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Dependent Merges and First-Class Environments

Authors Jinhao Tan, Bruno C. d. S. Oliveira

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Author Details

Jinhao Tan
  • The University of Hong Kong, China
Bruno C. d. S. Oliveira
  • The University of Hong Kong, China

Funding

Hong Kong Research Grant Council projects number 17209520 and 17209821 sponsored this work.

Acknowledgements

We thank the anonymous reviewers for their helpful comments.

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Jinhao Tan and Bruno C. d. S. Oliveira. Dependent Merges and First-Class Environments. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 34:1-34:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ECOOP.2023.34

Abstract

In most programming languages a (runtime) environment stores all the definitions that are available to programmers. Typically, environments are a meta-level notion, used only conceptually or internally in the implementation of programming languages. Only a few programming languages allow environments to be first-class values, which can be manipulated directly in programs. Although there is some research on calculi with first-class environments for statically typed programming languages, these calculi typically have significant restrictions.
In this paper we propose a statically typed calculus, called 𝖤_i, with first-class environments. The main novelty of the 𝖤_i calculus is its support for first-class environments, together with an expressive set of operators that manipulate them. Such operators include: reification of the current environment, environment concatenation, environment restriction, and reflection mechanisms for running computations under a given environment. In 𝖤_i any type can act as a context (i.e. an environment type) and contexts are simply types. Furthermore, because 𝖤_i supports subtyping, there is a natural notion of context subtyping. There are two important ideas in 𝖤_i that generalize and are inspired by existing notions in the literature. The 𝖤_i calculus borrows disjoint intersection types and a merge operator, used in 𝖤_i to model contexts and environments, from the λ_i calculus. However, unlike the merges in λ_i, the merges in 𝖤_i can depend on previous components of a merge. From implicit calculi, the 𝖤_i calculus borrows the notion of a query, which allows type-based lookups on environments. In particular, queries are key to the ability of 𝖤_i to reify the current environment, or some parts of it. We prove the determinism and type soundness of 𝖤_i, and show that 𝖤_i can encode all well-typed λ_i programs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
Keywords
  • First-class Environments
  • Disjointness
  • Intersection Types

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