J. H. Geuvers. The calculus of constructions and higher order logic. In Ph. de Groote, editor, The Curry-Howard Isomorphism, pages 139-191. Academia, Louvain-la-Neuve (Belgium), 1995. Home/Search Document Details and Download
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Checking Algorithms for Pure Type Systems - Jutting, McKinna, Pollack (1992) (10 citations) (Correct)
....that keep acquiring more and more types by reduction As an aside, notice that this PTS is strongly normalizing. It can be mapped into three levels of a strongly normalizing predicative type hierarchy (for definiteness we mention ECC [Luo90] but much weaker systems will do) by the PTS morphism ([Geu, Geu93]) 7 Type(0) 4 7 Type(1) 5 7 Type(1) 7 Type(2) Since this mapping preserves sorts, axioms and rules, any well typed term in the system above has a well typed image, and therefore strongly normalizes. Further, since S is finite, this system has decidable typechecking [vBJ93] ut It is ....
Herman Geuvers. The calculus of constructions and higher order logic. In preparation.
Use and Meaning of Open Terms in Interactive Formal Problem.. - Nederpelt, al. (Correct)
....Signatures June 2, 1998, R.P. Nederpelt J.H. Geuvers 2 Proposal 2.1 Content 2.1. 1 Scientific problem and context Many type theories, representing various kinds of logics, have been studied as formal systems for theorem proving ( Coquand and Huet 1985, Nordstrom et al. 1990, Barendregt 1992, Geuvers 1995] and have also been implemented as automated theorem provers ( NUPRL 1986, COQ 1995, LEGO 1992, ALF 1994] These implementations interact with the user via open terms : expressions with holes that have to be filled in, while obeying to some type conditions. Although it is generally accepted ....
J.H. Geuvers, The Calculus of Constructions and Higher Order Logic, in The Curry-Howard isomorphism, ed. Ph. de Groote, Volume 8 of the `Cahiers du Centre de logique' (Universit'e catholique de Louvain), Academia, Louvain-la-Neuve (Belgium), pp. 139-191.
Extending Models of Second Order Predicate Logic to Models of.. - Geuvers Self-citation (Geuvers) (Correct)
....also be applied to domains (and vice versa) For the Calculus of Constructions, that corresponds to constructive higher order order predicate logic (in the same way that P2 corresponds to PRED2) it is known that the formulas as types embedding is not conservative. See e.g. Berardi 1990] or [Geuvers 1995]. However, for P , that corresponds to constructive minimal first order order predicate logic, the formulas as types embedding is conservative. See e.g. Geuvers 1993] That (2) above does not prove completeness is due to the fact that CPRED2 (in general) also has non full models. So, it ....
J.H. Geuvers, The Calculus of Constructions and Higher Order Logic, in The Curry-Howard isomorphism, ed. Ph. de Groote, Volume 8 of the "Cahiers du Centre de logique" (Universit'e catholique de Louvain), Academia, Louvain-la-Neuve (Belgium), pp. 139-191.
Solving for Set Variables in Higher-Order Theorem Proving - Brown (Correct)
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J. H. Geuvers. The calculus of constructions and higher order logic. In Ph. de Groote, editor, The Curry-Howard Isomorphism, pages 139-191. Academia, Louvain-la-Neuve (Belgium), 1995.
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