A Unifying Framework for Type Inhabitation

Authors Sandra Alves , Sabine Broda



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Author Details

Sandra Alves
  • DCC-Faculty of Science & CRACS, University of Porto, Portugal
Sabine Broda
  • DCC-Faculty of Science & CMUP, University of Porto, Portugal

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Sandra Alves and Sabine Broda. A Unifying Framework for Type Inhabitation. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSCD.2018.5

Abstract

In this paper we define a framework to address different kinds of problems related to type inhabitation, such as type checking, the emptiness problem, generation of inhabitants and counting, in a uniform way. Our framework uses an alternative representation for types, called the pre-grammar of the type, on which different methods for these problems are based. Furthermore, we define a scheme for a decision algorithm that, for particular instantiations of the parameters, can be used to show different inhabitation related problems to be in PSPACE.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Theory of computation → Lambda calculus
  • Theory of computation → Rewrite systems
Keywords
  • simple types
  • type inhabitation
  • rewriting
  • PSPACE

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References

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