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Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL
2017
International Conference on Rewriting Techniques and Applications
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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]
2017
Lecture Notes in Computer Science
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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
2017
Zenodo
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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
2017
International Conference on Rewriting Techniques and Applications
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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
2017
18 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik
unpublished
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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]
2020
arXiv
pre-print
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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
2018
Logical Methods in Computer Science
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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]
2017
Lecture Notes in Computer Science
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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
1998
The Journal of Logic Programming
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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]
2022
arXiv
pre-print
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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]
2009
arXiv
pre-print
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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
1987
Theoretical Computer Science
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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]
2013
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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
2014
unpublished
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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]
2013
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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
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