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

  • SERGEI SOLOVIEV (a1) (a2)
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.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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