VDM-10 Language Manual

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$Course Material\Efficiently Coding Communication Protocols in C++ ...$

VDM-10 Language Manual Examples: Let the following function values be defined: ✞ ✡✝ f1 = lambda x : nat & lambda y : nat & x + y f2 = lambda x : nat & x + 2 inc1 = lambda x : nat & x + 1 inc2 = lambda y : nat & y + 1 ✆ then the following holds: f1(5) ≡ lambda y :nat & 5 + y f2(4) ≡ 6 f1 comp f2 ≡ lambda x :nat & lambda y :nat & (x + 2) + y f2 ** 4 ≡ lambda x :nat & x + 8 inc1 = inc2 ≡ false Notice that the equality test does not yield the expected result with respect to the semantics of the VDM languages. Thus, one should be very careful with the usage of equality for infinite values like functions. 3.3 Invariants If the data types specified by means of equations as described above contain values which should not be allowed, then it is possible to restrict the values in a type by means of an invariant. The result is that the type is restricted to a subset of its original values. Thus, by means of a predicate the acceptable values of the defined type are limited to those where this expression is true. The general scheme for using invariants looks like this: ✞ ✡✝ Id = Type inv pat == expr where pat is a pattern matching the values belonging to the type Id, and expr is a truth-valued expression, involving some or all of the identifiers from the pattern pat. If an invariant is defined, a new (total) function is implicitly created with the signature: ✞ ✡✝ inv_Id : Type +> bool This function can be used within other invariant, function or operation definitions. For instance, recall the record type Score defined on page 24. We can ensure that the number of points awarded is consistent with the number of games won and drawn using an invariant: ✞ Score :: team won : Team : nat 30 ✆ ✆
Chapter 3. Data Type Definitions ✡✝ drawn : nat lost : nat points : nat inv sc == sc.points = 3 * sc.won + sc.drawn; ✆ The invariant function implicitly created for this type is: ✞ ✡✝ inv_Score : Score +> bool inv_Score (sc) == sc.points = 3 * sc.won + sc.drawn; ✆ 31
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Page 3 and 4: Contents 1 Introduction 1 1.1 The V
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Page 81 and 82: Chapter 7 Patterns Syntax: pattern
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Page 87 and 88: Chapter 8 Bindings Syntax: bind = s
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Chapter 9 Value (Constant) Definiti
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Chapter 10 Instance Variables (VDM+
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Chapter 11 The State Definition (VD
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Chapter 11. The State Definition (V
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Chapter 12 Operation Definitions Op
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Chapter 12. Operation Definitions s
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Chapter 13 Statements In this secti
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Chapter 13. Statements ✡✝ def t
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Chapter 13. Statements block return
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Chapter 13. Statements Examples: Th
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Chapter 13. Statements elseif state
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Chapter 13. Statements ‘do’, st
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Chapter 13. Statements 13.7 The Whi
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Chapter 13. Statements ✡✝ (dcl
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Chapter 13. Statements ✞ ✡✝ R
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Chapter 13. Statements where expres
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Chapter 13. Statements result of th
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Chapter 13. Statements ✡✝ else
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Chapter 13. Statements ✞ bootSequ
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Chapter 13. Statements ✞ op1 : na
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Chapter 14 Top-level Specification
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Chapter 14. Top-level Specification
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Chapter 15 Synchronization Constrai
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Chapter 15. Synchronization Constra
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Chapter 16 Threads (VDM++ and VDM-R
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Chapter 16. Threads (VDM++ and VDM-
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Chapter 16. Threads (VDM++ and VDM-
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Chapter 17 Top-level Specification
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Chapter 18 Trace Definitions In ord
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Chapter 18. Trace Definitions stack
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Chapter 19 Static Semantics VDM spe
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Chapter 20 Scope Conflicts (VDM++ a
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References [Ada LRM] [Bicarregui&94
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Chapter 20. Scope Conflicts (VDM++
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Appendix A The Syntax of the VDM La
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Appendix A. The Syntax of the VDM L
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Appendix B Lexical Specification B.
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Appendix B. Lexical Specification B
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Appendix B. Lexical Specification S
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Appendix C Operator Precedence The
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Appendix C. Operator Precedence eva
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Appendix C. Operator Precedence pre
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Appendix D Differences between the
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Index abs, 9 and, 6 card, 14 comp f
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INDEX arithmetic minus, 185 arithme
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INDEX boolean type, 6 char, 11 func
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INDEX sequence enumeration, 53, 187
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