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Automorphisms of Types in Certain Type Theories and Representation of Finite Groups

Soloviev, Sergei Automorphisms of Types in Certain Type Theories and Representation of Finite Groups. (2018) Mathematical Structures in Computer Science, 29 (4). 511-551. ISSN 0960-1295

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Official URL: https://doi.org/10.1017/S0960129518000129

Abstract

The notion of automorphism of types is defined, as usual, it is an isomorphism A->A. The groups of automorphisms of types in different type theories are studied. It is shown that in simply typed lambda calculus the automorphism groups of types are exactly the groups of automorphisms of finite trees. In second-order lambda calculus (system F) and in case of dependent product types any finite group can be represented.

Item Type:Article
HAL Id:hal-02947763
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > National Research University of Information Technologies, Mechanics and Optics of St- Petersburg - ITMO (RUSSIA)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited On:09 Jul 2020 08:14

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