Steffen van Bakel, Franco Barbanera, Dezani Dezani-Ciancaglini, Fer-Jan de Vries
We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating lambda-terms (Bohm trees, Levy-Longo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by the corresponding tree representation of terms. More precisely, for each family of trees, two terms have the same tree if and only if they get assigned the same types in the corresponding type assignment system.
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