Expansion Postponement via Cut Elimination in Sequent Calculi for Pure Type Systems

The sequent calculus used in this paper is interesting because (1) it is equivalent to the standard formulation (natural) for Pure Type System (PTS), and (2) the corresponding cut-free subsystem makes it possible to introduce a notion of Cut Elimination (CE). This property has a deep impact on PTS and in logical frameworks based in PTS. CE is an open problem for normalizing generic PTS. Likewise, other proposed versions of cut elimination have not been solved in dependent type systems. Another interesting problem is Expansion Postponement (EP), posed by Henk Barendregt in August 1990. Except for PTS with important restrictions, EP is thus far an open problem, even for normalizing PTS. Surprisingly, in this paper we prove that EP is a consequence of CE.

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