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Type Reconstruction for the Linear π-Calculus with Composite and Equi-Recursive Types [chapter]

Luca Padovani
2014 Lecture Notes in Computer Science  
We extend the linear π-calculus with composite and equi-recursive types in a way that enables the sharing of data containing linear values, provided that there is no overlapping access on such values.  ...  We show that the extended type system admits a complete type reconstruction algorithm and, as a by-product, we solve the problem of reconstruction for equi-recursive session types.  ...  The author is grateful to the FoSSaCS'14 reviewers for their detailed and insightful comments.  ... 
doi:10.1007/978-3-642-54830-7_6 fatcat:crwkrkqddjerbbowyeoagznche

Linear Logic, the π-calculus, and their Metatheory: A Recipe for Proofs as Processes [article]

Fabrizio Montesi, Marco Peressotti
2021 arXiv   pre-print
What remains is reconstructing the expected metatheory of session types and the π-calculus.  ...  Initiated by Abramsky [1994], the Proofs as Processes agenda is to establish a solid foundation for the study of concurrent languages, by researching the connection between linear logic and the π-calculus  ...  ACKNOWLEDGMENTS The authors thank Luís Cruz-Filipe and Davide Sangiorgi for useful discussions.  ... 
arXiv:2106.11818v1 fatcat:yezqvwkjbjfjfi5w77zwvgcgze

Session Type Inference in Haskell

Keigo Imai, Shoji Yuen, Kiyoshi Agusa
2011 Electronic Proceedings in Theoretical Computer Science  
We present an inference system for a version of the Pi-calculus in Haskell for the session type proposed by Honda et al.  ...  The full session type implementation in Haskell was first presented by Pucella and Tov, which is 'semi-automatic' in that the manual operations for the type representation was necessary.  ...  Acknowledgments The first author thanks his colleagues in IT Planning Inc. for supporting him during the writing of this paper.  ... 
doi:10.4204/eptcs.69.6 fatcat:wuuktetbafhb3ffatkn2a4of3m

Syntactic soundness proof of a type-and-capability system with hidden state

2012 Journal of functional programming  
The type system's features include: universal, existential, and recursive types; subtyping; a distinction between affine and unrestricted data; support for strong updates; support for naming values and  ...  of resources, ownership, and the manner in which they evolve with time.  ...  Acknowledgements I would like to thank Arthur Charguéraud for a pleasant and fruitful collaboration and for proof-reading this paper.  ... 
doi:10.1017/s0956796812000366 fatcat:zfpt3g34qjcsxfn7higmtlqk6u

Monotone recursive types and recursive data representations in Cedille [article]

Christopher Jenkins, Aaron Stump
2021 arXiv   pre-print
As applications, we use monotone recursive types to generically derive two recursive representations of data in lambda calculus, the Parigot and Scott encoding.  ...  This allows us to give efficient and provably unique (up to function extensionality) solutions for the iteration and primitive recursion schemes for Scott-encoded data.  ...  With equi-recursive types, the recursive type and its one-step unrolling are considered definitionally equal, and unroll and roll are not needed to pass between the two.  ... 
arXiv:2001.02828v2 fatcat:cohsc3e5vvcnhm6agsj7wu23qi

Dependent Pearl: Normalization by realizability [article]

Pierre-Évariste Dagand, Lionel Rieg, Gabriel Scherer
2020 arXiv   pre-print
Hoping to build a programming intuition of these proofs, we implement a normalization argument for the simply-typed lambda-calculus with sums: instead of a proof, it is described as a program in a dependently-typed  ...  Interestingly, the choices that we make when we define the reducibility predicates -- truth and falsity witnesses for each connective -- determine the evaluation order of the proof, with each datatype  ...  We furthermore thank Adrien Guatto, Guillaume Munch-Maccagnoni, Étienne Miquey, Philip Wadler and anonymous reviewers for their feedback on the article.  ... 
arXiv:1908.09123v2 fatcat:35wkwqrljfazfplohxemxo5cuy

Structured Communication-Centered Programming for Web Services

Marco Carbone, Kohei Honda, Nobuko Yoshida
2012 ACM Transactions on Programming Languages and Systems  
The global calculus, which originates from a Web service description language (W3C WS-CDL), describes an interaction scenario from a vantage viewpoint; the end-point calculus, an applied typed π -calculus  ...  Three principles of well-structured description and the type structures play a fundamental role in the theory.  ...  We thank WS-CDL WG members, in particular Gary Brown, Steve Ross-Talbot and Nickolas Kavantzas for collaborations; and Joshua Guttman for his comments on an early version of the article.  ... 
doi:10.1145/2220365.2220367 fatcat:bdafotbko5bkdbwixjnm2t2324

Multiparty session types, beyond duality

Alceste Scalas, Nobuko Yoshida
2018 Journal of Logical and Algebraic Methods in Programming  
errors, and determine which processes can safely interact with P . 1 The reason for the consistency constraint, and its limitations, are rather technical; we discuss them in detail in Section 3.  ...  For example, to type Q 1 in (3), the guarantee context is 1 , while the rely context is 2 , . . . , n , abstracting the behaviour of other processes composed with Q 1 (in this case, Q 2 , . . . , Q n )  ...  We thank the anonymous reviewers for their valuable comments and suggestions, and Raymond Hu, Julien Lange, and Bernardo Toninho for the fruitful discussion.  ... 
doi:10.1016/j.jlamp.2018.01.001 fatcat:w2e3mpd4gvhuhfovubhqx7efue

Verifying higher-order functional programs with pattern-matching algebraic data types

C.-H. Luke Ong, Steven James Ramsay
2011 Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '11  
Type-based model checking algorithms for higher-order recursion schemes have recently emerged as a promising approach to the verification of functional programs.  ...  We introduce pattern-matching recursion schemes (PMRS) as an accurate model of computation for functional programs that manipulate algebraic data-types.  ...  We would like to thank the anonymous reviewers for many useful comments.  ... 
doi:10.1145/1926385.1926453 dblp:conf/popl/OngR11 fatcat:x3ducwulabfbxn2qsobmyck4em

Parallel Complexity Analysis with Temporal Session Types [article]

Ankush Das, Jan Hoffmann, Frank Pfenning
2018 arXiv   pre-print
correspondence with intuitionistic linear logic.  ...  To make the analysis local and compositional, it is based on a conservative extension of binary session types, which structure the type and direction of communication between processes and stand in a Curry-Howard  ...  Our type definitions are equi-recursive so we can silently replace X by A during type checking, and no explicit rules for recursive types are needed.  ... 
arXiv:1804.06013v1 fatcat:ajqgodmbejbbnbnbx2sua6rdhi

Session-based concurrency, declaratively

Mauricio Cano, Hugo A. López, Jorge A. Pérez, Camilo Rueda
2021 Acta Informatica  
We develop a correct encoding of session $$\pi $$ π -calculus processes into the linear concurrent constraint calculus ($$\texttt {lcc}$$ lcc ), a declarative model of concurrency based on partial information  ...  We demonstrate the applicability of our results by using our encoding in the specification of realistic communication patterns with time and contextual information.  ...  Acknowledgements We are most grateful to the anonymous reviewers, whose precise, insightful remarks and suggestions helped us to substantially improve the paper.  ... 
doi:10.1007/s00236-021-00395-w fatcat:7val5yjk6fem3dvcjznfaiagya

Gradual type theory

2021 Journal of functional programming  
We then show that we can derive the behavior of casts for simple types from the corresponding eta equality principle and the assumption that the language satisfies a property called graduality, also known  ...  For instance, for simple types, a language designer might desire that beta-eta equality is valid.  ...  Acknowledgments The authors would like to thank Ron Garcia, Kenji Maillard and Gabriel Scherer for helpful discussions about this work.  ... 
doi:10.1017/s0956796821000125 fatcat:q3aufkpinzavpgj3yox77izqyy

A cost-aware logical framework [article]

Yue Niu
2021 arXiv   pre-print
As a full-spectrum dependent type theory, calf presents a unified language for programming and specification of both cost and behavior that can be integrated smoothly with existing mathematical libraries  ...  We deploy these techniques on a variety of case studies: we prove a tight, closed bound for Euclid's algorithm, verify the amortized complexity of batched queues, and derive tight, closed bounds for the  ...  ACKNOWLEDGMENTS We are grateful to Carlo Angiuli and Alex Kavvos for productive discussions on the topic of this research, and to Tristan Nguyen at AFOSR for his support.  ... 
arXiv:2107.04663v2 fatcat:3bit6tz77ff65drvkyiid5zgne

Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations [article]

Ali Shojaei-Fard
2010 arXiv   pre-print
singular frame such that based on the universal nature of this special loop, one can expect a Hall tree type scattering formula for physical information such as counterterms.  ...  In the third aim, with attention to the given rooted tree version of H_U and by applying the Connes-Marcolli's universal investigation, we discover a new geometric explanation from Dyson-Schwinger equations  ...  Let C(n) be the set of compositions of n and C(n, k) be the set of compositions of n with length k.  ... 
arXiv:1011.3290v1 fatcat:4mjnaifgx5fmrlgcpnxb7a3mqu

Compiling With Classical Connectives [article]

Paul Downen, Zena M. Ariola
2020 arXiv   pre-print
with user-defined types.  ...  We expand on this idea of logical duality---"and" is dual to "or;" proof is dual to refutation---for the purpose of compiling a variety of types.  ...  Acknowledgments This work is supported by the National Science Foundation under grants CCF-1719158 and CCF-1423617.  ... 
arXiv:1907.13227v3 fatcat:mgi4u4zhi5bsne2wcfyhlbbxl4
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