Sequence Types for Hereditary Permutators

Author Pierre Vial

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Pierre Vial
  • Inria, Nantes, France

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Pierre Vial. Sequence Types for Hereditary Permutators. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The invertible terms in Scott’s model D_infty are known as the hereditary permutators. Equivalently, they are terms which are invertible up to beta eta-conversion with respect to the composition of the lambda-terms. Finding a type-theoretic characterization to the set of hereditary permutators was problem # 20 of TLCA list of problems. In 2008, Tatsuta proved that this was not possible with an inductive type system. Building on previous work, we use an infinitary intersection type system based on sequences (i.e., families of types indexed by integers) to characterize hereditary permutators with a unique type. This gives a positive answer to the problem in the coinductive case.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • hereditary permutators
  • Böhm trees
  • intersection types
  • coinduction
  • ridigity
  • sequence types
  • non-idempotent intersection


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