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Linearly Used Effects: Monadic and CPS Transformations into the Linear Lambda Calculus [chapter]

Masahito Hasegawa
2002 Lecture Notes in Computer Science  
We propose a semantic and syntactic framework for modelling linearly used effects, by giving the monadic transforms of the computational lambda calculus (considered as the core calculus of typed call-by-value  ...  s work on linearly used continuations can be put in this general picture. As a technical result we show the full completeness of the CPS transform into the linear lambda calculus.  ...  Part of this work was carried out while the author was visiting Laboratory for Foundations of Computer Science, University of Edinburgh.  ... 
doi:10.1007/3-540-45788-7_10 fatcat:yci7e6djxfa43amh2mdd5373ty

Semantics of Linear Continuation-Passing in Call-by-Name [chapter]

Masahito Hasegawa
2004 Lecture Notes in Computer Science  
Its semantic interpretation into a category of linear continuations then amounts to the call-by-name continuation-passing style (CPS) transformation into a linear lambda calculus with sum types.  ...  On the syntactic side, we give a simply typed call-by-name λµcalculus in which the use of names (continuation variables) is restricted to be linear.  ...  Acknowledgements I thank Oliver Danvy for asking me how linear CPS for callby-name can be semantically understood, and anonymous reviewers for helpful comments.  ... 
doi:10.1007/978-3-540-24754-8_17 fatcat:ehx7zccbaffv3belzzcd5nobyi

Algebraic effects and effect handlers for idioms and arrows

Sam Lindley
2014 Proceedings of the 10th ACM SIGPLAN workshop on Generic programming - WGP '14  
Plotkin and Power's algebraic effects combined with Plotkin and Pretnar's effect handlers provide a foundation for modular programming with effects.  ...  We present a generalisation of algebraic effects and effect handlers to support other kinds of effectful computations corresponding to McBride and Paterson's idioms and Hughes' arrows.  ...  Another direction is to explore algebraic effects and handlers for other variations on the basic theme, such as for linear and dependent types. the first equation is equivalent to the CPS term get ()(1  ... 
doi:10.1145/2633628.2633636 dblp:conf/icfp/Lindley14 fatcat:a4dopmlelva27axzbiifjav6ty

Linear-use CPS translations in the Enriched Effect Calculus

Jeff Egger, Rasmus Møgelberg, Alex Simpson, Luke Ong
2012 Logical Methods in Computer Science  
We first observe that established call-by-value and call-by name linear-use CPS translations of simply-typed lambda-calculus into intuitionistic linear logic (ILL) land in the fragment of ILL given by  ...  This paper explores the enriched effect calculus as a target language for continuation-passing-style (CPS) translations in which the typing of the translations enforces the linear usage of continuations  ...  Acknowledgements We thank Masahito Hasegawa, Paul Levy and the anonymous referees for helpful suggestions.  ... 
doi:10.2168/lmcs-8(4:2)2012 fatcat:a6ctwy4aszfvhhtubcxihtg6mi

Classical Linear Logic of Implications [chapter]

Masahito Hasegawa
2002 Lecture Notes in Computer Science  
The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a technically managable axiomatization without commuting conversions.  ...  We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin's system for the intuitionistic case.  ...  In [6] the {→, }-fragment of DILL (with recursive types) is used as the target language of CPS transformations. In [13] we extend the idea of [6] to general monadic transformations into the {!  ... 
doi:10.1007/3-540-45793-3_31 fatcat:7iuphna6mndvpdomudjssia6x4

Classical linear logic of implications

MASAHITO HASEGAWA
2005 Mathematical Structures in Computer Science  
The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a technically managable axiomatization without commuting conversions.  ...  We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin's system for the intuitionistic case.  ...  In [6] the {→, }-fragment of DILL (with recursive types) is used as the target language of CPS transformations. In [13] we extend the idea of [6] to general monadic transformations into the {!  ... 
doi:10.1017/s0960129504004621 fatcat:3eb5pyvykbg75ntfgfbpafkd7e

Equational axiomatization of call-by-name delimited control

Yukiyoshi Kameyama, Asami Tanaka
2010 Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10  
Control operators for delimited continuations are useful in various fields such as partial evaluation, CPS translation, and representation of monadic effects.  ...  The key observations in our proof are (1) we need to use the linearity of certain variables in the CPS terms, and (2) we must distinguish continuation variables from ordinary variables in the source terms  ...  Special thanks go to anonymous reviewers of FLOPS and PPDP, who have pointed out errors in the earlier versions of this paper.  ... 
doi:10.1145/1836089.1836100 dblp:conf/ppdp/KameyamaT10 fatcat:nxoi2vib2fgcvlc3g6hmhabkhe

Embedding session types in Haskell

Sam Lindley, J. Garrett Morris
2016 SIGPLAN notices  
We extend an existing HOAS embedding of linear λcalculus with a set of core session-typed primitives, using indexed type families to express the constraints of the session typing discipline.  ...  Our safety guarantees, including deadlock freedom, are assured statically and introduce no additional runtime overhead.  ...  Acknowledgments Thanks to Jeff Polakow for providing his Haskell embedding of linear λ-calculus and for discussions of this work. Thanks for Dominic Orchard for helpful feedback.  ... 
doi:10.1145/3241625.2976018 fatcat:idezyicg3vaprb3usfzs4rihzu

Embedding session types in Haskell

Sam Lindley, J. Garrett Morris
2016 Proceedings of the 9th International Symposium on Haskell - Haskell 2016  
We extend an existing HOAS embedding of linear λcalculus with a set of core session-typed primitives, using indexed type families to express the constraints of the session typing discipline.  ...  Our safety guarantees, including deadlock freedom, are assured statically and introduce no additional runtime overhead.  ...  Acknowledgments Thanks to Jeff Polakow for providing his Haskell embedding of linear λ-calculus and for discussions of this work. Thanks for Dominic Orchard for helpful feedback.  ... 
doi:10.1145/2976002.2976018 dblp:conf/haskell/LindleyM16 fatcat:vnfdahrezvgchdido4f5q6gj3q

On the semantics of parsing actions

Hayo Thielecke
2014 Science of Computer Programming  
Specifically, the semantics is inspired by the categorical semantics of lambda calculi and the use of premonoidal categories for the semantics of effects in programming languages.  ...  As an idealization of the input language of parser generators, we define a call-by-value calculus with first-order functions and a type-and-effect system where the effects are given by sequences of grammar  ...  Such a lambda calculus could be interpreted using the Kleisli category of a monad [4] or a Freyd category [16] .  ... 
doi:10.1016/j.scico.2013.04.010 fatcat:2grt423rdfggddgcjioophkxsa

Functional semantics of parsing actions, and left recursion elimination as continuation passing

Hayo Thielecke
2012 Proceedings of the 14th symposium on Principles and practice of declarative programming - PPDP '12  
Specifically, the semantics is inspired by the categorical semantics of lambda calculi and the use of premonoidal categories for the semantics of effects in programming languages.  ...  We prove the semantic transformation correct and relate it to continuation passing style, a widely studied transformation in lambda calculi and functional programming.  ...  Such a lambda calculus could be interpreted using the Kleisli category of a monad [17] or a Freyd category [24] .  ... 
doi:10.1145/2370776.2370789 dblp:conf/ppdp/Thielecke12 fatcat:d3wbbmzqv5gdfntjk7toqfxjxq

Implementing first-class polymorphic delimited continuations by a type-directed selective CPS-transform

Tiark Rompf, Ingo Maier, Martin Odersky
2009 SIGPLAN notices  
To tackle the problem of implementing first-class continuations under the adverse conditions brought upon by the Java VM, we employ a selective CPS transform, which is driven entirely by effect-annotated  ...  We use Scala's pluggable typing architecture to implement a simple type and effect system, which discriminates expressions with control effects from those without and accurately tracks answer type modification  ...  Acknowledgments We would like to thank Philipp Haller for suggesting the use of proceed to make Scala actors continuation aware.  ... 
doi:10.1145/1631687.1596596 fatcat:46levrwjozbyhpmr6qmq3e3bem

Implementing first-class polymorphic delimited continuations by a type-directed selective CPS-transform

Tiark Rompf, Ingo Maier, Martin Odersky
2009 Proceedings of the 14th ACM SIGPLAN international conference on Functional programming - ICFP '09  
To tackle the problem of implementing first-class continuations under the adverse conditions brought upon by the Java VM, we employ a selective CPS transform, which is driven entirely by effect-annotated  ...  We use Scala's pluggable typing architecture to implement a simple type and effect system, which discriminates expressions with control effects from those without and accurately tracks answer type modification  ...  Acknowledgments We would like to thank Philipp Haller for suggesting the use of proceed to make Scala actors continuation aware.  ... 
doi:10.1145/1596550.1596596 dblp:conf/icfp/RompfMO09 fatcat:z44qbxwb65enlmzzrkhkjzk5ou

Linear Regions Are All You Need [chapter]

Matthew Fluet, Greg Morrisett, Amal Ahmed
2006 Lecture Notes in Computer Science  
The type-and-effects system of the Tofte-Talpin region calculus makes it possible to safely reclaim objects without a garbage collector.  ...  We introduce λ rgnUL , a core calculus that is powerful enough to encode Tofte-Talpin-like languages, and that eliminates the LIFO restriction.  ...  The meat of this paper picks up where this translation left off by further translating F RGN to a substructural polymorphic lambda calculus where the internals of the indexed monad are exposed (Section  ... 
doi:10.1007/11693024_2 fatcat:vrtfv6ls7jcjlosrl45x6rbyea

Rolling your own mutable ADT---a connection between linear types and monads

Chih-Ping Chen, Paul Hudak
1997 Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '97  
A CPS-like translation from the original ADT axioms into monadic ones is also described and proven correct, so that reasoning can be accomplished at the monadic level without exposing the state.  ...  A methodology is described whereby a linear ADT may be rigorously encapsulated within a state monad.  ...  Acknowledgements Thanks to Phil Wadler and the anonymous referees for their helpful comments on previous versions of this paper. This research was supported in part by NSF under Grant CCR-9404786.  ... 
doi:10.1145/263699.263708 dblp:conf/popl/ChenH97 fatcat:dlmznz35r5hsvlzkvffxc6hvwe
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