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Recursion over Objects of Functional Type
, 1999
"... This paper presents an extension of the simpletyped lambdacalculus allowing iteration and case... ..."
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Cited by 14 (0 self)
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This paper presents an extension of the simpletyped lambdacalculus allowing iteration and case...
Categorical Term Rewriting: Monads and Modularity
 University of Edinburgh
, 1998
"... Term rewriting systems are widely used throughout computer science as they provide an abstract model of computation while retaining a comparatively simple syntax and semantics. In order to reason within large term rewriting systems, structuring operations are used to build large term rewriting syste ..."
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Cited by 12 (6 self)
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Term rewriting systems are widely used throughout computer science as they provide an abstract model of computation while retaining a comparatively simple syntax and semantics. In order to reason within large term rewriting systems, structuring operations are used to build large term rewriting systems from smaller ones. Of particular interest is whether key properties are modular, thatis,ifthe components of a structured term rewriting system satisfy a property, then does the term rewriting system as a whole? A body of literature addresses this problem, but most of the results and proofs depend on strong syntactic conditions and do not easily generalize. Although many specific modularity results are known, a coherent framework which explains the underlying principles behind these results is lacking. This thesis posits that part of the problem is the usual, concrete and syntaxoriented semantics of term rewriting systems, and that a semantics is needed which on the one hand elides unnecessary syntactic details but on the other hand still possesses enough expressive power to model the key concepts arising from
A Modal Lambda Calculus with Iteration and Case Constructs
 TYPES FOR PROOFS AND PROGRAMS: INTERNATIONAL WORKSHOP, TYPES ’98, KLOSTER IRSEE
, 1997
"... An extension of the simplytyped lambdacalculus allowing iteration and case reasoning over terms defined by means of higher order abstract syntax has recently been introduced by Joëlle Despeyroux, Frank Pfenning and Carsten Schürmann. This thorny mixing is achieved thanks to the help of the operato ..."
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Cited by 8 (1 self)
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An extension of the simplytyped lambdacalculus allowing iteration and case reasoning over terms defined by means of higher order abstract syntax has recently been introduced by Joëlle Despeyroux, Frank Pfenning and Carsten Schürmann. This thorny mixing is achieved thanks to the help of the operator ` ' of modal logic IS4. Here we give a new presentation of their system, with reduction rules, instead of evaluation judgments, that compute the canonical forms of terms. Our presentation is based on a modal lambdacalculus that is better from the user's point of view, is more concise and we do not impose a particular strategy of reduction during the computation. Our system enjoys the decidability of typability, soundness of typed reduction with respect to typing rules, the ChurchRosser and strong normalization properties. Finally it is a conservative extension of the simplytyped lambdacalculus.
A Modal Lambda Calculus with Iteration and Case Constructs
, 1998
"... An extension of the simplytyped calculus, allowing iteration and case reasoning over terms of functional types that arise when using higher order abstract syntax, has recently been introduced by Joëlle Despeyroux, Frank Pfenning and Carsten Schürmann. This thorny mixing is achieved thanks to the h ..."
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Cited by 1 (0 self)
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An extension of the simplytyped calculus, allowing iteration and case reasoning over terms of functional types that arise when using higher order abstract syntax, has recently been introduced by Joëlle Despeyroux, Frank Pfenning and Carsten Schürmann. This thorny mixing is achieved thanks to the help of the operator ` ' of modal logic S4. Here we give a new presentation of their system, with reduction rules, instead of evaluation judgments, that compute the canonical forms of terms. Our presentation is based on a modal calculus that is better from the user's point of view because it requires fewer annotations in terms. Moreover we do not impose a particular strategy of reduction during the computation. Our system enjoys the decidability of typability, soundness of typed reduction with respect to typing rules, the ChurchRosser and strong normalization properties and it is a conservative extension of the simplytyped calculus.