Z Logic and Its Applications

We provide an introduction to the specification language Z from a logical perspective. The possibility of presenting Z in this way is a consequence of a number of joint publications on Z logic that Henson and Reeves have co-written since 1997. We provide an informal as well as a formal introduction to Z logic and show how it may be used, and extended, to investigate issues such as equational logic, the logic of preconditions, operation and data refinement, and monotonicity.

[1]  Jim Woodcock,et al.  Refinement of State-Based Concurrent Systems , 1990, VDM Europe.

[2]  Moshe Deutsch,et al.  The specification logic νZ , 2006, Formal Aspects of Computing.

[3]  Jim Woodcock,et al.  Using Z - specification, refinement, and proof , 1996, Prentice Hall international series in computer science.

[4]  Carroll Morgan,et al.  The specification statement , 1988, TOPL.

[5]  Steve King.  ‘The Standard Logic for Z’: A Clarification , 1999, Formal Aspects of Computing.

[6]  Rob Arthan.  On Free Type Definitions in Z , 1991, Z User Workshop.

[7]  Jim Woodcock,et al.  A Weakest Precondition Semantics for Z , 1998, Comput. J..

[8]  Kai Engelhardt,et al.  Data Refinement: Model-Oriented Proof Methods and their Comparison , 1998 .

[9]  Patrick Suppes,et al.  Logic, Methodology and Philosophy of Science , 1963 .

[10]  Martin C. Henson,et al.  New foundations for Z , 1998 .

[11]  Moshe Deutsch,et al.  An Analysis of Forward Simulation Data Refinement , 2003, ZB.

[12]  Ben Strulo.  How Firing Conditions Help Inheritance , 1995, ZUM.

[13]  S. M. Brien,et al.  W: A Logic for Z , 1991, Z User Workshop.

[14]  C. A. R. Hoare,et al.  Prespecification in Data Refinement , 1987, Inf. Process. Lett..

[15]  Susan Stepney,et al.  Z in practice , 1995, BCS practitioner series.

[16]  Eerke Albert Boiten.  REFINE 2002: The BCS FACS Refinement Workshop , 2002 .

[17]  Moshe Deutsch,et al.  An analysis of backward simulation data-refinement for partial relation semantics , 2003, Tenth Asia-Pacific Software Engineering Conference, 2003..

[18]  C. A. R. Hoare,et al.  Data Refinement Refined , 1986, ESOP.

[19]  Moshe Deutsch,et al.  Operation Refinement and Monotonicity in the Schema Calculus , 2003, ZB.

[20]  Jim Woodcock.  The Rudiments of Algorithm Refinement , 1992, Comput. J..

[21]  Per Martin-Löf,et al.  Constructive mathematics and computer programming , 1984 .

[22]  J. Michael Spivey,et al.  Understanding Z : A specification language and its formal semantics , 1985, Cambridge tracts in theoretical computer science.

[23]  Stephan Merz,et al.  The Specification Language TLA , 2008 .

[24]  Willem-Paul de Roever,et al.  Data Refinement by Willem-Paul de Roever , 1998 .

[25]  Jim Woodcock,et al.  On the Refinement and Simulation of Data Types and Processes , 1999, IFM.

[26]  J. C. P. Woodcock.  Properties of Z specifications , 1989, SOEN.

[27]  Steve King.  Z and the Refinement Calculus , 1990, VDM Europe.

[28]  Cliff B. Jones,et al.  Software development - a rigorous approach , 1980, Prentice Hall international series in computer science.

[29]  Jonathan P. Bowen,et al.  ZB 2003: Formal Specification and Development in Z and B , 2003, Lecture Notes in Computer Science.

[30]  Martin C. Henson,et al.  A Logic for Schema-Based Program Development , 2003, Formal Aspects of Computing.

[31]  Martin C. Henson,et al.  Program Development and Specification Refinement in the Schema Calculus , 2000, ZB.

[32]  Martin C. Henson.  The Standard Logic of Z is Inconsistent , 2005, Formal Aspects of Computing.

[33]  Moshe Deutsch,et al.  Results on formal stepwise design in Z , 2002, Ninth Asia-Pacific Software Engineering Conference, 2002..

[34]  J. Michael Spivey.  The consistency theorem for free type definitions in Z , 2005, Formal Aspects of Computing.

[35]  Jonathan P. Bowen,et al.  ZUM '95: The Z Formal Specification Notation , 1995, Lecture Notes in Computer Science.

[36]  Michael Clarke,et al.  Logic for computer science , 1990, International computer science series.

[37]  Frank Waters,et al.  The B Book , 1971 .

[38]  Cliff B. Jones,et al.  Systematic software development using VDM (2. ed.) , 1990, Prentice Hall International Series in Computer Science.

[39]  Eerke Albert Boiten,et al.  Refinement in Z and Object-Z: Foundations and Advanced Applications , 2001 .

[40]  Jim Woodcock.  The Refinement Calculus , 1991 .

[41]  John Wordsworth.  Software development with Z - a practical approach to formal methods in software engineering , 1992, International computer science series.

[42]  Mark B. Josephs.  The Data Refinement Calculator for Z Specifications , 1988, Inf. Process. Lett..

[43]  Lindsay Groves,et al.  Refinement and the Z schema calculus , 2002, Refine.

[44]  Eerke A. Boiten,et al.  Calculating upward and downward simulations of state-based specifications , 1999, Inf. Softw. Technol..

[45]  Martin C. Henson,et al.  Revising Z: Part II – logical development , 1999, Formal Aspects of Computing.

[46]  Eerke A. Boiten,et al.  Guards, Preconditions, and Refinement in Z , 2000, ZB.

[47]  Carroll Morgan,et al.  Programming from specifications (2nd ed.) , 1994 .

[48]  Martin C. Henson,et al.  An Analysis of Total Correctness Refinement Models for Partial Relation Semantics I , 2003, Log. J. IGPL.

[49]  Willem-Paul de Roever,et al.  Data Refinement: Theory , 1998 .

[50]  Xu Qiwen,et al.  Advanced Features of Duration Calculus and Their Applications in Sequential Hybrid Programs , 2003, Formal Aspects of Computing.

[51]  Martin C. Henson,et al.  Revising Z: Part I – logic and semantics , 1999, Formal Aspects of Computing.

[52]  Jim Woodcock.  An Introduction to Refinement in Z , 1991, VDM Europe.