Formal Methods in Software Design. Markus Roggenbach
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1 Formal Methods in Software Design Markus Roggenbach October 2001
2 2 Formal Methods Use of mathematics in software development main activities: writing formal specifications
3 2 Formal Methods Use of mathematics in software development main activities: writing formal specifications proving properties about formal specifications
4 2 Formal Methods Use of mathematics in software development main activities: writing formal specifications proving properties about formal specifications constructing a program by mathematical manipulating a formal specification
5 2 Formal Methods Use of mathematics in software development main activities: writing formal specifications proving properties about formal specifications constructing a program by mathematical manipulating a formal specification verifying a program by mathematical argument
6 3 Non Formal, Semi Formal, Formal It has been widely accepted that syntax can be mathematically defined for quite some time, but there has been more resitance to the mathematical definition of semantics. (quoted freely from [1]
7 4 non formal: in natural languague (open to arbitrary new symbols) formal: in a (fixed) language with mathematically defined Syntax and Semantics
8 5 semi formal: in a language with Syntax definition by mathematical methods Semantics definition in natural language or by tool
9 6 Specifications Specification: description by properties Main question on specifications: What happens if... Specifications should be
10 6 Specifications Specification: description by properties Main question on specifications: What happens if... Specifications should be complete
11 6 Specifications Specification: description by properties Main question on specifications: What happens if... Specifications should be complete precise
12 6 Specifications Specification: description by properties Main question on specifications: What happens if... Specifications should be complete precise consistent (no contradictions)
13 6 Specifications Specification: description by properties Main question on specifications: What happens if... Specifications should be complete precise consistent (no contradictions)
14 7 Why formal Specifications? formal specifications are precise (non formal and sometimes even semi formal specifications are open to re-interpretation)
15 7 Why formal Specifications? formal specifications are precise (non formal and sometimes even semi formal specifications are open to re-interpretation) syntactical and semantical correctness independent of tools
16 7 Why formal Specifications? formal specifications are precise (non formal and sometimes even semi formal specifications are open to re-interpretation) syntactical and semantical correctness independent of tools mathematical methods (consistency, completeness)
17 8 Limitations of Formal Methods The world is not a formal system. I. Modelling means Abstraction (only essentials are considered) II. Errors within Formalisms.
18 9 III. Behaviour of a Program depends on Compiler Operating System Computer Hardware Embedding in a Technical Process Human Operator
19 10 Waterfall Modell Requirement Elicitation and Analysis Nat. Lang. Non Formal Specification Validation Spec. Lang. Formal Specification Inv. & Verify or Progr. Lang. Implementation Transformation Test Maintenance
20 11 Specification Languages No single technique is adequate to address all issues of complex system development. Classification of Specification Languages: Model-oriented: Z, VDM Property-oriented: Larch, OBJ, CASL Process algebras: CCS, CSP, π-calculus
21 Bibliography 12 [1] J. P. Bowen and M. G. Hinchey. High-Integrity System Specification and Design. Springer, 1999.
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