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449
Reasoning with Inductively Defined Relations in the HOL Theorem Prover
, 1992
"... : Inductively defined relations are among the basic mathematical tools of computer science. Examples include evaluation and computation relations in structural operational semantics, labelled transition relations in process algebra semantics, inductivelydefined typing judgements, and proof systems ..."
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in general. This paper describes a set of HOL theoremproving tools for reasoning about such inductively defined relations. We also describe a suite of worked examples using these tools. First printed: August 1992 Parts of this report have previously appeared as: T. Melham, `A Package for Inductive
Reasoning with inductively defined relations in the HOL theorem prover
, 1992
"... Abstract: Inductively defined relations are among the basic mathematical tools of computer science. Examples include evaluation and computation relations in structural operational semantics, labelled transition relations in process algebra semantics, inductivelydefined typing judgements, and proof ..."
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Cited by 49 (0 self)
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systems in general. This paper describes a set of HOL theoremproving tools for reasoning about such inductively defined relations. We also describe a suite of worked examples using these tools. First printed: August 1992
A Package for Inductive Relation Definitions in HOL
 in Proceedings of the 1991 International Workshop on the HOL Theorem Proving System and its Applications
, 1992
"... This paper describes a set of theorem proving tools based on a new derived principle of definition in HOL, namely the introduction of relations inductively defined by a set of rules. Such inductive definitions abound in computer science. Example application areas include reasoning about structured o ..."
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Cited by 30 (2 self)
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This paper describes a set of theorem proving tools based on a new derived principle of definition in HOL, namely the introduction of relations inductively defined by a set of rules. Such inductive definitions abound in computer science. Example application areas include reasoning about structured
Nominal techniques in Isabelle/HOL
 Proceedings of the 20th International Conference on Automated Deduction (CADE20
, 2005
"... Abstract. In this paper we define an inductive set that is bijective with the ffequated lambdaterms. Unlike deBruijn indices, however, our inductive definition includes names and reasoning about this definition is very similar to informal reasoning on paper. For this we provide a structural induc ..."
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Cited by 101 (14 self)
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Abstract. In this paper we define an inductive set that is bijective with the ffequated lambdaterms. Unlike deBruijn indices, however, our inductive definition includes names and reasoning about this definition is very similar to informal reasoning on paper. For this we provide a structural
Reasoning Inductively about Z Specifications via Unification
, 2000
"... . Selecting appropriate induction cases is one of the major problems in proof by induction. Heuristic strategies often use the recursive pattern of definitions and lemmas in making these selections. In this paper, we describe a general framework, based upon unification, that encourages and suppo ..."
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different strategies, including a simultaneous proof of two theorems concerning mutuallydefined relations; these theorems are expressed in a nonequational form, involving both universal and existential quantifiers. 1 Motivation Proof by induction is a necessary tool for reasoning about the properties
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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that in weak reconstruction FFT can still be applied if kspace is sampled in a regular Cartesian fashion. For this reason sensitivity encoding with Cartesian sampling is particularly feasible. Moreover, the reconstruction mechanism is relatively easily understood in this case. Therefore, the first part
A Social Reasoning Mechanism Based On Dependence Networks
, 1994
"... This paper describes the fundamental concepts of a social reasoning mechanism, designed to be part of an agent's internal model, in a multiagent systems (MAS) context. It enables an agent to reason about the others using information about their goals, actions, resources and plans. Every agent ..."
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Cited by 105 (23 self)
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his own plans or those of the others. As a result, we have defined a preliminary taxonomy of dependence situations regarding the goal being analysed (unilateral, mutual or reciprocal) and the sets of plans used in this reasoning mechanism (mutually or locally believed). We have used this model
Relational Properties of Domains
 Information and Computation
, 1996
"... New tools are presented for reasoning about properties of recursively defined domains. We work within a general, categorytheoretic framework for various notions of `relation' on domains and for actions of domain constructors on relations. Freyd's analysis of recursive types in terms of a ..."
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Cited by 115 (6 self)
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New tools are presented for reasoning about properties of recursively defined domains. We work within a general, categorytheoretic framework for various notions of `relation' on domains and for actions of domain constructors on relations. Freyd's analysis of recursive types in terms of a
Reasoning about terminating . . .
, 1999
"... This thesis addresses two basic problems with the current crop of mechanized proof systems. The first problem is largely technical: the act of soundly introducing a recursive definition is not as simple and direct as it should be. The second problem is largely social: there is very little codeshar ..."
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function definition facility, based on mechanically proven wellfounded recursion and induction theorems. Reasoning support is embodied by automatically derived induction theorems, which are customised to the recursion structure of definitions. This provides a powerful, guaranteed sound, definitionandreasoning
Mechanisms for Commonsense Reasoning about Sets
, 1988
"... The SEt Reasoning Facility (SERF) integrates mechanisms for propagating membership propositions, deriving relations between sets, and reasoning about closure and cardinality into an efficient utility package for reasoning about sets. Assertions about relations between sets are compiled into a constr ..."
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The SEt Reasoning Facility (SERF) integrates mechanisms for propagating membership propositions, deriving relations between sets, and reasoning about closure and cardinality into an efficient utility package for reasoning about sets. Assertions about relations between sets are compiled into a
Results 1  10
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