Signature restriction for polymorphic algebraic effects

Sekiyama, Taro; Tsukada, Takeshi; Igarashi, Atsushi

doi:10.1145/3408999

Cited by 4 publications

(1 citation statement)

References 51 publications

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“…This article revises and extends the paper presented at ICFP’20 (Sekiyama et al, 2020). In summary, the following are added.…”

Section: Introductionsupporting

confidence: 77%

Signature restriction for polymorphic algebraic effects

SEKIYAMA,

TSUKADA,

IGARASHI

2024

J. Funct. Prog.

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The naive combination of polymorphic effects and polymorphic type assignment has been well known to break type safety. In the literature, there are two kinds of approaches to this problem: one is to restrict how effects are triggered and the other is to restrict how they are implemented. This work explores a new approach to ensuring the safety of the use of polymorphic effects in polymorphic type assignment. A novelty of our work is to restrict effect interfaces. To formalize our idea, we employ algebraic effects and handlers, where an effect interface is given by a set of operations coupled with type signatures. We propose signature restriction, a new notion to restrict the type signatures of operations and show that signature restriction ensures type safety of a language equipped with polymorphic effects and unrestricted polymorphic type assignment. We also develop a type-and-effect system to enable the use of both of the operations that satisfy and those that do not satisfy the signature restriction in a single program.

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“…This article revises and extends the paper presented at ICFP’20 (Sekiyama et al, 2020). In summary, the following are added.…”

Section: Introductionsupporting

confidence: 77%

Signature restriction for polymorphic algebraic effects

SEKIYAMA,

TSUKADA,

IGARASHI

2024

J. Funct. Prog.

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CPS transformation with affine types for call-by-value implicit polymorphism

Sekiyama

Tsukada

2021

Proc. ACM Program. Lang.

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Transformation of programs into continuation-passing style (CPS) reveals the notion of continuations, enabling many applications such as control operators and intermediate representations in compilers. Although type preservation makes CPS transformation more beneficial, achieving type-preserving CPS transformation for implicit polymorphism with call-by-value (CBV) semantics is known to be challenging. We identify the difficulty in the problem that we call scope intrusion. To address this problem, we propose a new CPS target language Λ open that supports two additional constructs for polymorphism: one only binds and the other only generalizes type variables. Unfortunately, their unrestricted use makes Λ open unsafe due to undesired generalization of type variables. We thus equip Λ open with affine types to allow only the type-safe generalization. We then define a CPS transformation from Curry-style CBV System F to type-safe Λ open and prove that the transformation is meaning and type preserving. We also study parametricity of Λ open as it is a fundamental property of polymorphic languages and plays a key role in applications of CPS transformation. To establish parametricity, we construct a parametric, step-indexed Kripke logical relation for Λ open and prove that it satisfies the Fundamental Property as well as soundness with respect to contextual equivalence.

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On Model-Checking Higher-Order Effectful Programs

Dal Lago,

Ghyselen

2024

Proc. ACM Program. Lang.

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Model-checking is one of the most powerful techniques for verifying systems and programs, which since the pioneering results by Knapik et al., Ong, and Kobayashi, is known to be applicable to functional programs with higher-order types against properties expressed by formulas of monadic second-order logic. What happens when the program in question, in addition to higher-order functions, also exhibits algebraic effects such as probabilistic choice or global store? The results in the literature range from those, mostly positive, about nondeterministic effects, to those about probabilistic effects, in the presence of which even mere reachability becomes undecidable. This work takes a fresh and general look at the problem, first of all showing that there is an elegant and natural way of viewing higher-order programs producing algebraic effects as ordinary higher-order recursion schemes. We then move on to consider effect handlers, showing that in their presence the model checking problem is bound to be undecidable in the general case, while it stays decidable when handlers have a simple syntactic form, still sufficient to capture so-called generic effects. Along the way, we hint at how a general specification language could look like, this way justifying some of the results in the literature, and deriving new ones.

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Signature restriction for polymorphic algebraic effects

Cited by 4 publications

References 51 publications

Signature restriction for polymorphic algebraic effects

Signature restriction for polymorphic algebraic effects

CPS transformation with affine types for call-by-value implicit polymorphism

On Model-Checking Higher-Order Effectful Programs

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