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Miniagda: Integrating sized and dependent types
 In Partiality and Recursion (PAR
, 2010
"... Sized types are a modular and theoretically wellunderstood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make termination checking robust and suitable for strong abstrac ..."
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Cited by 12 (2 self)
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Sized types are a modular and theoretically wellunderstood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make termination checking robust and suitable for strong abstractions like higherorder functions and polymorphism. To study the application of sized types to proof assistants and programming languages based on dependent type theory, we have implemented a core language, MiniAgda, with explicit handling of sizes. New considerations were necessary to soundly integrate sized types with dependencies and pattern matching, which was made possible by modern concepts such as inaccessible patterns and parametric function spaces. This paper provides an introduction to MiniAgda by example and informal explanations of the underlying principles. 1
Semicontinuous sized types and termination
 In Zoltán Ésik, editor, Computer Science Logic, 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL
"... Abstract. Some typebased approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls occur just at a smaller size. This approach is onl ..."
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Cited by 10 (5 self)
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Abstract. Some typebased approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls occur just at a smaller size. This approach is only sound if the type of the recursive function is admissible, i.e., depends on the size index in a certain way. To explore the space of admissible functions in the presence of higherkinded data types and impredicative polymorphism, a semantics is developed where sized types are interpreted as functions from ordinals into sets of strongly normalizing terms. It is shown that upper semicontinuity of such functions is a sufficient semantic criterion for admissibility. To provide a syntactical criterion, a calculus for semicontinuous functions is developed. 1.
Proof Exchange for Theorem Proving — Second
, 2012
"... Proceedings Edited by David Pichardie and Tjark WeberCopyright c ○ 2012 for the individual papers by the papers ’ authors. Copying permitted for private and academic purposes. This volume is published and copyrighted by its editors. Preface The goal of the PxTP workshop series is to bring together r ..."
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Proceedings Edited by David Pichardie and Tjark WeberCopyright c ○ 2012 for the individual papers by the papers ’ authors. Copying permitted for private and academic purposes. This volume is published and copyrighted by its editors. Preface The goal of the PxTP workshop series is to bring together researchers working on proof production from automated theorem provers with potential consumers of proofs. Machinecheckable proofs have been proposed for applications like proofcarrying code and certified compilation, as well as for exchanging knowledge between different automated reasoning systems. For example, interactive theorem provers can import results from otherwise untrusted highperformance solvers, by means of proofs the solvers produce. In such situations, one automated reasoning tool can make use of the results of another, without having to trust that the second tool is sound. It is only necessary to be able to reconstruct a proof that the first tool will accept, in order to import the result without increasing the size of the trusted computing base. This simple idea of proof exchange for theorem proving becomes quite complicated under the realworld constraints of highly complex and heterogeneous proof producers and proof consumers. For example, even the issue of a standard proof format for a single class of solvers, like SMT solvers, is quite difficult to address, as different solvers use different inference systems. It may be quite challenging, from an engineering and possibly also theoretical point of view, to fit these into a single standard format. Emerging work from several groups proposes standard metalanguages or parametrised formats to achieve flexibility while retaining a universal proof language.