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Applicative Intersection Types

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Programming Languages and Systems (APLAS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13658))

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Abstract

Calculi with intersection types have been used over the years to model various features, including: overloading, extensible records and, more recently, nested composition and return type overloading. Nevertheless no previous calculus supports all those features at once. In this paper we study expressive calculi with intersection types and a merge operator. Our first calculus supports an unrestricted merge operator, which is able to support all the features, and is proven to be type sound. However, the semantics is non-deterministic. In the second calculus we employ a previously proposed disjointness restriction, to make the semantics deterministic. Some forms of overloading are forbidden, but all other features are supported. The main challenge in the design is related to the semantics of applications and record projections. We propose an applicative subtyping relation that enables the inference of result types for applications and projections. Correspondingly, there is an applicative dispatching relation that is used for the dynamic semantics. The two calculi and their proofs are formalized in the Coq theorem prover.

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Acknowledgement

We thank the anonymous reviewers for their helpful comments and our colleagues of HKU Programming Languages Group for their discussions to understand this work better. We thank Chen Cui for his valuable feedback on the draft. This work has been sponsored by Hong Kong Research Grant Council projects number 17209519, 17209520 and 17209821.

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Authors and Affiliations

  1. University of Hong Kong, Hong Kong, China

    Xu Xue & Bruno C. d. S. Oliveira

  2. University of Cambridge, Cambridge, UK

    Ningning Xie

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  1. Xu Xue
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  2. Bruno C. d. S. Oliveira
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  3. Ningning Xie
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Correspondence to Xu Xue .

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  1. National University of Singapore, Singapore, Singapore

    Ilya Sergey

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Xue, X., Oliveira, B.C.d.S., Xie, N. (2022). Applicative Intersection Types. In: Sergey, I. (eds) Programming Languages and Systems. APLAS 2022. Lecture Notes in Computer Science, vol 13658. Springer, Cham. https://doi.org/10.1007/978-3-031-21037-2_8

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  • DOI: https://doi.org/10.1007/978-3-031-21037-2_8

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