Abstract
Regular trees are potentially infinite trees such that the set of distinct subtrees is finite. This paper describes an implementation of regular trees in dependent type theory. Regular trees are semantically characterised as a coinductive type and syntactically as a nested datatype. We show how tree transducers can be used to define regular tree homomorphisms by guarded corecursion. Finally, we give examples on how transducers are used to obtain decidability of properties over regular trees. All results have been mechanized in the proof assistant Coq.
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