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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| Vydáno v: | Logical methods in computer science Ročník 20, Issue 4 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science e.V
14.11.2024
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| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-20(4:14)2024 |