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Better-quasi-orderings and coinduction

Thomas Forster
2003 Theoretical Computer Science  
We can characterise the class of BQOs as the largest class of well-founded quasiorders closed under the Hoare powerdomain construction and colimits.  ...  A binary relation that is transitive and re exive will here be called a quasiorder. (The expressions "quasi-order", "quasiordering" and "preorder" are also to be seen in the literature).  ...  natural wellfounded parts) is the class of wellquasiorders, and a special subclass of that family is the class of better quasiorders.  ... 
doi:10.1016/s0304-3975(03)00131-2 fatcat:e2urpn3jyjaupki4ihwcyqbzfq

A realizability interpretation of Church's simple theory of types

ULRICH BERGER, TIE HOU
2016 Mathematical Structures in Computer Science  
Although definable in CST we include operators for monotone induction and coinduction and provide simple realizers for them.  ...  The advantages of our approach are that (a) induction and coinduction are not restricted to the strictly positive case, (b) abstract mathematical structures and results may be imported, (c) the formalization  ...  Quasi-domains may also be defined order-theoretically as those quasi-orders (D, ), i.e. transitive and reflexive relations, whose quotients by the equivalence relation x ∼ y :⇔ x y ∧ y x are (Scott-)  ... 
doi:10.1017/s0960129516000104 fatcat:hiec7u46jrabbmn6xlv3c7ztzi

Coinductive Proof Techniques for Language Equivalence [chapter]

Jurriaan Rot, Marcello Bonsangue, Jan Rutten
2013 Lecture Notes in Computer Science  
Language equivalence can be checked coinductively by establishing a bisimulation on suitable deterministic automata.  ...  First, we focus on the regular operations of union, concatenation and Kleene star, and illustrate our method with new proofs of classical results such as Arden's rule.  ...  Conclusions We presented a proof method for language equivalence, based on coinduction and bisimulation-up-to.  ... 
doi:10.1007/978-3-642-37064-9_42 fatcat:fy6mexeq5bawpovgqdlgae6sqy

Duality in Computer Science (Dagstuhl Seminar 15441)

Mai Gehrke, Achim Jung, Victor Selivanov, Dieter Spreen, Marc Herbstritt
2016 Dagstuhl Reports  
sharing tools and techniques between areas based on their common use of topological methods and duality.  ...  In this seminar, we focused on applications of duality to semantics for probability in computation, to algebra and coalgebra, and on applications in complexity theory.  ...  On the other hand, the Chu-like category may turn out to be a better setting than the cartesian closed one in which to do this study.  ... 
doi:10.4230/dagrep.5.10.66 dblp:journals/dagstuhl-reports/GehrkeJSS15 fatcat:qyd6kvvxq5ehlhmevzr5b7l27u

On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces

DANIELE TURI, JAN RUTTEN
1998 Mathematical Structures in Computer Science  
The properties of coalgebraic coinduction are studied both at an abstract categorical level and in some specific categories used in semantics, namely categories of non-well-founded sets, partial orders  ...  The programme is based on a suitable interplay between the induction principle, which pervades modern mathematics, and a dual, non-standard 'coinduction principle', which underlies many of the recursive  ...  X, k and Y , exists, and it is the ordered pullback of the coinductive extensions k @ and @ .  ... 
doi:10.1017/s0960129598002588 fatcat:yszyhcmjsjeqbgzj73exutmbem

Concurrency Theory: A Historical Perspective on Coinduction and Process Calculi [chapter]

Jos C.M. Baeten, Davide Sangiorgi
2014 Handbook of the History of Logic  
Acknowledgements The authors are grateful to Luca Aceto and Rob van Glabbeek for comments on an earlier draft of the paper.  ...  Further, there are ⊔ and cases denoting alternative composition, ; denoting sequential composition, and // denoting (quasi-)parallel composition.  ...  In [Bekič, 1971] , Bekič addresses the semantics of what he calls "quasi-parallel execution of processes".  ... 
doi:10.1016/b978-0-444-51624-4.50009-5 fatcat:o4fvjxxppvf2pkpjkcpj3erfym

Least and Greatest Fixed Points in Linear Logic [article]

David Baelde
2010 arXiv   pre-print
and ?), we add least and greatest fixed point operators.  ...  The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior.  ...  ones, and limits the coinduction rule to coinvariants of smaller "level" than the considered coinductive object.  ... 
arXiv:0910.3383v4 fatcat:3znfpcjtd5e5rfoffvxkltibyq

A verified prover based on ordered resolution

Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel
2019 Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019  
The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning.  ...  As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establish its soundness and refutational completeness.  ...  Eugene Kotelnikov, Stephan Schulz, and Geoff Sutcliffe graciously answered our questions about Vampire, E, and TPTP.  ... 
doi:10.1145/3293880.3294100 dblp:conf/cpp/SchlichtkrullBT19 fatcat:ftlcitpp7rbsbevdkf6nl6r25y

Polymorphic Higher-Order Termination

Lukasz Czajka, Cynthia Kop, Michael Wagner
2019 International Conference on Rewriting Techniques and Applications  
We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism.  ...  As an illustration of the potential of our method, we prove termination of a substantial fragment of full intuitionistic second-order propositional logic with permutative conversions.  ...  In fact, we will do more: rather than a single partial ordering, we will define an ordering pair: a pair of a quasi-ordering and a compatible well-founded ordering .  ... 
doi:10.4230/lipics.fscd.2019.12 dblp:conf/rta/0001K19 fatcat:k3okaqzorngmnegbc6inmnuj7u

Interactive key frame selection model

Jian-quan Ouyang, Jin-tao Li, Huanrong Tang
2006 Journal of Visual Communication and Image Representation  
The model of KFS and IKFS are proved to satisfy the criterion of induction and coinduction, respectively.  ...  Video summarization can provide a fine representation of the content of video stream and reduce a large amount of data involved in video indexing, browsing, and retrieval.  ...  This work is supported by Digital Olympic Project in China (2001BA904B07) and Scientific Research Fund of Hunan Provincial Education Department (03C484).  ... 
doi:10.1016/j.jvcir.2006.03.003 fatcat:mjr7i47u5nexhos5keyq3on4mm

Canonical proof-objects for coinductive programming: infinets with infinitely many cuts

Abhishek De, Luc Pellissier, Alexis Saurin
2021 23rd International Symposium on Principles and Practice of Declarative Programming  
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.  ...  HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not.  ...  benefit from less sequential proof structures and (iii) infinets would serve as better models of coinductive programs.  ... 
doi:10.1145/3479394.3479402 fatcat:dvy2ybadtzbcbjiwqid6c6zr3a

All the λ-Terms are Meaningful for the Infinitary Relational Model [article]

Pierre Vial
2018 arXiv   pre-print
Then, using the resource-awareness of sequential intersection types (system S) and tracking, we prove that infinite types are able to characterize the order (arity) of every λ-terms and that, in the infinitary  ...  Infinite types and formulas are known to have really curious and unsound behaviors.  ...  3: the behaviour of normal chains is far better understandable.  ... 
arXiv:1612.06740v2 fatcat:xg32k4mqcfbnxasezbt4uk7asa

Polymorphic Higher-order Termination [article]

Łukasz Czajka, Cynthia Kop
2019 arXiv   pre-print
We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism.  ...  As an illustration of the potential of our method, we prove termination of a substantial fragment of full intuitionistic second-order propositional logic with permutative conversions.  ...  In fact, we will do more: rather than a single partial ordering, we will define an ordering pair: a pair of a quasi-ordering and a compatible well-founded ordering .  ... 
arXiv:1904.09859v1 fatcat:p4tgxmlepbdqvcveegzqa5dlu4

Strong Symmetry Defined by Twisting Modules, Applied to Quasi-Hereditary Algebras with Triangular Decomposition and Vanishing Radical Cube

Steffen König, Changchang Xi
1998 Communications in Mathematical Physics  
This covers both Temperley-Lieb algebras and q-Schur algebras of finite representation type.  ...  Using the structure of these modules, for some algebras with vanishing radical cube the characteristic tilting module is described and its endomorphism ring is computed.  ...  The partial order of partitions indexing simple modules in these diagrams is the same as the partial order used for defining quasi-heredity.  ... 
doi:10.1007/s002200050458 fatcat:sduigczfkfcfhll4vrmosm7a2u

Modal Reasoning = Metric Reasoning, via Lawvere [article]

Ugo Dal Lago, Francesco Gavazzo
2021 arXiv   pre-print
In this work, we show that coinductive equivalences can be extended to a modal setting, and we do so by generalising Abramsky's applicative bisimilarity to coeffectful behaviours.  ...  The theory of program equivalence for modal and coeffectful languages, however, is considerably underdeveloped if compared to the denotational and operational semantics of such languages.  ...  Therefore, a better question is: how much of the theory of non-modal program equivalence can be extended to a modal and coeffectful setting?  ... 
arXiv:2103.03871v1 fatcat:x6prnsruf5fdtpyrhgv5fzk4vu
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