On the Semantic Expressiveness of Iso- and Equi-Recursive Types

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-...

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Bibliographic Details
Published in:Logical methods in computer science Vol. 20, Issue 4
Main Authors: Devriese, Dominique, Martin, Eric Mark, Patrignani, Marco
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science e.V 14.11.2024
Subjects:
computer science - programming languages
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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Summary: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.
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-20(4:14)2024