(2021) On the Semantic Expressiveness of Recursive Types.
|
Text
mu-expr.pdf Download (1MB) | Preview |
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.
| Item Type: | Conference or Workshop Item (A Paper) (Paper) |
|---|---|
| Uncontrolled Keywords: | Iso-recursive types, Coinductive Equi-recursive types, Recursive types, Lambda Calculus, Fully-abstract compilation, Backtranslation |
| Conference: | POPL ACM-SIGACT Symposium on Principles of Programming Languages |
| Depositing User: | Marco Patrignani |
| Date Deposited: | 11 Aug 2021 10:07 |
| Last Modified: | 11 Aug 2021 10:16 |
| Primary Research Area: | NRA1: Trustworthy Information Processing |
| URI: | https://publications.cispa.saarland/id/eprint/3462 |
Actions
Actions (login required)
 |
View Item |