Calculi, types and applications: Essays in honour of M. Coppo, M. Dezani-Ciancaglini and S. Ronchi Della Rocca
The method described in Ref. 1 does not always correctly establish the bonds between the variables. In fact, during the reduction to normal form of the λ-formula ((ty)(λyy)) and of all those in which the same variable that is free in the left subformula of an application occurs bound in the right subformula, this variable is wrongly considered as bound. To prevent this, it is necessary to modify the levels assigned to the formulas in the β-generation. We therefore give the correct β-generation statements and the correct algorithm of the β-generation.