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Recovering Purity with Comonads and Capabilities [article]

Vikraman Choudhury, Neel Krishnaswami
2019 arXiv   pre-print
purity with a comonadic type discipline.  ...  We then identify the axiomatic categorical structure that the capability space model validates, and use these axioms to give a categorical semantics for our comonadic type system.  ...  Entertainingly, it turns out that just as monads are a good tool to extend pure languages with effects, comonads are a good tool to extend impure languages with purity!  ... 
arXiv:1907.07283v2 fatcat:o5ilmhffqnfudgohwdc3x32wg4

Quantitative Foundations for Resource Theories

Dan Marsden, Maaike Zwart, Michael Wagner
2018 Annual Conference for Computer Science Logic  
Our approach is compositional, with rich algebraic structure facilitating calculations.  ...  Much of the current research on these resource theories focuses on the analysis of specific resources such quantum entanglement, purity, randomness or asymmetry.  ...  Experts will be able to recover our definitions from the more abstract formulations.  ... 
doi:10.4230/lipics.csl.2018.32 dblp:conf/csl/MarsdenZ18 fatcat:47fgsrsfzbgt5pmtmbvfz5ehvq

Normalization for Fitch-Style Modal Calculi [article]

Nachiappan Valliappan, Fabian Ruch, Carlos Tomé Cortiñas
2022 arXiv   pre-print
Fitch-style modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock.  ...  We show that NbE models can be constructed for calculi that incorporate the K, T and 4 axioms of modal logic, as suitable instantiations of the possible-world semantics.  ...  RIT17-0023R) and WebSec (Ref. RIT17-0011).  ... 
arXiv:2207.12807v1 fatcat:xjvcaeor5jdv5kc5o6gqpg2dcu

Effects, capabilities, and boxes: from scope-based reasoning to type-based reasoning and back

Jonathan Immanuel Brachthäuser, Philipp Schuster, Edward Lee, Aleksander Boruch-Gruszecki
2022 Proceedings of the ACM on Programming Languages (PACMPL)  
Capabilities coupled with escape analysis offer safety and natural signatures, but are often overly coarse grained and restrictive.  ...  We present System C, which builds on and generalizes ideas from type-based escape analysis and demonstrates that capabilities and effects can be reconciled harmoniously.  ...  Comonadic Type Systems Comonadic type systems, as presented by Choudhury and Krishnaswami [2020] , allow programmers to reason about purity in an impure language.  ... 
doi:10.1145/3527320 fatcat:djxabuspmrd4bbnwwy4k4peo24

IMP with exceptions over decorated logic [article]

Burak Ekici
2018 arXiv   pre-print
In this paper, we facilitate the reasoning about impure programming languages, by annotating terms with 'decorations' that describe what computational (side) effect evaluation of a term may involve.  ...  In a point-free categorical language,called the 'decorated logic', we formalize the mutable state and the exception effects first separately, exploiting anice duality between them, and then combined.  ...  Acknowledgements We wish to thank the two anonymous reviewers for their careful reading of our manuscript and for insightful comments and suggestions.  ... 
arXiv:1503.05496v9 fatcat:pgde3xwx7ne2xhqjzfvosonan4

IMP with exceptions over decorated logic

Burak Ekici
2018 Discrete Mathematics & Theoretical Computer Science  
In this paper, we facilitate the reasoning about impure programming languages, by annotating terms with "decorations"that describe what computational (side) effect evaluation of a term may involve.  ...  In a point-free categorical language,called the "decorated logic", we formalize the mutable state and the exception effects first separately, exploiting anice duality between them, and then combined.  ...  Acknowledgements We wish to thank the two anonymous reviewers for their careful reading of our manuscript and for insightful comments and suggestions.  ... 
doi:10.23638/dmtcs-20-2-11 fatcat:gpyhuuhqrrfbbj5imftey3mq3i

Contextual Modal Types for Algebraic Effects and Handlers [article]

Nikita Zyuzin, Aleksandar Nanevski
2021 arXiv   pre-print
Programming languages with algebraic effects often track the computations' effects using type-and-effect systems.  ...  In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose to track algebraic effects of a computation with contextual modal types.  ...  ACKNOWLEDGMENTS We are grateful to Miëtek Bak, Alexander Gryzlov, and Patrick Cousot for their comments and discussions on the earlier presentation of the work.  ... 
arXiv:2103.02976v2 fatcat:sffmeshlanhojnn7w6rh4ahn7m

Scoped Capabilities for Polymorphic Effects [article]

Martin Odersky, Aleksander Boruch-Gruszecki, Edward Lee, Jonathan Brachthäuser, Ondřej Lhoták
2022 arXiv   pre-print
We describe CCsubBox, a calculus where such captured variables are succinctly represented in types, and show it can be used to safely implement effects and effect polymorphism via scoped capabilities.  ...  We discuss how the decision to track captured variables guides key aspects of the calculus, and show that CCsubBox admits simple and intuitive types for common data structures and their typical usage patterns  ...  In particular, we paraphrased with permission one reviewer's summary of our design decisions in the conclusion.  ... 
arXiv:2207.03402v2 fatcat:vzylmzpbifhi5jd2tmtmtlmrqi

A modal calculus for effect handling

Aleksandar Nanevski
2018
, the purity of the surrounding computation cannot be restored.  ...  Our idea is to use the [square] modality (which is a comonad) for hygienic propagation of effects, and leave the globalization of effect scope to [diamond].  ...  raise, and therefore, which handlers can restore its purity.  ... 
doi:10.1184/r1/6591038 fatcat:daaqgwklbnck5bo5rqsasvnsha

Galois extensions over commutative and non-commutative base [article]

Gabriella Böhm
2008 arXiv   pre-print
Extensions by coalgebras,bialgebras and Hopf algebras (over a commutative base ring) and by corings,bialgebroids and Hopf algebroids (over a non-commutative base algebra) are systematically recalled and  ...  It gives a review of various notions of Galois (and in particular cleft) extensions.  ...  For an invitation to the conference "New techniques in Hopf algebras and graded ring theory" in Brussels, September 19-23, 2006  ... 
arXiv:math/0701064v2 fatcat:uwjyqvbxmrepffczg6ae43yqbu

Scalable Handling of Effects (Dagstuhl Seminar 21292)

Danel Ahman, Amal Ahmed, Sam Lindley, Andreas Rossberg
2021
Built on solid mathematical foundations, effect handlers offer a uniform and elegant approach to programming with user-defined computational effects.  ...  Inspired by experience of developing, programming with, and reasoning about effect handlers in practice, we identify five key problem areas to be addressed at this Dagstuhl Seminar in order to enable effect  ...  Comonadic type systems enable transitioning between type-based and scope-based reasoning These systems allow programmers to reason about purity in an impure languages [2] .  ... 
doi:10.4230/dagrep.11.6.54 fatcat:daqhu5kcyffxvjxtl3qef6tid4

Dagstuhl Reports, Volume 11, Issue 6, July 2021, Complete Issue [article]

2021
socializing outside the official program, especially in these difficult times during the COVID-19 pandemic with all participants being eager to meet and do research together in real life.  ...  The unique scientific atmosphere and the historic building provided not only all the room we needed for our program and the working groups, but also plenty of opportunities for continued discussions and  ...  Comonadic type systems enable transitioning between type-based and scope-based reasoning These systems allow programmers to reason about purity in an impure languages [2] .  ... 
doi:10.4230/dagrep.11.6 fatcat:4ojdxh5mknhx5op4bxxc7ypgna

Coinductive Equivalences and Metrics for Higher-order Languages with Algebraic Effects

Francesco Gavazzo
2019
This dissertation investigates notions of program equivalence and metric for higher-order sequential languages with algebraic e ects.  ...  The rst part of this dissertation studies bisimulation-based notions of equivalence and re nement for λ-calculi enriched with algebraic e ects.  ...  As a consequence, as e ects are modelled as monads, coe ects are modelled as comonads.  ... 
doi:10.6092/unibo/amsdottorato/9075 fatcat:w3krkurbubdvxmaxlhxyhjwypy