Java generics are turing complete

Grigore, Radu

doi:10.1145/3009837.3009871

Cited by 29 publications

(18 citation statements)

References 16 publications

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“…As shown in Fig. 1, the new results here, together with the proof that S ⊤ is undecidable due to Kennedy and Pierce and the subsequent proof by Grigore [2017] implying that ⟨C, X⟩ is undecidable, completely characterize the computing power of all eight points of the lattice. This characterization is not in terms of the Chomsky hierarchy of classes of formal languages, but rather in terms of a similar hierarchy of classes of forests, also called formal tree languages (see, e.g., [Comon et al 2007]), as depicted by Fig.…”

Section: Kennedy and Pierce's Type System And Its Decidable Fragmentssupporting

confidence: 53%

“…Fling [Gil and Roth 2019] and TypeLevelLR [Yamazaki et al 2019] are two prominent fluent API generators that support all deterministic context-free languages (DCFLs). Grigore [2017] implemented a generator that accepts context-free grammars describing general context-free DSLs-a proper super-set of DCFLs. Specifically, his implementation coded a CYK parser in an intermediate simple, yet high level language, and then translated the code in this language into a Turing machine, being emulated in a subtyping query.…”

Section: Fluent Apis and Treetopmentioning

confidence: 99%

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Study of the Subtyping Machine of Nominal Subtyping with Variance (full version)

Roth

2021

Preprint

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This is a study of the computing power of the subtyping machine behind Kennedy and Pierce's nominal subtyping with variance. We depict the lattice of fragments of Kennedy and Pierce's type system and characterize their computing power in terms of regular, context-free, deterministic, and non-deterministic tree languages. Based on the theory, we present Treetop-a generator of C # implementations of subtyping machines. The software artifact constitutes the first feasible (yet POC) fluent API generator to support context-free API protocols in a decidable type system fragment.CCS Concepts: • Software and its engineering → General programming languages; Inheritance; API languages; Software development techniques.

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Section: Kennedy and Pierce's Type System And Its Decidable Fragmentssupporting

confidence: 53%

Section: Fluent Apis and Treetopmentioning

confidence: 99%

Study of the Subtyping Machine of Nominal Subtyping with Variance (full version)

Roth

2021

Preprint

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“…Firstly, unlike in traditional existential types [Pierce 1992], types such as ∃T t 2 t 1 .T are instantaneously rewritten into the upper bound of T by the frontend and do not appear in subtyping. Secondly, unlike in Java, where subtyping has been proved undecidable [Grigore 2017], neither of the following is allowed in Julia: recursive bounds on type variables (e.g. Ref{T} where T<:Foo{T}) [Wehr and Thiemann 2009], contravariant type constructors [Kennedy and Pierce 2007], existential types in type definitions (e.g.…”

Section: Related Workmentioning

confidence: 99%

Julia subtyping: a rational reconstruction

Nardelli

Belyakova

Pelenitsyn

et al. 2018

Proc. ACM Program. Lang.

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Programming languages that support multiple dispatch rely on an expressive notion of subtyping to specify method applicability. In these languages, type annotations on method declarations are used to select, out of a potentially large set of methods, the one that is most appropriate for a particular tuple of arguments. Julia is a language for scientific computing built around multiple dispatch and an expressive subtyping relation. This paper provides the first formal definition of Julia's subtype relation and motivates its design. We validate our specification empirically with an implementation of our definition that we compare against the existing Julia implementation on a collection of real-world programs. Our subtype implementation differs on 122 subtype tests out of 6,014,476. The first 120 differences are due to a bug in Julia that was fixed once reported; the remaining 2 are under discussion. CCS Concepts: • Software and its engineering → Data types and structures; Semantics;

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“…Java wildcards represent a restricted form of the existential types in JavaGI however, and were not necessarily implicated by this proof. Java Generics were ultimately proven Turing Complete by Grigore in 2017 [40], and thus undecidable. Grigore encoded Turing machines into a fragment of Java's subtyping that was limited to Java Generics and contravariant type parameters.…”

Section: Decidability Of Subtyping In Javamentioning

confidence: 99%

“…Grigore [40] showed that Java Generics was Turing complete by demonstrating that Java subtyping could encode a Turing machine. The mechanism that allows such a reduction is the recursive manner in which Java generics can be used coupled with the contra-variant subtyping of Java wildcards, and Java's multiple inheritance (but not necessarily multiple instantiation inheritance).…”

Section: Encoding Java Genericsmentioning

confidence: 99%

Decidable Subtyping for Path Dependent Types

Mackay¹

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<p>Path dependent types form a central component of the Scala programming language. Coupled with other expressive type forms, path dependent types provide for a diverse set of concepts and patterns, from nominality to F-bounded polymorphism. Recent years have seen much work aimed at formalising the foundations of path dependent types, most notably a hard won proof of type safety. Unfortunately subtyping remains undecidable, presenting problems for programmers who rely on the results of their tools. One such tool is Dotty, the basis for the upcoming Scala 3. Another is Wyvern, a new programming language that leverages path dependent types to support both first class modules and parametric polymorphism. In this thesis I investigate the issues with deciding subtyping in Wyvern. I define three decidable variants that retain several key instances of expressiveness including the ability to encode nominality and parametric polymorphism. Wyvfix fixes types to the contexts they are defined in, thereby eliminating expansive environments. Wyvnon-μ removes recursive subtyping, thus removing the key source of expansive environments during subtyping. Wyvμ places a syntactic restriction on the usage of recursive types. I discuss the formal properties of these variants, and the implications each has for expressing the common programming patterns of path dependent types. I have also mechanized the proofs of decidability for both Wyvfix and Wyvμ in Coq.</p>

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Java generics are turing complete

Cited by 29 publications

References 16 publications

Study of the Subtyping Machine of Nominal Subtyping with Variance (full version)

Study of the Subtyping Machine of Nominal Subtyping with Variance (full version)

Julia subtyping: a rational reconstruction

Decidable Subtyping for Path Dependent Types

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