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Operation Refinement and Monotonicity in the Schema Calculus
, 2003
"... The schema calculus of Z provides a means for expressing structured, modular specifications. Extending this modularity to program development requires the monotonicity of these operators with respect to refinement. This paper provides a thorough mathematical analysis of monotonicity with respect ..."
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Cited by 6 (4 self)
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The schema calculus of Z provides a means for expressing structured, modular specifications. Extending this modularity to program development requires the monotonicity of these operators with respect to refinement. This paper provides a thorough mathematical analysis of monotonicity with respect to four schema operations for three notions of operation refinement. The mathematical connection between the equational schema logic and monotonicity is discussed and evaluated.
Window inference in isabelle
 University of Cambridge Computer Laboratory
, 1995
"... Window inference is a transformational style of reasoning that provides an intuitive framework for managing context during the transformation of subterms under transitive relations. This report describes the design for a prototype window inference tool in Isabelle, and discusses possible directions ..."
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Cited by 5 (2 self)
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Window inference is a transformational style of reasoning that provides an intuitive framework for managing context during the transformation of subterms under transitive relations. This report describes the design for a prototype window inference tool in Isabelle, and discusses possible directions for the final tool. 1
An Analysis of Forward Simulation Data Refinement
 ZB 2003: Formal Specification and Development in Z and B, volume 2651 of Lecture Notes in Computer Science
, 2003
"... This paper investigates data refinement by forward simulation for specifications whose semantics is given by partial relations. The most wellknown example of such a semantics is that for Z. The standard modeltheoretic approach is based on totalisation and lifting. The paper examines this model, ..."
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Cited by 3 (1 self)
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This paper investigates data refinement by forward simulation for specifications whose semantics is given by partial relations. The most wellknown example of such a semantics is that for Z. The standard modeltheoretic approach is based on totalisation and lifting. The paper examines this model, exploring and isolating the precise roles played by lifting and totalisation in the standard account by introducing a simpler, normative theory of forward simulation data refinement (SFrefinement) which captures refinement directly in the language and in terms of the natural properties of preconditions and postconditions. This theory is used in conjunction with four other modeltheoretic approaches to determine the extent to which the standard approach is canonical, and the extent to which it is arbitrary.
Modular reasoning in Z: scrutinising monotonicity and refinement
, 2004
"... The schema calculus operators of Z provide an excellent means for expressing modular specifications but not for undertaking modular reasoning: it is wellknown that these operators have poor monotonicity properties. The paper addresses three topics in this context: first, we provide a thorough mathe ..."
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Cited by 3 (0 self)
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The schema calculus operators of Z provide an excellent means for expressing modular specifications but not for undertaking modular reasoning: it is wellknown that these operators have poor monotonicity properties. The paper addresses three topics in this context: first, we provide a thorough mathematical analysis of monotonicity with respect to four schema operations and for three notions of operation refinement. Second, we provide a comprehensive analysis of the relational completion operator, known as liftedtotalisation, that underlies the standard notion of refinement in Z. Third, we provide a new semantics which induces a fully monotonic schema calculus.
Doing High School Mathematics Carefully
, 1997
"... We show how solutions to typical problems of High School and firstyear University mathematics can be written using structured derivations. Such a derivation extends the calculational proof format with subderivations that allow inferences to presented at different levels of detail. By using structur ..."
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Cited by 3 (1 self)
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We show how solutions to typical problems of High School and firstyear University mathematics can be written using structured derivations. Such a derivation extends the calculational proof format with subderivations that allow inferences to presented at different levels of detail. By using structured derivations and a minimal amount of logical syntax, we can write solution to typical problems in algebra but also in, e.g., real analysis. We argue why structured derivations give students a better grasp of problem solutions and better possibilities to reread and discuss solutions afterwards, as compared with traditional informal approaches to writing down solutions. TUCS Research Group Programming Methodology Research Group 1 Introduction We are concerned with the way in which High School mathematics is taught. In our view, a more careful use of logical derivations would make the material easier to grasp, and would enhance the manipulative skill of the students. In this paper, we fir...
An Interactive Metatool for Exploring Program Algebras
, 1999
"... We describe how anexisting tool is extended to allow exploratory reasoning in program algebras with theorem proving support. The existing tool (TkWinHOL and the Re nement Calculator) provides a graphical user interface to the window inference reasoning system for the HOL theorem prover. We show how ..."
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Cited by 1 (0 self)
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We describe how anexisting tool is extended to allow exploratory reasoning in program algebras with theorem proving support. The existing tool (TkWinHOL and the Re nement Calculator) provides a graphical user interface to the window inference reasoning system for the HOL theorem prover. We show how a user with a small amount ofwork can build an extension to this tool, which can then be used to build, interactively and stepbystep, a whole theory for the program algebra in question. The ideas are illustrated with an extension for a simple whilelanguage.
A Framework for Generic and Reusable Tactics
, 1999
"... In this paper we present a framework for the definition of generic and thus reusable tactics. We present an extension of the window inference technique which is the formal basis of a hierarchical, problemreduction style of reasoning. The window inference technique is analyzed and general reasoni ..."
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In this paper we present a framework for the definition of generic and thus reusable tactics. We present an extension of the window inference technique which is the formal basis of a hierarchical, problemreduction style of reasoning. The window inference technique is analyzed and general reasoning rules are separated from logic specific rules. The separation between logic specific and general rules is used to define a framework offering generic window reasoning rules to allow for the definition of generic tactics, where logic specific parts are separated from the tactic level. 1 Introduction Interactive theorem proving systems are used to support strict mathematical reasoning wrt. different logics, as for example classical firstorder logic, higherorder logic or modal logics. These systems are either metalogical systems allowing the declarative encoding of a large variety of logics or they are "multilogical" systems, where the different logics are build into the system on t...