Polymorphic symmetric multiple dispatch with variance

Park, Gyunghee; Hong, Jaemin; Steele, Guy L.; Ryu, Sukyoung

doi:10.1145/3290324

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…Multiple dispatching. Clifton et al (2000), Chambers & Chen (1999), Muschevici et al (2008), Park et al (2019) generalize object-oriented dynamic dispatch to determine the overloaded method to invoke based on the runtime type of all its arguments. Similar to TDOS, much of the type information is recovered from type annotations in multiple dispatching mechanisms, but, unlike TDOS, they only use input types to determine the semantics.…”

Section: Languages and Calculi With Type-dependent Semanticsmentioning

confidence: 99%

Taming the Merge Operator

Huang¹,

Zhao²,

Oliveira³

2021

J. Funct. Prog.

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Calculi with disjoint intersection types support a symmetric merge operator with subtyping. The merge operator generalizes record concatenation to any type, enabling expressive forms of object composition, and simple solutions to hard modularity problems. Unfortunately, recent calculi with disjoint intersection types and the merge operator lack a (direct) operational semantics with expected properties such as determinism and subject reduction, and only account for terminating programs. This paper proposes a type-directed operational semantics (TDOS) for calculi with intersection types and a merge operator. We study two variants of calculi in the literature. The first calculus, called λ i , is a variant of a calculus presented by Oliveira et al. (2016) and closely related to another calculus by Dunfield (2014). Although Dunfield proposes a direct small-step semantics for her calculus, her semantics lacks both determinism and subject reduction. Using our TDOS, we obtain a direct semantics for λ i that has both properties. The second calculus, called λ i + , employs the well-known subtyping relation of Barendregt, Coppo and Dezani-Ciancaglini (BCD). Therefore, λ i + extends the more basic subtyping relation of λ i , and also adds support for record types and nested composition (which enables recursive composition of merged components). To fully obtain determinism, both λ i and λ i + employ a disjointness restriction proposed in the original λ i calculus. As an added benefit the TDOS approach deals with recursion in a straightforward way, unlike previous calculi with disjoint intersection types where recursion is problematic. We relate the static and dynamic semantics of λ i to the original version of the calculus and the calculus by Dunfield. Furthermore, for λ i + , we show a novel formulation of BCD subtyping, which is algorithmic, has a very simple proof of transitivity and allows for the modular addition of distributivity rules (i.e. without affecting other rules of subtyping). All results have been fully formalized in the Coq theorem prover.

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Section: Languages and Calculi With Type-dependent Semanticsmentioning

confidence: 99%

Taming the Merge Operator

Huang¹,

Zhao²,

Oliveira³

2021

J. Funct. Prog.

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“…Though multiple dispatch is more often found in dynamic languages, there has been research on safe integration of dynamic dispatch into statically typed languages [1,6,7,9,18]. There, subtyping is used for both static type checking and dynamic method resolution.…”

Section: Related Workmentioning

confidence: 99%

Decidable tag-based semantic subtyping for nominal types, tuples, and unions

Belyakova

2019

Proceedings of the 21st Workshop on Formal Techniques for Java-Like Programs

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Semantic subtyping enables simple, set-theoretical reasoning about types by interpreting a type as the set of its values. Previously, semantic subtyping has been studied primarily in the context of statically typed languages with structural typing. In this paper, we explore the applicability of semantic subtyping in the context of a dynamic language with nominal types. Instead of static type checking, dynamic languages rely on run-time checking of type tags associated with values, so we propose using the tags for semantic subtyping. We base our work on a fragment of the Julia language and present tag-based semantic subtyping for nominal types, tuples, and unions, where types are interpreted set-theoretically as sets of type tags. The proposed subtyping relation is shown to be decidable, and a corresponding analytic definition is provided. The implications of using semantic subtyping for multiple dispatch are also discussed.CCS Concepts • Software and its engineering → Formal language definitions;

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“…If I look at the prior work many typed languages with multiple dispatch identified ambiguities. Eliminating the potential for ambiguities was a major goal and challenge for both Fortress and Cecil [4,64,50]. Julia's experience suggests, however, that ambiguity checking may actually be undesirable, particularly at definition sites.…”

Section: ¦ ¥mentioning

confidence: 99%

A type system for Julia

Chung

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8 2 the julia lanugage 10 2.1 Related work 13 2.2 Julia in action 15 2.3 Evaluating relative performance 18 2.4 The Julia programming language 20 2.4.1 Values, types, and annotations 20 2.4.2 Multiple dispatch 23 2.4.3 Metaprogramming 26 2.4.4 Discussion 33 2.5 Implementing Julia 35 2.5.1 Method specialization 36 2.5.2 Type inference 37 2.5.3 Method inlining 39 2.5.4 Object unboxing 39 2.6 Julia in Practice 39 2.6.1 Typeful programming 41 2.6.2 Multiple dispatch 42 2.6.3 Specializations 44 2.6.4 Impact on performance 45 3 subtyping in julia 47 3.1 Related Work 47 3.2 Formalization of Subtyping 48 3.3 Proof of Undecidability 53 3.3.1 System F P 53 3.3.2 Reduction from System F P to Julia subtyping 54 3.4 Undecidability in Practice 58 4 gradual typing for julia 62 4.1 Related Work 73 4.1.1 Gradual Typing 73 v contents vi 4.1.2 Eval 76 4.1.3 Static Typing of Multiple Dispatch 77 4.2 A Core Calculus for Julia 79 4.2.1 Syntax 81 4.2.2 Semantics 82 4.3 Static Type System 85 4.3.1 Static Dispatch Resolution 87 4.3.2 Protocols 91 4.4 Typed Dynamic Semantics 93 5 typed julia in practice 104 5.1 Implementation 104 5.1.1 Syntactic analysis 105 5.1.2 Semantic analysis 105 5.1.3 Scope analysis 107 5.1.4 Type analysis 109 5.2 Evaluation 111 5.2.1 Picking a method table 112 5.2.2 Protocols 115 5.2.3 Case Study 118 6 conclusion 124 6.1 Future Work 125 § ¤ > using ForwardDiff > ForwardDiff.derivative(f, 5) 5.537670211431911

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Polymorphic symmetric multiple dispatch with variance

Cited by 5 publications

References 20 publications

Taming the Merge Operator

Taming the Merge Operator

Decidable tag-based semantic subtyping for nominal types, tuples, and unions

A type system for Julia

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