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Formal Methods
Jos Baeten, TU/e
12Formal methods
Is the mathematics of software engineering.
Modeling, calculation.
12Formal 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.
Why Formal Methods?
12Why 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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Quality control
Process
Product
Quality assurance
safety + liveness
12Formal Methods
Specification - descriptive
Verification - analysis
12Specification
Communication between designers.
Control and data.
“What” over “how”.
Reactive, parallel, distributed systems.
12Verification
Not pde but discrete math calculation.
Logic and deduction.
All behaviours. Parameters.
Hierarchy of abstraction.
Model needs to be validated against reality.
12Issues 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
12Specification: varieties
• Model-oriented: operational. Z.
• Property-oriented: logical. CTL/LTL.
• Concurrency. Process algebra.
12Verification: 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
12Certification of critical systems
Can never achieve failure rate of 10-9.
12User
req. def.
Sw. req. def.
Arch.design
Detailed design
Code
Acceptance tests
System tests
Integration tests
Unit testsDocs
Verif.
12Alexander
theory
EREA,PVS
ADL
SDL, MSC,Spin, PVS, Z
Invariants,PVS
RPA
Spin, PVS,TTCN, TorXDocs
Verif.
12Advantages of FM
Precision engineering
Complexity engineering
Correctness engineering
Automation engineering
12History1956 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
12History1968 Dana Scott denotational sem. for 1969 Tony Hoare axiomatic semantics1970 N.G. de Bruijn Automath1972 IBM Vienna: FM for PL/I design1974 Goguen Thatcher init. alg. sem. data types1977 Joseph Stoy book denotational sem.1978 Dines Bjørner, Cliff Jones VDM1979 Philips Brussels CHILL design
12History1980 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, …
12History1993 VDM Europe becomes FME
1997 Intel establishes FM group after Pentium
1999 FM World
Commercial firms offering FM (Verum, FDR)
FMICS, IFM
12IngredientsSyntax States
Logic Transitions
Proof Execution
Data types Communication
Modularisation Abstraction
Type system Timing
Object orientation Hybrid systems
12Semantics
Denotational
De Bakker, Rozenberg
Operational
Axiomatic - assertional
Kuiper, Jonkers, De Boer
12Varieties
LogicLogic: 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
12Varieties
EquationalEquational: -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
12Varieties
OperationalOperational: sequential: Z, VDM, LarchSOS Fokkink, ReniersI/O automata VaandragerPetri nets Van Hee, Van der AalstModel checking Larsen KatoenGraphs Rozenberg Rensink RoodaTorX Tretmans
12VarietiesVisualVisual: MSC, Petri nets
12ApplicationsSoftware Engineering,
in particular components, coordinationEmbedded Systems (hybrid systems)Business ProcessesBiological ProcessesSecurityWeb services & grid computingAgents, games, quantum & relativistic
comput.
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