34th European Conference on Object-Oriented Programming (ECOOP 2020)

Document

Complete Volume

DOI: 10.4230/LIPIcs.ECOOP.2020

LIPIcs, Volume 166, ECOOP 2020, Complete Volume

Authors: Robert Hirschfeld and Tobias Pape

Abstract

LIPIcs, Volume 166, ECOOP 2020, Complete Volume

Cite as

34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 1-906, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{hirschfeld_et_al:LIPIcs.ECOOP.2020,
  title =	{{LIPIcs, Volume 166, ECOOP 2020, Complete Volume}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{1--906},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020},
  URN =		{urn:nbn:de:0030-drops-131566},
  doi =		{10.4230/LIPIcs.ECOOP.2020},
  annote =	{Keywords: LIPIcs, Volume 166, ECOOP 2020, Complete Volume}
}

@InProceedings{imai_et_al:LIPIcs.ECOOP.2020.9,
  author =	{Imai, Keigo and Neykova, Rumyana and Yoshida, Nobuko and Yuen, Shoji},
  title =	{{Multiparty Session Programming With Global Protocol Combinators}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{9:1--9:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.9},
  URN =		{urn:nbn:de:0030-drops-131662},
  doi =		{10.4230/LIPIcs.ECOOP.2020.9},
  annote =	{Keywords: Multiparty Session Types, Communication Protocol, Concurrent and Distributed Programming, OCaml}
}

@InProceedings{madsen_et_al:LIPIcs.ECOOP.2020.12,
  author =	{Madsen, Magnus and Lhot\'{a}k, Ond\v{r}ej and Tip, Frank},
  title =	{{A Semantics for the Essence of React}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{12:1--12:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.12},
  URN =		{urn:nbn:de:0030-drops-131697},
  doi =		{10.4230/LIPIcs.ECOOP.2020.12},
  annote =	{Keywords: JavaScript, React, operational semantics, lifecycle, reconciliation}
}

@InProceedings{vandenvonder_et_al:LIPIcs.ECOOP.2020.19,
  author =	{Van den Vonder, Sam and Renaux, Thierry and Oeyen, Bjarno and De Koster, Joeri and De Meuter, Wolfgang},
  title =	{{Tackling the Awkward Squad for Reactive Programming: The Actor-Reactor Model}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{19:1--19:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.19},
  URN =		{urn:nbn:de:0030-drops-131768},
  doi =		{10.4230/LIPIcs.ECOOP.2020.19},
  annote =	{Keywords: functional reactive programming, reactive programming, reactive streams, actors, reactors}
}

Document

Pearl

DOI: 10.4230/LIPIcs.ECOOP.2020.20

A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl)

Authors: Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede

Abstract

Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold.

Cite as

Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede. A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 20:1-20:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{demuijnckhughes_et_al:LIPIcs.ECOOP.2020.20,
  author =	{de Muijnck-Hughes, Jan and Brady, Edwin and Vanderbauwhede, Wim},
  title =	{{A Framework for Resource Dependent EDSLs in a Dependently Typed Language}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{20:1--20:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.20},
  URN =		{urn:nbn:de:0030-drops-131773},
  doi =		{10.4230/LIPIcs.ECOOP.2020.20},
  annote =	{Keywords: Dependent Types, Algebraic Effect Handlers, Domain-Specific Languages, Embedded Domain Specific Languages, Idris, Substructural Type-Systems}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2020.21

Data Consistency in Transactional Storage Systems: A Centralised Semantics

Authors: Shale Xiong, Andrea Cerone, Azalea Raad, and Philippa Gardner

Abstract

We introduce an interleaving operational semantics for describing the client-observable behaviour of atomic transactions on distributed key-value stores. Our semantics builds on abstract states comprising centralised, global key-value stores and partial client views. Using our abstract states, we present operational definitions of well-known consistency models in the literature, and prove them to be equivalent to their existing declarative definitions using abstract executions. We explore two applications of our operational framework: 1) verifying that the COPS replicated database and the Clock-SI partitioned database satisfy their consistency models using trace refinement, and 2) proving invariant properties of client programs.

Cite as

Shale Xiong, Andrea Cerone, Azalea Raad, and Philippa Gardner. Data Consistency in Transactional Storage Systems: A Centralised Semantics. In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 21:1-21:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{xiong_et_al:LIPIcs.ECOOP.2020.21,
  author =	{Xiong, Shale and Cerone, Andrea and Raad, Azalea and Gardner, Philippa},
  title =	{{Data Consistency in Transactional Storage Systems: A Centralised Semantics}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{21:1--21:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.21},
  URN =		{urn:nbn:de:0030-drops-131782},
  doi =		{10.4230/LIPIcs.ECOOP.2020.21},
  annote =	{Keywords: Operational Semantics, Consistency Models, Transactions, Distributed Key-value Stores}
}

@InProceedings{fallin:LIPIcs.ECOOP.2020.30,
  author =	{Fallin, Chris},
  title =	{{Safe, Flexible Aliasing with Deferred Borrows}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{30:1--30:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.30},
  URN =		{urn:nbn:de:0030-drops-131878},
  doi =		{10.4230/LIPIcs.ECOOP.2020.30},
  annote =	{Keywords: Rust, type systems, ownership types, borrowing}
}

Document

SCICO Journal-first

DOI: 10.4230/LIPIcs.ECOOP.2020.31

Reshape Your Layouts, Not Your Programs: A Safe Language Extension for Better Cache Locality (SCICO Journal-first)

Authors: Alexandros Tasos, Juliana Franco, Sophia Drossopoulou, Tobias Wrigstad, and Susan Eisenbach

Abstract

The vast gap between CPU and RAM speed means that on modern architectures, developers need to carefully consider data placement in memory to exploit spatial and temporal cache locality and use CPU caches effectively. To that extent, developers have devised various strategies regarding data placement; for objects that should be close in memory, a contiguous pool of objects is allocated and then new instances are constructed inside it; an array of objects is clustered into multiple arrays, each holding the values of a specific field of the objects. Such data placements, however, have to be performed manually, hence readability, maintainability, memory safety, and key OO concepts such as encapsulation and object identity need to be sacrificed and the business logic needs to be modified accordingly. We propose a language extension, SHAPES, which aims to offer developers high-level fine-grained control over data placement, whilst retaining memory safety and the look-and-feel of OO. SHAPES extends an OO language with the concepts of pools and layouts: Developers declare pools that contain objects of a specific type and specify the pool’s layout. A layout specifies how objects in a pool are laid out in memory. That is, it dictates how the values of the fields of the pool’s objects are grouped together into clusters. Objects stored in pools behave identically to ordinary, standalone objects; the type system allows the code to be oblivious to the layout being used. This means that the business logic is completely decoupled from any placement concerns and the developer need not deviate from the spirit of OO to better utilise the cache. In this paper, we present the features of SHAPES, as well as the design rationale behind each feature. We then showcase the merit of SHAPES through a sequence of case studies; we claim that, compared to the manual pooling and clustering of objects, we can observe improvement in readability and maintainability, and comparable (i.e., on par or better) performance. We also present SHAPES^h, an OO calculus which models the SHAPES ideas, we formalise the type system, and prove soundness. The SHAPES^h type system uses ideas from Ownership Types [Clarke et al., 2013] and Java Generics [Gosling et al., 2014]: In SHAPES^h, pools are part of the types; SHAPES^h class and type definitions are enriched with pool parameters. Moreover, class pool parameters are enriched with bounds, which is what allows the business logic of SHAPES to be oblivious to the layout being used. SHAPES^h types also enforce pool uniformity and homogeneity. A pool is uniform if it contains objects of the same class only; a pool is homogeneous if the corresponding fields of all its objects point to objects in the same pool. These properties allow for more efficient implementation. For performance considerations, we also designed SHAPES^l, an untyped, unsafe low-level language with no explicit support for objects or pools. We argue that it is possible to translate SHAPES^l into existing low-level intermediate representations, such as LLVM [Lattner and Adve, 2004], present the translation of SHAPES^h into SHAPES^l, and show its soundness. Thus, we expect SHAPES to offer developers more fine-grained control over data placement, without sacrificing memory safety or the OO look-and-feel.

Cite as

Alexandros Tasos, Juliana Franco, Sophia Drossopoulou, Tobias Wrigstad, and Susan Eisenbach. Reshape Your Layouts, Not Your Programs: A Safe Language Extension for Better Cache Locality (SCICO Journal-first). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 31:1-31:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{tasos_et_al:LIPIcs.ECOOP.2020.31,
  author =	{Tasos, Alexandros and Franco, Juliana and Drossopoulou, Sophia and Wrigstad, Tobias and Eisenbach, Susan},
  title =	{{Reshape Your Layouts, Not Your Programs: A Safe Language Extension for Better Cache Locality}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{31:1--31:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.31},
  URN =		{urn:nbn:de:0030-drops-131887},
  doi =		{10.4230/LIPIcs.ECOOP.2020.31},
  annote =	{Keywords: Cache utilisation, Data representation, Memory safety}
}

Document

SCICO Journal-first

DOI: 10.4230/LIPIcs.ECOOP.2020.32

A Big Step from Finite to Infinite Computations (SCICO Journal-first)

Authors: Davide Ancona, Francesco Dagnino, Jurriaan Rot, and Elena Zucca

Abstract

The known is finite, the unknown infinite - Thomas Henry Huxley The behaviour of programs can be described by the final results of computations, and/or their interactions with the context, also seen as observations. For instance, a function call can terminate and return a value, as well as have output effects during its execution. Here, we deal with semantic definitions covering both results and observations. Often, such definitions are provided for finite computations only. Notably, in big-step style, infinite computations are simply not modelled, hence diverging and stuck terms are not distinguished. This becomes even more unsatisfactory if we have observations, since a non-terminating program may have significant infinite behaviour. Recently, examples of big-step semantics modeling divergence have been provided [Davide Ancona et al., 2017; Davide Ancona et al., 2018] by means of generalized inference systems [Davide Ancona et al., 2017; Francesco Dagnino, 2019], which allow corules to control coinduction. Indeed, modeling infinite behaviour by a purely coinductive interpretation of big-step rules would lead to spurious results [Xavier Leroy and Hervé Grall, 2009] and undetermined observation, whereas, by adding appropriate corules, we can correctly get divergence (∞) as the only result, and a uniquely determined observation. This approach has been adopted in [Davide Ancona et al., 2017; Davide Ancona et al., 2018] to design big-step definitions including infinite behaviour for lambda-calculus and a simple imperative Java-like language. However, in such works the designer of the semantics is in charge of finding the appropriate corules, and this is a non-trivial task. In this paper, we show a general construction that extends a given big-step semantics, modeling finite computations, to include infinite behaviour as well, notably by generating appropriate corules. The construction consists of two steps: 1) Starting from a monoid O modeling finite observations (e.g., finite traces), we construct an ω-monoid ⟨O, O_∞⟩ also modeling infinite observations (e.g., infinite traces). The latter structure is a variation of the notion of ω-semigroup [Dominique Perrin and Jean-Eric Pin, 2004], including a mixed product composing a finite with a possibly infinite observation, and an infinite product mapping an infinite sequence of finite observations into a single one (possibly infinite). 2) Starting from an inference system defining a big-step judgment c⇒⟨r, o⟩, with c denoting a configuration, r ∈ R a result, and o ∈ O a finite observation, we construct an inference system with corules defining an extended big-step judgment c⇒c ⇒ ⟨r_∞, o_∞⟩ with r_∞ ∈ R_∞ = R+{∞}, and o_∞ ∈ O_∞ a "possibly infinite" observation. The construction generates additional rules for propagating divergence, and corules for introducing divergence in a controlled way. The exact corules added in the construction depend on the type of observations that one starts with. To show the effectiveness of our approach, we provide several instances of the framework, with different kinds of (finite) observations. Finally, we prove a correctness result for the construction. To this end, we assume the original big-step semantics to be equivalent to (finite sequences of steps in) a reference small-step semantics, and we show that, by applying the construction, we obtain an extended big-step semantics which is still equivalent to the small-step semantics, where we consider possibly infinite sequences of steps.} As hypotheses, rather than {just} equivalence in the finite case {(which would be not enough)}, we assume a set of equivalence conditions between individual big-step rules and the small-step relation. This proof of equivalence holds for deterministic semantics; issues arising in the non-deterministic case and a possible solution are sketched in the conclusion of the full paper.

Cite as

Davide Ancona, Francesco Dagnino, Jurriaan Rot, and Elena Zucca. A Big Step from Finite to Infinite Computations (SCICO Journal-first). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 32:1-32:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ancona_et_al:LIPIcs.ECOOP.2020.32,
  author =	{Ancona, Davide and Dagnino, Francesco and Rot, Jurriaan and Zucca, Elena},
  title =	{{A Big Step from Finite to Infinite Computations}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{32:1--32:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.32},
  URN =		{urn:nbn:de:0030-drops-131895},
  doi =		{10.4230/LIPIcs.ECOOP.2020.32},
  annote =	{Keywords: Operational semantics, coinduction, infinite behaviour}
}

Document

SCICO Journal-first

DOI: 10.4230/LIPIcs.ECOOP.2020.33

Abstracting Gradual References (SCICO Journal-first)

Authors: Matías Toro and Éric Tanter

Abstract

Gradual typing is an effective approach to integrate static and dynamic typing, which supports the smooth transition between both extremes via the (programmer-controlled) precision of type annotations [Jeremy Siek and Walid Taha, 2006; Siek et al., 2015]. Imprecision is normally introduced via the unknown type ?, e.g. function type Int → Bool is more precise than ? → ?, and both more precise than ?. Gradual typing relates types of different precision using consistent type relations, such as type consistency (resp. consistent subtyping), the gradual counterpart of type equality (resp. subtyping). For instance, ? → Int is consistent with Bool → ?. This approach has been applied in a number of settings, such as objects [Jeremy Siek and Walid Taha, 2007], subtyping [Jeremy Siek and Walid Taha, 2007; Ronald Garcia et al., 2016], effects [Bañados Schwerter et al., 2014; Bañados Schwerter et al., 2016], ownership [Ilya Sergey and Dave Clarke, 2012], typestates [Roger Wolff et al., 2011; Ronald Garcia et al., 2014], information-flow typing [Tim Disney and Cormac Flanagan, 2011; Luminous Fennell and Peter Thiemann, 2013; Matías Toro et al., 2018], session types [Igarashi et al., 2017], refinements [Nico Lehmann and {É}ric Tanter, 2017], set-theoretic types [Castagna and Lanvin, 2017], Hoare logic [Johannes Bader et al., 2018], parametric polymorphism [Amal Ahmed et al., 2011; Ahmed et al., 2017; Ina and Igarashi, 2011; Igarashi et al., 2017; Ningning Xie et al., 2018; Matías Toro et al., 2019], and references [Jeremy Siek and Walid Taha, 2006; Herman et al., 2010; Siek et al., 2015]. In particular, gradual typing for mutable references has seen the elaboration of various possible semantics: invariant references [Jeremy Siek and Walid Taha, 2006], guarded references [Herman et al., 2010], monotonic references [Siek et al., 2015], and permissive references [Siek et al., 2015]. Invariant references are a form of references where reference types are invariant with respect to type consistency. Guarded references admit variance thanks to systematic runtime checks on reference reads and writes; the runtime type of an allocated cell never changes during execution. Guarded references have been formulated in a space-efficient coercion calculus, which ensures that gradual programs do not accumulate unbounded pending checks during execution. Hereafter, we refer to this language as HCC. Monotonic references favor efficiency over flexibility by only allowing reference cells to vary towards more precise types. This allows reference operations in statically-typed regions to safely proceed without any runtime checks. Permissive references are the most flexible approach, in which reference cells can be initialized and updated to any value of any type at any time. These four developments reflect different design decisions with respect to gradual references: is the reference type constructor variant under consistency? Can the programmer specify a precise bound on the static type of a reference, and hence on the corresponding heap cell type? Can the heap cell type evolve its precision at runtime, and if yes, how? There is obviously no absolute answer to these questions, as they reflect different tradeoffs such as in efficiency and precision. This work explores the semantics that results from the application of a systematic methodology to gradualize static type systems. Currently we can find in the literature two methodologies to gradualize statically-typed languages: Abstracting Gradual Typing (AGT) [Ronald Garcia et al., 2016], and the Gradualizer [Matteo Cimini and Jeremy Siek, 2016]. In this work, we consider the AGT methodology as it naturally scales to auxiliary structures such as a mutable heap. The AGT methodology helps to systematically construct gradually-typed languages by using abstract interpretation [Cousot and Cousot, 1977] at the type level. In brief, AGT interprets gradual types as an abstraction of sets of possible static types, formally captured through a Galois connection. The static semantics of a gradual language are then derived by lifting the semantics of a statically-typed language through this connection, and the dynamic semantics follow by Curry-Howard from proof normalization of the type safety argument. The AGT methodology has been shown to be effective in many contexts: records and subtyping [Ronald Garcia et al., 2016], type-and-effects [Bañados Schwerter et al., 2014; Bañados Schwerter et al., 2016], refinement types [Nico Lehmann and Éric Tanter, 2017; Niki Vazou et al., 2018], set-theoretic and union types [Castagna and Lanvin, 2017; Matías Toro and Éric Tanter, 2017], information-flow typing [Matías Toro et al., 2018], and parametric polymorphism [Matías Toro et al., 2019]. However, this methodology has never been applied to mutable references in isolation. Although Toro et al. [Matías Toro et al., 2018] apply AGT to a language with references, they only gradualize security levels of types (e.g. Ref Int_?), not whole types (e.g. Ref ? is not supported). In this article we answer the following open questions: Which semantics for gradually-type references follows by systematically applying AGT? Does AGT justify one of the existing approaches, or does it suggest yet another design? Can we recover other semantics for gradual references, if yes, how? This article first reviews the different existing gradual approaches to mutable references through examples. It then presents the semantics for gradual references that is obtained by applying AGT, and how to accommodate the other semantics. More specifically, this work makes the following contributions: - We present λ_REF~, a gradual language with support for mutable references. We derive λ_REF~ by applying the AGT methodology to a fully-static simple language with mutable references called λ_REF. This is the first application of AGT that focuses on gradually-typed mutable references. - We prove that λ_REF~ satisfies the gradual guarantee of Siek et al. [Siek et al., 2015]. We also present the first formal statement and proof of the conservative extension of the dynamic semantics of the static language [Siek et al., 2015], for a gradual language derived using AGT. - We prove that the derived language, λ_REF~, corresponds to the semantics of guarded references from HCC. Formally, given a λ_REF~ term and its compilation to HCC^+ (an adapted version of HCC extended with conditionals and binary operations) we prove that both terms are bisimilar, and that consequently they either both terminate, both fail, or both diverge. - We observe that λ_REF~ and HCC^+ differ in the order of combination of runtime checks. As a result, HCC is space efficient whereas λ_REF~ is not: we can write programs in λ_REF~ that may accumulate an unbounded number of checks. We formalize the changes needed in the dynamic semantics of λ_REF~ to achieve space efficiency. This technique to recover space efficiency is in fact independent from mutable references, and is therefore applicable to other gradual languages derived with AGT. - We formally describe how to support other gradual reference semantics in λ_REF~ by presenting λ_REF~^𝗉𝗆, an extension that additionally supports both permissive and monotonic references. Finally, we prove for the first time that monotonic references satisfy the dynamic gradual guarantee, a non-trivial result that requires careful consideration of updates to the store. Additionally, we implemented λ_REF~ as an interactive prototype that displays both typing derivations and reduction traces. All the examples mentioned in this paper are readily available in the online prototype available at https://pleiad.cl/grefs. As a result, this paper sheds further light on the design space of gradual languages with mutable references and contributes to deepening the understanding of the AGT methodology.

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Matías Toro and Éric Tanter. Abstracting Gradual References (SCICO Journal-first). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 33:1-33:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{toro_et_al:LIPIcs.ECOOP.2020.33,
  author =	{Toro, Mat{\'\i}as and Tanter, \'{E}ric},
  title =	{{Abstracting Gradual References}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{33:1--33:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.33},
  URN =		{urn:nbn:de:0030-drops-131900},
  doi =		{10.4230/LIPIcs.ECOOP.2020.33},
  annote =	{Keywords: Gradual Typing, Mutable References, Abstract interpretation}
}

LIPIcs, Volume 166

34th European Conference on Object-Oriented Programming (ECOOP 2020)

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