G. D. Plotkin. -definability in the full type hierarchy, in J. P. Seldin, and J. R. Hindley, editors, Combinatory Logic, Lambda Calculus and Formalism. Academic Press, 1980. Bibliography 84 Home/Search Document Not in Database Summary Related Articles Check |
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Models of Lambda Calculi and Linear Logic: Structural, Equational .. - Loader (1994) (8 citations) (Correct)
....just provability, rather than the actual proofs, is captured in the model. The term full completeness was coined in [Abramsky Jagadeesan 94] for the result there, which gives full completeness 7 Linear Logical Predicates 8 for a game theoretic semantics. Other results of this nature appear in [Plotkin 80] and [Hyland Ong 93] 1.1 Linear Operators on Linear Logical Predicates In this section, we define a category with linear logical predicates for objects, and the connectives of linear logic are interpreted as functors on this category, so as to give a denotational model of linear logic, in which ....
G. D. Plotkin. -definability in the full type hierarchy, in J. P. Seldin, and J. R. Hindley, editors, Combinatory Logic, Lambda Calculus and Formalism. Academic Press, 1980. Bibliography 84
Linear Logic, Totality and Full Completeness - Loader (1994) (Correct)
....complexity of functions in the model) it does not hold for higher order logics, or those with a natural numbers type. The term full completeness was first used in [1] for the result there, although an earlier non trivial result of this kind, for the simply typed calculus, appears in [8]. 2 Totality Spaces and Linear Operators Definition 1 A totality space A = jAj; A ; A ) consists of a set jAj together with sets A ; A ae PjAj such that: T1 A is the set of those s ae jAj such that s t is a singleton whenever t 2 A . T2 and similarly with A and A interchanged. T3 ....
G. Plotkin. -definability in the full type hierarchy, in J. P. Seldin and J. R. Hindley, editors, Combinatory Logic, Lambda Calculus and Formalism. Academic Press, 1980.
The Undecidability of lambda-Definability - Loader (Correct)
....by restricting the number of bound variables in a term, by using modifications of the notion of logical relation. Appendix: The Failure of Logical Relations One of the main reasons for formulating the notion of logical relations was to use them to characterise definablility. For example, in [5], a Kripke logical relation is used to characterise definability in infinite models. However, as will be shown in this section, logical relations must fail to give such a characterisation in finite models, as otherwise this would yield a decision procedure for definability. As our proof of ....
G. D. Plotkin. -definability in the full type hierarchy, in J. P. Seldin, and J. R. Hindley, editors, Combinatory Logic, Lambda Calculus and Formalism. Academic Press, 1980.
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