Isomorphism Types of Trees

Isomorphism Types of Trees1

Isomorphism of "Functional" Intersection Types

Type isomorphism for intersection types is quite odd, since it is not a congruence and it does not extend type equality in the standard interpretation of types. The lack of congruence is due to the proof theoretic nature of the intersection introduction rule, which requires the same term to be the subject of both premises. A partial congruence can be recovered by introducing a suitable notion o...

Finite Automata and Isomorphism Types

Isomorphism of Regular Trees and Words

The complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are represented by NFAs (DFAs), the isomorphism problem for regular trees turns out to be EXPTIME-complete (resp. P-complete). In case the input automata are acyclic NFAs (acy...

Isomorphism of intersection and union types

This paper gives a complete characterisation of type isomorphism definable by terms of a λ-calculus in a type system with intersection and union types. Type isomorphism is usually proved using a form of Inversion Lemma to relate terms and types. Currently in the literature no inversion lemma for intersection and union types is provided. Moreover, the subject reduction property does not hold in ...