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The gradualizer: a methodology and algorithm for generating gradual type systems

Matteo Cimini, Jeremy G. Siek
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
We also report on an implementation of the Gradualizer that takes a type system expressed in lambda-prolog and outputs its gradually typed version and a compiler to the cast calculus in lambda-prolog.  ...  Based on this methodology, we present the Gradualizer, an algorithm that generates a gradual type system from a well-formed type system and also generates a compiler to the cast calculus.  ...  Restriction 1 is a common restriction for many reasonable logic programs.  ... 
doi:10.1145/2837614.2837632 dblp:conf/popl/CiminiS16 fatcat:7sky5l3o6ncojixkqjsmsgvgsu

Gradualizing the Calculus of Inductive Constructions [article]

Meven Lennon-Bertrand, Kenji Maillard, Nicolas Tabareau, Éric Tanter
2021 arXiv   pre-print
Acknowledging the ordeal of a fully formal development in a proof assistant such as Coq, we investigate gradual variations on the Calculus of Inductive Construction (CIC) for swifter prototyping with imprecise  ...  We first present a bidirectional elaboration of GCIC to a dependently-typed cast calculus, CastCIC, which elucidates the interrelation between typing, conversion, and the gradual guarantees.  ...  A gradual version of the simply-typed lambda calculus (STLC) enjoys such expressiveness that it can embed the untyped lambda calculus.  ... 
arXiv:2011.10618v3 fatcat:u2pca6lkdzfwtd7i5k3gh4mela

Design and evaluation of gradual typing for python

Michael M. Vitousek, Andrew M. Kent, Jeremy G. Siek, Jim Baker
2014 Proceedings of the 10th ACM Symposium on Dynamic languages - DLS '14  
In this paper we present Reticulated Python, a system for experimenting with gradual-typed dialects of Python.  ...  Siek and Taha (2006) introduced an approach to combining static and dynamic typing in a fine-grained manner through the notion of type consistency in the static semantics and run-time casts in the dynamic  ...  Acknowledgments We thank Steev Young and Matteo Cimini for their help in testing the Reticulated Python implementation.  ... 
doi:10.1145/2661088.2661101 dblp:conf/dls/VitousekKSB14 fatcat:snwsjwzahjfbdhcmgszpqznepe

Design and evaluation of gradual typing for python

Michael M. Vitousek, Andrew M. Kent, Jeremy G. Siek, Jim Baker
2014 SIGPLAN notices  
In this paper we present Reticulated Python, a system for experimenting with gradual-typed dialects of Python.  ...  Siek and Taha (2006) introduced an approach to combining static and dynamic typing in a fine-grained manner through the notion of type consistency in the static semantics and run-time casts in the dynamic  ...  Acknowledgments We thank Steev Young and Matteo Cimini for their help in testing the Reticulated Python implementation.  ... 
doi:10.1145/2775052.2661101 fatcat:3omqb5wdszaj3motvwr2wqeuym

Consistent Subtyping for All [chapter]

Ningning Xie, Xuan Bi, Bruno C. d. S. Oliveira
2018 Lecture Notes in Computer Science  
Consistent subtyping is employed in some gradual type systems to validate type conversions.  ...  The second goal of this paper is to present a gradually typed calculus for implicit (higher-rank) polymorphism that uses our new notion of consistent subtyping.  ...  In order to preserve the orthogonality between subtyping and consistency, we require to be a common supertype of all static types, as shown in rule S-Top.  ... 
doi:10.1007/978-3-319-89884-1_1 fatcat:zlxtuitbrvga5eak4n2hsu64w4

Towards Gradually Typed Capabilities in the Pi-Calculus

Matteo Cimini
2019 Electronic Proceedings in Theoretical Computer Science  
We present our preliminary work towards a gradually typed version of this calculus.  ...  Gradual typing is an approach to integrating static and dynamic typing within the same language, and puts the programmer in control of which regions of code are type checked at compile-time and which are  ...  We also have discussed our future plans, especially w.r.t. the key properties that a gradually typed calculus such as ours should afford.  ... 
doi:10.4204/eptcs.304.5 fatcat:vnrzanplrvarxf2j7qgy7udzim

Page 4355 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
This type of reasoning under uncertainty involves what is in the A. I. literature sometimes described as common sense reasoning.  ...  constraint subnetwork will be searched with a gradually shrinking domain.  ... 

Extending Dylan's type system for better type inference and error detection

Hannes Mehnert
2010 Proceedings of the 2010 international conference on Lisp - ILC '10  
Gradual typing [26] provides the best of both worlds. This paper shows how to define and implement gradual typing in Dylan, traditionally a dynamically typed language.  ...  In this paper Dylan is extended with function types and parametric polymorphism. We implemented the type system and a unification-based type inference algorithm in the mainstream Dylan compiler.  ...  A type system for Ob ? <: (the gradual object calculus) is defined in [27] , as well as a type checking algorithm, operational semantics and safety proofs.  ... 
doi:10.1145/1869643.1869645 dblp:conf/lfp/Mehnert10 fatcat:4z4umzuzhzepbkvdubyxzfp7km

KafKa: Gradual Typing for Objects

Benjamin Chung, Paley Li, Francesco Zappa Nardelli, Jan Vitek, Michael Wagner
2018 European Conference on Object-Oriented Programming  
In this paper, we show that four of the most common gradual type systems provide distinct guarantees, and we give a formal framework for comparing gradual type systems for objectoriented languages.  ...  Within this framework, different gradual type systems become translations between a common source and target language, allowing for direct comparison of semantics and guarantees.  ...  To enable direct comparison, we propose to translate gradually typed languages down to a common calculus designed to highlight the distinctions between designs.  ... 
doi:10.4230/lipics.ecoop.2018.12 dblp:conf/ecoop/ChungLNV18 fatcat:fafnygxomvgdzhi6d3lbebyn5m

Operation Refinement and Monotonicity in the Schema Calculus [chapter]

Moshe Deutsch, Martin C. Henson, Steve Reeves
2003 Lecture Notes in Computer Science  
Combining Operation Refinement with the Schema Calculus A schema calculus operator is monotonic with respect to refinement if the schema expression denoted by its application to the individual (and independent  ...  It is well known that, and in contrast to other paradigms such as the refinement calculus and even B, the most powerful characteristic of Z, as a specification language, is  ...  Moreover, in many contexts we need to compare bindings over a common restricted type. Definition 5. Ø Ì 0 0 = Ì Ø Ì 1 1 = Ø 0 ↾ Ì = Ø 1 ↾ Ì (Ì Ì 0 and Ì Ì 1 ).  ... 
doi:10.1007/3-540-44880-2_9 fatcat:fek47wcs65dahgw2fxjshbtglu

Efficient Gradual Typing [article]

Andre Kuhlenschmidt and Deyaaeldeen Almahallawi and Jeremy G. Siek
2018 arXiv   pre-print
One would hope that the performance in a gradually typed language would range between that of a dynamically typed language and a statically typed language.  ...  Gradual typing combines static and dynamic typing in the same program.  ...  Semantics of a Gradual Language The type system of Grift's input language is the standard one for the gradually typed lambda calculus [30, 36, 39] .  ... 
arXiv:1802.06375v1 fatcat:jtrkr2j6mbfpvb4ilzh2ceeoo4

Abstracting gradual typing

Ronald Garcia, Alison M. Clark, Éric Tanter
2016 SIGPLAN notices  
In this paper, we propose a new formal foundation for gradual typing, drawing on principles from abstract interpretation to give gradual types a semantics in terms of pre-existing static types.  ...  Given a syntax-directed static typing judgment, the AGT approach induces a corresponding gradual typing judgment.  ...  Acknowledgments We would like to thank Joshua Dunfield, Matteo Cimini, Jeremy Siek, Khurram A. Jafery, Felipe Bañados Schwerter, Matías Toro, and the anonymous referees for their feedback.  ... 
doi:10.1145/2914770.2837670 fatcat:4qy6yaeimvabhexpwp7qqky2hq

Abstracting gradual typing

Ronald Garcia, Alison M. Clark, Éric Tanter
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
In this paper, we propose a new formal foundation for gradual typing, drawing on principles from abstract interpretation to give gradual types a semantics in terms of pre-existing static types.  ...  Given a syntax-directed static typing judgment, the AGT approach induces a corresponding gradual typing judgment.  ...  Acknowledgments We would like to thank Joshua Dunfield, Matteo Cimini, Jeremy Siek, Khurram A. Jafery, Felipe Bañados Schwerter, Matías Toro, and the anonymous referees for their feedback.  ... 
doi:10.1145/2837614.2837670 dblp:conf/popl/GarciaCT16 fatcat:r3o6vix23rc4bkns4xosbhdxui

Reasoning about continuous change [chapter]

Tyrone O'Neill, Norman Foo
1998 Lecture Notes in Computer Science  
In this paper we show that a long-existing systems theoretic reasoning methodology, that of Zeigler's DEVS (discrete event system speci cation), not only subsumes the standard situation calculus but is  ...  event calculus t neatly into a DEVS framework.  ...  Such systems are described in a discrete event system speci cation (DEVS), a seven-tuple of the form <X,Y,States,ta, int , ext , >: X is a set of external input types Y is a set of external output types  ... 
doi:10.1007/bfb0095278 fatcat:c2zbgciktrenfh332nurhdxley

Call-by-name Gradual Type Theory [article]

Max S. New, Daniel R. Licata
2020 arXiv   pre-print
We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism,  ...  which were developed in blame calculi and to state the "gradual guarantee" theorem of gradual typing.  ...  We conjecture that much of our semantics will hold over, but with the dynamism and casts being in a different (preorder) category.  ... 
arXiv:1802.00061v6 fatcat:j2cf2pesejhdfms5b7u5snsknu
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