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Inductive and Coinductive Predicate Liftings for Effectful Programs

Niccolò Veltri, Niels F.W. Voorneveld
2021 Electronic Proceedings in Theoretical Computer Science  
Appropriate definitions of inductive and coinductive predicate liftings are given for a multitude of effect examples. The whole development has been fully formalized in the Agda proof assistant.  ...  The predicate liftings are used as a basis for an endogenous logic of behavioural properties for higher-order programs.  ...  From the inductive and coinductive predicate liftings, we generate a logic for higher-order programs, extending the logic from [27] with coinductive predicate liftings (modalities).  ... 
doi:10.4204/eptcs.351.16 fatcat:r6nneo25tngdzej5aqfqqjtnme

Coinduction in Flow: The Later Modality in Fibrations

Henning Basold, Michael Wagner
2019 Conference on Algebra and Coalgebra in Computer Science  
First, we provide in Section 2 a brief overview over fibrations, coinductive predicates and well-founded induction.  ...  For instance, we will show how recursive proofs can be obtained for arbitrary (syntactic) first-order logics, for coinductive set-predicates, and for the probabilistic modal µ-calculus.  ...  In this paper, we will focus on the use of recursion as a method for coinductive proofs and coinductive programming.  ... 
doi:10.4230/lipics.calco.2019.8 dblp:conf/calco/Basold19 fatcat:de4sngban5ggll2hp2ifba3shm

A Fibrational Method of Indexed Coinductive Data Types

2020 Tehnički Vjesnik  
Example analyses prove the effectiveness of the proposed fibrational method and its applicability in program languages.  ...  As a fundamental issue in type theory, indexed coinductive data types (ICDT, for short) is of crucial importance, which is essentially semantic computing problem in programming.  ...  Inductive and coinductive data types form a complementary solution to improve the abilities of syntax construction and the semantic computation of program languages.  ... 
doi:10.17559/tv-20191130092745 fatcat:kvzljd7ewbaalk4w7hlindrpty

A coinductive semantics of the Unlimited Register Machine

Alberto Ciaffaglione
2011 Electronic Proceedings in Theoretical Computer Science  
We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus  ...  of (Co)Inductive Constructions type theory.  ...  Actually, the computation under URM programs is captured by the more involved inductive predicate cp + , with arity Pgm ×Cgn ∞ × PC ×Cgn ∞ , and the coinductive predicate cp ∞ , with arity Pgm ×Cgn ∞ ×  ... 
doi:10.4204/eptcs.73.7 fatcat:6eztb747uvhc5m3heabqwmblmq

Dijkstra monads forever: termination-sensitive specifications for interaction trees

Lucas Silver, Steve Zdancewic
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
We model such programs using interaction trees, a coinductive datatype for representing programs with algebraic effects in Coq, which we further develop by adding trace semantics.  ...  This paper extends the Dijkstra monad framework, designed for writing specifications over effectful programs using monadic effects, to handle termination sensitive specifications over interactive programs  ...  We are grateful to all the members of Penn's PL Club and the DeepSpec project for their collaboration and feedback, and we greatly appreciate the the reviewers' comments and suggestions.  ... 
doi:10.1145/3434307 fatcat:4h7fstdnvbbdle33g3z2s6f2c4

Indexed Induction and Coinduction, Fibrationally

Neil Ghani, Patricia Johann, Clement Fumex, Bartek Klin
2013 Logical Methods in Computer Science  
Secondly, we show that inductive and coinductive indexed types also admit sound induction and coinduction rules.  ...  We finish the paper by considering the more general case of sound induction and coinduction rules for indexed data types when the indexing is itself given by a fibration.  ...  Acknowledgement We thank the reviewers for their helpful comments and suggestions.  ... 
doi:10.2168/lmcs-9(3:6)2013 fatcat:77pcj77n5zfshpvcwstsrvx5zq

Proving partial-correctness and invariance properties of transition-system models

Vlad Rusu, Gilles Grimaud, Michaël Hauspie
2019 Science of Computer Programming  
We propose an approach for proving partial-correctness and invariance properties of transition systems, and illustrate it on a model of a security hypervisor.  ...  We propose a coinductive proof system for the resulting logic, which can be seen as performing an "infinite symbolic execution" of the transition-system model under verification.  ...  We thank the anonymous reviewers of earlier versions of this paper for their useful hints and suggestions, especially the suggestion to use coinduction, and David Nowak for his lessons on coinduction in  ... 
doi:10.1016/j.scico.2019.102342 fatcat:aqregmbhdfau7i6ncnibu37n7m

Coalgebras in functional programming and type theory

Venanzio Capretta
2011 Theoretical Computer Science  
This is a survey article on the use of coalgebras in functional programming and type theory. It presents the basic theory underlying the implementation of coinductive types, families and predicates.  ...  It gives an overview of the application of corecursive methods to the study of general recursion, formal power series, tabulations of functions on inductive data.  ...  Readers are encouraged to delve deeper into the cited literature for more technical and ample expositions of these topics and others that had to be omitted here.  ... 
doi:10.1016/j.tcs.2011.04.024 fatcat:rh7dkwzphvd3tcc5xzfe3kwquu

Indexed Induction and Coinduction, Fibrationally [chapter]

Clément Fumex, Neil Ghani, Patricia Johann
2011 Lecture Notes in Computer Science  
Secondly, we show that inductive and coinductive indexed types also admit sound induction and coinduction rules.  ...  Secondly, we show that inductive and coinductive indexed types also admit sound induction and coinduction rules.  ...  Acknowledgement We thank the reviewers for their helpful comments and suggestions.  ... 
doi:10.1007/978-3-642-22944-2_13 fatcat:lons4fr3xnfndmrzhi7roncwaa

Coinductive Logic Programming [chapter]

Luke Simon, Ajay Mallya, Ajay Bansal, Gopal Gupta
2006 Lecture Notes in Computer Science  
We describe the implementation of coinductive logic programming found in Logtalk, discussing its features and limitations.  ...  As Logtalk uses as a back-end compiler a compatible Prolog system, we discuss the status of key Prolog features for an efficient and usable implementation of coinduction.  ...  We thank Gopal Gupta, Feliks Kluźniak, Neda Saeedloei, Brian DeVries, and Kyle Marple for helpful discussions on coinduction during a sabbatical visit to U.T.Dallas and for most of the coinduction examples  ... 
doi:10.1007/11799573_25 fatcat:y2kxgo26uvdzvpqp5w5kwyg7n4

Quotienting the Delay Monad by Weak Bisimilarity [chapter]

James Chapman, Tarmo Uustalu, Niccolò Veltri
2015 Lecture Notes in Computer Science  
We have fully formalized our results in the Agda dependently typed programming language.  ...  In this setting, it is difficult to define the intended monad multiplication for the quotiented datatype.  ...  Acknowledgement We thank Thorsten Altenkirch, Andrej Bauer, Bas Spitters and our anonymous referees for comments.  ... 
doi:10.1007/978-3-319-25150-9_8 fatcat:pqu25mdn7zgilgchcj7tzkeeku

The power of parameterization in coinductive proof

Chung-Kil Hur, Georg Neis, Derek Dreyer, Viktor Vafeiadis
2013 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '13  
In this paper, we show how to support coinductive proofs that are both compositional and incremental, using a dead simple construction we call the parameterized greatest fixed point.  ...  In addition to presenting the lattice-theoretic foundations of parameterized coinduction, demonstrating its utility on representative examples, and studying its composition with "up-to" techniques, we  ...  We would also like to thank Andreas Abel, Fritz Henglein, Neel Krishnaswami, Andy Pitts, and Glynn Winskel for helpful discussions, as well as the anonymous reviewers for their constructive feedback.  ... 
doi:10.1145/2429069.2429093 dblp:conf/popl/HurNDV13 fatcat:rt4pdbucxrdujkrwfiusg3rgsa

The power of parameterization in coinductive proof

Chung-Kil Hur, Georg Neis, Derek Dreyer, Viktor Vafeiadis
2013 SIGPLAN notices  
In this paper, we show how to support coinductive proofs that are both compositional and incremental, using a dead simple construction we call the parameterized greatest fixed point.  ...  In addition to presenting the lattice-theoretic foundations of parameterized coinduction, demonstrating its utility on representative examples, and studying its composition with "up-to" techniques, we  ...  We would also like to thank Andreas Abel, Fritz Henglein, Neel Krishnaswami, Andy Pitts, and Glynn Winskel for helpful discussions, as well as the anonymous reviewers for their constructive feedback.  ... 
doi:10.1145/2480359.2429093 fatcat:5b5cn5fn5jbq5k3uce56ppsexi

Quotienting the delay monad by weak bisimilarity

JAMES CHAPMAN, TARMO UUSTALU, NICCOLÒ VELTRI
2017 Mathematical Structures in Computer Science  
This type suffices for constructing a monad, which is isomorphic to the one of Altenkirch et al. We have fully formalized our results in the Agda dependently typed programming language.  ...  We give a solution where we postulate some principles, crucially proposition extensionality and the (semi-classical) axiom of countable choice.  ...  Acknowledgement We thank Thorsten Altenkirch, Andrej Bauer, Bas Spitters and our anonymous referees for comments.  ... 
doi:10.1017/s0960129517000184 fatcat:ihp5hr4obbb3jcgqwyjndd77l4

A supposedly fun thing i may have to do again

Alberto Momigliano
2012 Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice - LFMTP '12  
This turns out to be a very challenging task for HOAS-based systems, as it entails a demanding combination of inductive and coinductive reasoning on open terms, for which no other existing HOAS-based system  ...  is equipped for.  ...  Thanks to Andrew Gacek for his help with Abella in general and in particular with the inductive structure of the Howe substitution lemma, to David Baelde, who told me to embrace the use of meta-level contexts  ... 
doi:10.1145/2364406.2364411 fatcat:xipggcki5ja2re6xefiq2r6icu
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