On Girard's "Candidats de Reductibilit'e". In Logic and Computer Science, ed. P.G. Odifreddi, APIC series, vol. 31, Academic Press, pp 123-204. Home/Search Document Not in Database Summary Related Articles Check |
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A short and flexible proof of Strong Normalization for the.. - Geuvers (1994) (7 citations) (Correct)
....of Technology The Netherlands 1. Introduction In the literature there are several different proofs of Strong Normalization (SN) for the Calculus of Constructions (CC) Some of them are of purely syntactical nature (like the ones in [Coquand 1985] Geuvers and Nederhof 1991] and in [Coquand and Gallier 1990] while others give a proof of normalization by describing an appropriate semantics (like [Ong and Ritter 1994] and [Altenkirch 1993] who describe an denotational semantics, but also [Goguen 1994] who describes a typed operational semantics) Apart from these, proofs of SN for CC can be found ....
....complicated by the fact that the system is higher order, which means that there are reductions in type constructors. One possible approach to coping with type dependency is to look at sets of typed terms instead of untyped terms. This is done, for example, in [Berardi 1988] and [Coquand and Gallier 1990] Another possibility is to reduce the question e mail: herman win.tue.nl of SN for a system with type dependency to SN for a system without type dependency. This is done in [Geuvers and Nederhof 1991] Both approaches lead to rather involved proofs that consist of putting several steps ....
On Girard's "Candidats de Reductibilit'e". In Logic and Computer Science, ed. P.G. Odifreddi, APIC series, vol. 31, Academic Press, pp 123-204.
The Calculus of Constructions and Higher Order Logic - Geuvers (1992) (3 citations) (Correct)
....for proving strong normalisation for his system F and F . See [Girard et al. 1989] for the proof for system F. The idea is to define a kind of realisability model in which propositions are interpreted as sets of lambda terms (the realisers) A detailed explanation of the method can be found in [Gallier 1990]. It is also possible to obtain the strong normalisation for CC more or less directly from the strong normalisation property of F , as is shown in [Geuvers and Nederhof 1991] The importance of the (strong) normalisation property lies in the fact that it gives a handle on the number of proofs of ....
On Girard's "Candidats de Reductibilit'e". In Logic and Computer Science, ed. P.G. Odifreddi, APIC series, vol. 31, Academic Press, pp 123-204.
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