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Elementary Type Inference

Authors Jinxu Zhao, Bruno C. d. S. Oliveira

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Author Details

Jinxu Zhao
  • Department of Computer Science, The University of Hong Kong, China
Bruno C. d. S. Oliveira
  • Department of Computer Science, The University of Hong Kong, China

Funding

The research is supported by the Type Inference for Complex Type Systems collaboration project (TC20210422012) between Huawei, and the University of Hong Kong and Hong Kong Research Grants Council projects number 17209520 and 17209821.

Acknowledgements

We are grateful to the anonymous reviewers for their valuable comments which helped to improve the presentation of this work. We also thank Chen Cui for creating the implementation for our prototype.

Cite As Get BibTex

Jinxu Zhao and Bruno C. d. S. Oliveira. Elementary Type Inference. In 36th European Conference on Object-Oriented Programming (ECOOP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 222, pp. 2:1-2:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ECOOP.2022.2

Abstract

Languages with polymorphic type systems are made convenient to use by employing type inference to avoid redundant type information. Unfortunately, features such as impredicative types and subtyping make complete type inference very challenging or impossible to realize. 
This paper presents a form of partial type inference called elementary type inference. Elementary type inference adopts the idea of inferring only monotypes from past work on predicative higher-ranked polymorphism. This idea is extended with the addition of explicit type applications that work for any polytypes. Thus easy (predicative) instantiations can be inferred, while all other (impredicative) instantiations are always possible with explicit type applications without any compromise in expressiveness. Our target is a System F extension with top and bottom types, similar to the language employed by Pierce and Turner in their seminal work on local type inference. We show a sound, complete and decidable type system for a calculus called F_{< :}^e, that targets that extension of System F. A key design choice in F_{< :}^e is to consider top and bottom types as polytypes only. An important technical challenge is that the combination of predicative implicit instantiation and impredicative explicit type applications, in the presence of standard subtyping rules, is non-trivial. Without some restrictions, key properties, such as subsumption and stability of type substitution lemmas, break. To address this problem we introduce a variant of polymorphic subtyping called stable subtyping with some mild restrictions on implicit instantiation. All the results are mechanically formalized in the Abella theorem prover.

Subject Classification

ACM Subject Classification
  • Software and its engineering → General programming languages
Keywords
  • Type Inference

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References

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