Fulfilling OCaml Modules with Transparency
Article No.: 101, Pages 194 - 222
Abstract
ML modules come as an additional layer on top of a core language to offer large-scale notions of composition and abstraction. They largely contributed to the success of OCaml and SML. While modules are easy to write for common cases, their advanced use may become tricky. Additionally, despite a long line of works, their meta-theory remains difficult to comprehend, with involved soundness proofs. In fact, the module layer of OCaml does not currently have a formal specification and its implementation has some surprising behaviors.
Building on previous translations from ML modules to Fω, we propose a type system, called Mω, that covers a large subset of OCaml modules, including both applicative and generative functors, and extended with transparent ascription. This system produces signatures in an OCaml-like syntax extended with Fω quantifiers. We provide a reverse translation from Mω signatures to path-based source signatures along with a characterization of signature avoidance cases, making Mω signatures well suited to serve as a new internal representation for a typechecker.
The soundness of the type system is shown by elaboration in Fω. We improve over previous encodings of sealing within applicative functors, by the introduction of transparent existential types, a weaker form of existential types that can be lifted out of universal and arrow types. This shines a new light on the form of abstraction provided by applicative functors and brings their treatment much closer to those of generative functors.
Supplementary Material
This document contains the supplementary material for the main paper Fulfilling OCaml modules with transparency. §1 contains a few small additional illustrative examples. This document also provides the complete set of typing rules (§2) and anchoring rules (§3) for M𝜔, typing rules for F𝜔 (§4) and the elaboration rules of M𝜔 into F𝜔 (§5). Proofs of the anchoring properties can be found in §3.
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Published: 29 April 2024
Published in PACMPL Volume 8, Issue OOPSLA1
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