Contractive Signatures with Recursive Types, Type Parameters, and Abstract Types

Im, Hyeonseung; Nakata, Keiko; Park, Sung Woo

doi:10.1007/978-3-642-39212-2_28

Cited by 8 publications

(5 citation statements)

References 15 publications

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“…The usefulness of a type system is directly related to its capability to be used in a programming language. Type systems such as the ones discussed in this work lend themselves quite readily to functional term languages [45]. For session types, existing term languages are either inspired in the pi calculus [26,73,69] or in the lambda calculus [35,54,70], or even the two [71].…”

Section: Related Workmentioning

confidence: 99%

System $$F^\mu _\omega $$ with Context-free Session Types

Poças

Costa

Mordido

et al. 2023

Lecture Notes in Computer Science

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We study increasingly expressive type systems, from $$F^\mu $$ F μ —an extension of the polymorphic lambda calculus with equirecursive types—to $$F^{\mu ;}_\omega $$ F ω μ ; —the higher-order polymorphic lambda calculus with equirecursive types and context-free session types. Type equivalence is given by a standard bisimulation defined over a novel labelled transition system for types. Our system subsumes the contractive fragment of $$F^\mu _\omega $$ F ω μ as studied in the literature. Decidability results for type equivalence of the various type languages are obtained from the translation of types into objects of an appropriate computational model: finite-state automata, simple grammars and deterministic pushdown automata. We show that type equivalence is decidable for a significant fragment of the type language. We further propose a message-passing, concurrent functional language equipped with the expressive type language and show that it enjoys preservation and absence of runtime errors for typable processes.

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Section: Related Workmentioning

confidence: 99%

System $$F^\mu _\omega $$ with Context-free Session Types

Poças

Costa

Mordido

et al. 2023

Lecture Notes in Computer Science

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“…α) are not inhabited by any value, so it is reasonable to elide them (Lemma 1). Moreover, they do not have an infinite unfolding and (without restrictions on the type equality relation) can be proven equivalent to any other type [Im et al 2013], which is undesirable.…”

Section: Syntaxmentioning

confidence: 99%

On the semantic expressiveness of recursive types

Patrignani

Martin

Devriese

2021

Proc. ACM Program. Lang.

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Recursive types extend the simply-typed lambda calculus (STLC) with the additional expressive power to enable diverging computation and to encode recursive data-types (e.g., lists). Two formulations of recursive types exist: iso-recursive and equi-recursive. The relative advantages of iso- and equi-recursion are well- studied when it comes to their impact on type-inference. However, the relative semantic expressiveness of the two formulations remains unclear so far. This paper studies the semantic expressiveness of STLC with iso- and equi-recursive types, proving that these formulations are equally expressive. In fact, we prove that they are both as expressive as STLC with only term-level recursion. We phrase these equi-expressiveness results in terms of full abstraction of three canonical compilers between these three languages (STLC with iso-, with equi-recursive types and with term-level recursion). Our choice of languages allows us to study expressiveness when interacting over both a simply-typed and a recursively-typed interface. The three proofs all rely on a typed version of a proof technique called approximate backtranslation. Together, our results show that there is no difference in semantic expressiveness between STLCs with iso- and equi-recursive types. In this paper, we focus on a simply-typed setting but we believe our results scale to more powerful type systems like System F.

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“…Ordinary types (denoted by ) include type variables (denoted by ), type constructor applications or contractive types [24] (denoted by ), and equi-recursive types (denoted by as ). We require types appearing under an equi-recursive binder to be contractive, which excludes meaningless types such as as and guarantees the existence of an unique solution to the recursive equation(s) [19,35]. Contractive types (denoted by ) include function types (denoted by 1 → 2 ), record types (denoted by { }) and variant types (denoted by ).…”

Section: Syntaxmentioning

confidence: 99%

Row-Polymorphic Types for Strategic Rewriting

Fu¹,

Qin²,

Dardha³

et al. 2021

Preprint

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We present a type system for strategy languages that express program transformations as compositions of rewrite rules. Our row-polymorphic type system assists compiler engineers to write correct strategies by statically rejecting non meaningful compositions of rewrites that otherwise would fail during rewriting at runtime. Furthermore, our type system enables reasoning about how rewriting transforms the shape of the computational program. We present a formalization of our language at its type system and demonstrate its practical use for expressing compiler optimization strategies.Our type system builds the foundation for many interesting future applications, including verifying the correctness of program transformations and synthesizing program transformations from specifications encoded as types.

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Contractive Signatures with Recursive Types, Type Parameters, and Abstract Types

Cited by 8 publications

References 15 publications

System $$F^\mu _\omega $$ with Context-free Session Types

System $$F^\mu _\omega $$ with Context-free Session Types

On the semantic expressiveness of recursive types

Row-Polymorphic Types for Strategic Rewriting

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