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Type Inference for Rank-2 Intersection Types Using Set Unification

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Theoretical Aspects of Computing – ICTAC 2022 (ICTAC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13572))

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Abstract

Several type inference approaches for rank-2 idempotent and commutative intersection types have been presented in the literature. Type inference relies on two stages: type constraint generation and solving. Defining constraint generation rules is rather straightforward, with one exception. To infer the type of an application, several derivations of the argument are required, one for each instance of the domain type of the function. The types of these derivations are then constrained against the instances. Noting that these derivations are isomorphic, by renaming of type variables, they can be obtained via a duplication operation on a single derivation of the argument. The application rule then constrains the intersection type resulting from duplication against the domain type of the function, resulting in an equality constraint between intersections. By treating intersections as sets, these constraints can be solved by solving a set unification problem, thus ensuring the types of the argument unify with the domain type of the function. Here we present a new type inference algorithm for rank-2 intersection types, which relies on set unification to solve equality constraints between intersections, and show it is both sound and complete.

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Acknowledgements

This work was partially financially supported by the portuguese Fundação para a Ciência e a Tecnologia, under the PhD grant number SFRH/BD/145183/2019 and by Base Funding - UIDB/00027/2020 of the Artificial Intelligence and Computer Science Laboratory – LIACC - funded by national funds through the FCT/MCTES (PIDDAC).

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  1. LIACC, Departamento de Ciência de Computadores, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre s/n, 4169-007, Porto, Portugal

    Pedro Ângelo & Mário Florido

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  1. Pedro Ângelo
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  2. Mário Florido
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Correspondence to Pedro Ângelo .

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  1. TU München, München, Germany

    Helmut Seidl

  2. Southwest University, Chongqing, China

    Zhiming Liu

  3. NASA Ames Research Center, Moffett Field, CA, USA

    Corina S. Pasareanu

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Ângelo, P., Florido, M. (2022). Type Inference for Rank-2 Intersection Types Using Set Unification. In: Seidl, H., Liu, Z., Pasareanu, C.S. (eds) Theoretical Aspects of Computing – ICTAC 2022. ICTAC 2022. Lecture Notes in Computer Science, vol 13572. Springer, Cham. https://doi.org/10.1007/978-3-031-17715-6_29

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  • DOI: https://doi.org/10.1007/978-3-031-17715-6_29

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