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Automorphisms of types in certain type theories and representation of finite groups

Published online by Cambridge University Press:  23 May 2018

SERGEI SOLOVIEV
SERGEI SOLOVIEV*
Affiliation:
IRIT, University of Toulouse-3, 118, route de Narbonne, 31062, Toulouse, France. Email: soloviev@irit.fr ITMO University, 49, Kronverkski prospekt, 197101, St. Petersburg, Russia (associated researcher)
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Abstract

The automorphism groups of types in several systems of type theory are studied. It is shown that in simply typed λ-calculus λ1βη and in its extension with surjective pairing and terminal object these groups correspond exactly to the groups of automorphisms of finite trees. In second-order λ-calculus and in Luo's framework (LF) with dependent products, any finite group may be represented.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 4 , April 2019 , pp. 511 - 551
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

In memoriam Kosta Doen

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