

Operational: sequential: Z, VDM, Larch SOS Fokkink, Reniers I/O automata Vaandrager Petri nets Van Hee, Van der Aalst Model checking Larsen Katoen Graphs Rozenberg Rensink  Rooda TorX Tretmans

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Varieties

Visual: MSC, Petri nets

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Applications

Software Engineering, in particular components, coordination Embedded Systems (hybrid systems) Business Processes Biological Processes Security Web services & grid computing Agents, games, quantum & relativistic comput.