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Hierarchical Contextual Reasoning
, 2003
"... VII Zusammenfassung IX Extended Abstract XI Acknowledgements XIII I ..."
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VII Zusammenfassung IX Extended Abstract XI Acknowledgements XIII I
Annotated Reasoning
 Annals of Mathematics and Artificial Intelligence (AMAI). Special Issue on Strategies in Automated Deduction
, 2000
"... Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given ..."
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Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given goal, prove its abstracted version and then use the information about the resulting abstract proof as an outline to construct the proof at the ground level. Dierent techniques to abstract from details have been studied in the literature. The problem is to nd out which details should be abstracted away. On one hand, if we abstract too much information then we often obtain abstract solutions that cannot be transferred to the ground level. Then, planning at the abstract level is even more dicult than planning at the ground level because the abstraction removes necessary control information, or we obtain only little information from the abstract proof how to guide the proof at the ground leve...
Representing WP Semantics in Isabelle/ZF
 TPHOLs: The 12th International Conference on Theorem Proving in HigherOrder Logics, number 1690 in lncs
, 1999
"... . We present a shallow embedding of the weakest precondition semantics for a program renement language. We use the Isabelle/ZF theorem prover for untyped set theory, and statements in our renement language are represented as set transformers. Our representation is signi cant in making use of the ..."
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. We present a shallow embedding of the weakest precondition semantics for a program renement language. We use the Isabelle/ZF theorem prover for untyped set theory, and statements in our renement language are represented as set transformers. Our representation is signi cant in making use of the expressiveness of Isabelle/ZF's set theory to represent states as dependentlytyped functions from variable names to their values. This lets us give a uniform treatment of statements such as variable assignment, framed specication statements, local blocks, and parameterisation. ZF set theory requires set comprehensions to be explicitly bounded. This requirement propagates to the denitions of statements in our renement language, which have operands for the state type. We reduce the syntactic burden of repeatedly writing the state type by using Isabelle's metalogic to dene a lifted set transformer language which implicitly passes the state type to statements. Weakest precondi...
TAS  A Generic Window Inference System
"... This paper presents work on technology for transformational proof and program development, as used by window inference calculi and transformation systems. The calculi are characterised by a certain class of theorems in the underlying logic. Our transformation system TAS compiles these rules to concr ..."
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This paper presents work on technology for transformational proof and program development, as used by window inference calculi and transformation systems. The calculi are characterised by a certain class of theorems in the underlying logic. Our transformation system TAS compiles these rules to concrete deduction support, complete with a graphical user interface with commandlanguagefree user interaction by gestures like drag&drop and proofbypointing, and a development management for transformational proofs. It is generic in the sense that it is completely independent of the particular window inference or transformational calculus, and can be instantiated to many different ones; three such instantiations are presented in the paper.
Transformational reasoning with incomplete information
"... Abstract. Starting a proof without having complete information about the proof term can be beneficial. While the proof is carried out newly introduced constraints can make the information more precise. Window inference, a proof paradigm based on hierarchical term rewriting, is very well suited for g ..."
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Abstract. Starting a proof without having complete information about the proof term can be beneficial. While the proof is carried out newly introduced constraints can make the information more precise. Window inference, a proof paradigm based on hierarchical term rewriting, is very well suited for general transformational reasoning and especially for reasoning about programs. The HOL implementation of window inference does not support proofs with uninstantiated terms since the HOL system does not have a formalized metalogic. We show how, without having to redo proofs, higher order variables (metavariables) can be used to perform proofs with uninstantiated terms in HOL window inference. We illustrate the uses of metavariables with a few examples related to program reasoning. 1
Flexible Interactive Transformational Reasoning
, 1996
"... Window inference is a transformational style of reasoning with support for the contextual transformation of subterms. Window inference has been successfully used as the basis of various refinement tools. Normal presentations of completed program refinements closely match the presentations of comp ..."
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Window inference is a transformational style of reasoning with support for the contextual transformation of subterms. Window inference has been successfully used as the basis of various refinement tools. Normal presentations of completed program refinements closely match the presentations of completed window inference proofs. However, in the development of a program refinement, window inference is not as flexible as it should be. Current implementations of window inference allow a user to work on only one subproblem at a time. While developing a program refinement, a user may wish to work on many subproblems at the same timeto quickly switch backwards and forwards between working on the subproblems. This paper describes a design for a window inference system which provides simultaneous access to multiple subproblems. In the core of the design, access is available to any subproblem, but constraints can be added on top of the core in order to provide a hierarchical inter...