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F-ing modules

Published online by Cambridge University Press:  19 November 2014

ANDREAS ROSSBERG
Affiliation:
Google, Dienerstr. 12, 80331 Munich, Germany (e-mail: rossberg@mpi-sws.org)
CLAUDIO RUSSO
Affiliation:
Microsoft Research 21 Station Road, Cambridge CB1 2FB, United Kingdom (e-mail: crusso@microsoft.com)
DEREK DREYER
Affiliation:
Max Planck Institute for Software Systems (MPI-SWS), 66123 Saarbrücken, Germany (e-mail: dreyer@mpi-sws.org)
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Abstract

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ML modules are a powerful language mechanism for decomposing programs into reusable components. Unfortunately, they also have a reputation for being “complex” and requiring fancy type theory that is mostly opaque to non-experts. While this reputation is certainly understandable, given the many non-standard methodologies that have been developed in the process of studying modules, we aim here to demonstrate that it is undeserved. To do so, we present a novel formalization of ML modules, which defines their semantics directly by a compositional “elaboration” translation into plain System Fω (the higher-order polymorphic λ-calculus). To demonstrate the scalability of our “F-ing” semantics, we use it to define a representative, higher-order ML-style module language, encompassing all the major features of existing ML module dialects (except for recursive modules). We thereby show that ML modules are merely a particular mode of use of System Fω.

To streamline the exposition, we present the semantics of our module language in stages. We begin by defining a subset of the language supporting a Standard ML-like language with second-class modules and generative functors. We then extend this sublanguage with the ability to package modules as first-class values (a very simple extension, as it turns out) and OCaml-style applicative functors (somewhat harder). Unlike previous work combining both generative and applicative functors, we do not require two distinct forms of functor or signature sealing. Instead, whether a functor is applicative or not depends only on the computational purity of its body. In fact, we argue that applicative/generative is rather incidental terminology for pure versus impure functors. This approach results in a semantics that we feel is simpler and more natural than previous accounts, and moreover prohibits breaches of abstraction safety that were possible under them.

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Copyright © Cambridge University Press 2014 

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