On the semantic expressiveness of recursive types

Marco Patrignani, Eric Mark Martin, Dominique Devriese

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Abstract

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.

Original languageEnglish
Article number21
Pages (from-to)1-29
Number of pages29
JournalProceedings of the ACM on Programming Languages
Volume5
Issue numberPOPL
DOIs
Publication statusPublished - 4 Jan 2021
EventPrinciples of Programming Languages -
Duration: 17 Jan 202122 Jan 2021

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