Handbook of logic in computer science (vol. 2)
Information and Computation
Checking algorithms for pure type systems
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Proff-search in type-theoretic languages: an introduction
Theoretical Computer Science - Special issue on proof-search in type-theoretic languages
Cut-elimination and redundancy-elimination by resolution
Journal of Symbolic Computation - Special issue on advances in first-order theorem proving
Handbook of automated reasoning
Proof-assistants using dependent type systems
Handbook of automated reasoning
Type-checking injective pure type systems
Journal of Functional Programming
Expansion postponement for normalising pure type systems
Journal of Functional Programming
A cut-free sequent calculus for pure type systems verifying the structural rules of Gentzen/Kleene
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Pure type systems with judgemental equality
Journal of Functional Programming
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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.