Semantics of higher-order recursion schemes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00179796" target="_blank" >RIV/68407700:21230/11:00179796 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2168/LMCS-7(1:15)2011" target="_blank" >http://dx.doi.org/10.2168/LMCS-7(1:15)2011</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2168/LMCS-7(1:15)2011" target="_blank" >10.2168/LMCS-7(1:15)2011</a>

Result language
angličtina
Original language name
Semantics of higher-order recursion schemes
Original language description
Higher-order recursion schemes are recursive equations defining new operations from given ones called terminals. Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of lambda-calculus in which the terminalsare interpreted as continuous operations. For the uninterpreted semantics based on infinite lambda-terms we follow the idea of Fiore, Plotkin and Turi and work in the category of sets in context, which are presheaves on the category of finite sets. Fioreet al showed how to capture the type of variable binding in lambda-calculus by an endofunctor H and they explained simultaneous substitution of lambda-terms by proving that the presheaf of lambda-terms is an initial H-monoid. Here we work with the presheaf of rational infinite lambda-terms and prove that this is an initial iterative H-monoid. We conclude that every guarded higher-order recursion scheme has a unique uninterpreted solution in this monoid.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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