Filters








21 Hits in 3.7 sec

Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL

Jasmin Christian Blanchette, Mathias Fleury, Dmitriy Traytel, Marc Herbstritt
2017 International Conference on Rewriting Techniques and Applications  
Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below 0 .  ...  Our formal library also provides, somewhat nonstandardly, multisets with negative multiplicities and syntactic ordinals with negative coefficients.  ...  Uwe Waldmann shared his insights about syntactic ordinals with us, including the lemma and the proof of Example 3.  ... 
doi:10.4230/lipics.fscd.2017.11 dblp:conf/rta/BlanchetteFT17 fatcat:ctzlp6kstbfnpcqrkraxnhwz6q

Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic [chapter]

Julian Biendarra, Jasmin Christian Blanchette, Aymeric Bouzy, Martin Desharnais, Mathias Fleury, Johannes Hölzl, Ondřej Kunčar, Andreas Lochbihler, Fabian Meier, Lorenz Panny, Andrei Popescu, Christian Sternagel (+2 others)
2017 Lecture Notes in Computer Science  
We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype  ...  These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction.  ...  We first want to acknowledge the support and encouragement of past and current bosses: David Basin, Wan Fokkink, Stephan Merz, Aart Middeldorp, Tobias Nipkow, and Christoph Weidenbach.  ... 
doi:10.1007/978-3-319-66167-4_1 fatcat:oyojuyu32rc4dk3ritsvdzqhma

Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic

Julian Biendarra, Jasmin Christian Blanchette, Aymeric Bouzy, Martin Desharnais, Mathias Fleury, Johannes Hölzl, Ondřej Kunčar, Andreas Lochbihler, Fabian Meier, Lorenz Panny, Andrei Popescu, Christian Sternagel (+2 others)
2017 Zenodo  
We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype  ...  These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction.  ...  We first want to acknowledge the support and encouragement of past and current bosses: David Basin, Wan Fokkink, Stephan Merz, Aart Middeldorp, Tobias Nipkow, and Christoph Weidenbach.  ... 
doi:10.5281/zenodo.3228083 fatcat:qcnc36ufqbea3ghgqu7hhkkuw4

Front Matter, Table of Contents, Preface, Steering Committee, Program Committee, External Reviewers

Dale Miller, Marc Herbstritt
2017 International Conference on Rewriting Techniques and Applications  
Witold Charatonik, and Klara Zielińska . . . . . . . . . . . . . . . . . . 10:1-10:17 Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL Jasmin Christian Blanchette, Mathias  ...  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0:vii-0:viii Invited Papers Type Systems for the Relational Verification of  ...  FSCD (http://fscdconference.org/) covers all aspects of formal structures for computation and deduction, from theoretical foundations to applications.  ... 
doi:10.4230/lipics.fscd.2017.0 dblp:conf/rta/X17 fatcat:4q3jzxkc2zgrtjikg3atumrjgi

Editor: Dale Miller

Jasmin Blanchette, Mathias Fleury, Dmitriy Traytel
2017 18 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik   unpublished
Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below 0.  ...  In Isabelle/HOL, both nested and hereditary multisets can be comfortably defined as inductive datatypes.  ...  Uwe Waldmann shared his insights about syntactic ordinals with us, including the lemma and the proof of Example 3.  ... 
fatcat:imq4mk2z65ejpei3cz4zcktgna

An operational interpretation of coinductive types [article]

Łukasz Czajka
2020 arXiv   pre-print
This may be seen as a refinement and generalization of the notion of productivity in term rewriting to a setting with higher-order functions and with data specified by nested higher-order inductive and  ...  We introduce a sufficient syntactic correctness criterion, in the form of a type system, for finite terms decorated with type information.  ...  This ordinal exists, as we may take any ordinal larger than the cardinality of P(T ∞ ).  ... 
arXiv:1808.05059v5 fatcat:63rgyxx6enetfeowj2yadg4fkm

An operational interpretation of coinductive types

Łukasz Czajka
2018 Logical Methods in Computer Science  
This may be seen as a refinement and generalization of the notion of productivity in term rewriting to a setting with higher-order functions and with data specified by nested higher-order inductive and  ...  We introduce a sufficient syntactic correctness criterion, in the form of a type system, for finite terms decorated with type information.  ...  This ordinal exists, as we may take any ordinal larger than the cardinality of P(T ∞ ).  ... 
doi:10.23638/lmcs-16(1:11)2020 fatcat:azklqdhuy5aldb3il6ki3smbnq

Completeness for Ancestral Logic via a Computationally-Meaningful Semantics [chapter]

Liron Cohen
2017 Lecture Notes in Computer Science  
In order for AL to be able to serve as a reasonable (and better) substitute to the use of F OL in computer science, it is crucial to develop adequate, user-friendly proof systems for it.  ...  In this paper we show that such a Gentzen-style approximation is both sound and complete with respect to a natural, computationally-meaningful Henkin-style semantics for AL.  ...  Acknowledgments This research was supported by: Ministry of Science, Technology and Space, Israel; Fulbright Post-doctoral Scholar program; Weizmann Institute of Science -National Postdoctoral Award Program  ... 
doi:10.1007/978-3-319-66902-1_15 fatcat:4eucgtab3zcfdbszl6fkowadre

Combining negation as failure and embedded implications in logic programs

Laura Giordano, Nicola Olivetti
1998 The Journal of Logic Programming  
Since the property of being an e-query is undecidable, we give a syntactical decidable condition which ensures this property.  ...  The fixed point semantics is a generalization of those developed by Fitting and Kunen for flat logic programs and makes use of Kleene strong three-valued logic.  ...  Acknowledgements We are indebted to the referees for their careful checking of the work and for their helpful comments.  ... 
doi:10.1016/s0743-1066(97)10014-0 fatcat:3shsn3vsy5bk3ff2gkvcpmyuuy

Type-Theoretic Approaches to Ordinals [article]

Nicolai Kraus and Fredrik Nordvall Forsberg and Chuangjie Xu
2022 arXiv   pre-print
Using homotopy type theory as the foundational setting, we develop an abstract framework for ordinal theory and establish a collection of desirable properties and constructions.  ...  We then study and compare three concrete implementations of ordinals in homotopy type theory: first, a notation system based on Cantor normal forms (binary trees); second, a refined version of Brouwer  ...  Acknowledgements References Acknowledgements We would like to thank the participants of the conferences MFCS'21, TYPES'21, TYPES'22, and PC'22 for their comments and suggestions related to this work.  ... 
arXiv:2208.03844v1 fatcat:nfut227d35atjgn7r565y4ejzu

A Framework for Specifying, Prototyping, and Reasoning about Computational Systems [article]

Andrew Gacek
2009 arXiv   pre-print
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems.  ...  Specifically, this framework provides a specification language which supports the concise and direct description of formal systems, a mechanism for animating the specification language thereby producing  ...  Formal systems of these kinds typically manipulate syntactically complex objects such as formulas, proofs, and programs.  ... 
arXiv:0910.0747v2 fatcat:lwdpd37pdvayjn73b2apt3okpa

Linear logic

Jean-Yves Girard
1987 Theoretical Computer Science  
The familiar connective of negation is broken into two operations: linear negation which is the purely negative part of negation and the modality "of course" which has the meaning of a reaffirmation.  ...  Following this basic discovery, a completely new approach to the whole area between constructive logics and programmation is initiated.  ...  Also, the author wishes to express his indebtedness to Gianfranco Mascari who introduced him to the subject of parallelism and whose influence was important for the shift to 'classical' framework and parallel  ... 
doi:10.1016/0304-3975(87)90045-4 fatcat:2pz66b65i5fzjaggrqhwyeimki

LIPIcs, Volume 15, RTA'12, Complete Volume [article]

Ashish Tiwari
2013
We thank Ashish Tiwari, Nachum Dershowitz, the referees, and the attendants of TeReSe and the TF-lunch seminar, for feedback and interesting discussions.  ...  the presentation of the final version.  ...  Note that, according to our reasoning, [y/u] is an hereditary head substitution also for s = (x y)[x/(y r)[y/u]], but we get around these nested cases because we only have to deal with shallow terms.  ... 
doi:10.4230/lipics.rta.2012 fatcat:i53phqg7yvahdovzjpatxgb7hq

The semantic analysis of advanced programming languages THE SEMANTIC ANALYSIS OF ADVANCED PROGRAMMING LANGUAGES

Harley Eades, Harley Eades, Cesare Tinelli, Stephanie Weirich, Gregory Landini, Kasturi Varadarajan
2014 unpublished
He is one of the kindest and most intelligent people I have had the pleasure to work with, and without his guidance I would have never made it this far.  ...  Furthermore, I would like to thank him for introducing me to my research area in type theory and the foundations of functional programming languages.  ...  He is one of the kindest and most intelligent people I have had the pleasure to work with, and without his guidance I would have never made it this far.  ... 
fatcat:mszkfweminggdagazody6huqeq

LIPIcs, Volume 7, ICLP'10, Complete Volume [article]

Manuel Hermenegildo, Torsten Schaub
2013
an early draft of this paper; and to the anonymous reviewers, who aided in the clarification of many points.  ...  This research was funded in part by the National Science Foundation under grants 0541183 (Deep and Scalable Analysis of Software), and 0707612 (CRI: CRD -Development of Alloy Tools, Technology and Materials  ...  limit ordinals β.  ... 
doi:10.4230/lipics.iclp.2010 fatcat:j7jd7dpsffbs7plm5qa6qi2wem
« Previous Showing results 1 — 15 out of 21 results