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Abstract: The semantics of typed lambda calculus is usually described using Henkin models, consisting of functions over some collection of sets, or concrete cartesian closed categories, which are essentially equivalent. We describe a more general class of Kripke-style models. In categorical terms, our Kripke lambda models are cartesian closed subcategories of the presheaves over a poset. To those familiar with Kripke models of modal or intuitionistic logics, Kripke lambda models are likely to seem... (Update)
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BibTeX entry: (Update)
J. Mitchell and E. Moggi. Kripke-style models for typed lambda calculus. Annals of Pure And Applied Logic 51:99--124 (1991). http://citeseer.ist.psu.edu/mitchell96kripkestyle.html More
@inproceedings{ john87kripkestyle,
author = "Mitchell, John C. and Eugenio Moggi",
title = "Kripke-style Models for Typed Lambda Calculus",
booktitle = "Proceedings, Symposium on Logic in Computer Science",
publisher = "The Computer Society of the IEEE",
isbn = "0-8186-0793-9",
pages = "303--314",
year = "1987",
url = "citeseer.ist.psu.edu/mitchell96kripkestyle.html" }
Citations (may not include all citations):729 The Lambda Calculus: Its Syntax and Semantics (context) - Barendregt - 1984
359 Introduction to Higher-Order Categorical Logic (context) - Lambek, Scott - 1986
131 The essence of algol (context) - Reynolds - 1981 ACM
86 Completeness in the theory of types (context) - Henkin - 1950 DBLP
56 The formulas-as-types notion of construction (context) - Howard - 1980
43 Completeness of many-sorted equational logic (context) - Goguen, Meseguer - 1982 ACM DBLP
41 Equality between functionals (context) - Friedman - 1975
38 A type-inference approach to reduction properties and semant.. (context) - Mitchell - 1986
31 What is a model of the lambda calculus (context) - Meyer - 1982
30 Relating theories of the lambda calculus (context) - Scott - 1980
30 Logical relations and the typed lambda calculus (context) - Statman - 1985
21 functor categories and block structure (context) - Oles - 1985
15 Empty types in polymorphic lambda calculus (context) - Meyer, Mitchell et al. - 1987 ACM DBLP
14 The logic of topoi (context) - Fourman - 1977
11 A condition for identifying two elements of whatever model o.. (context) - Jacopini - 1975 ACM DBLP
10 Recursive models for constructive set theories (context) - Beeson - 1982
9 Remarks on remarks on many-sorted equational logic (context) - Goguen, Meseguer - 1986 ACM DBLP
9 Open maps of toposes (context) - Johnstone - 1980
7 Equality between functionals (context) - Statman - 1985
5 An abstract notion of realizability for which intuitionistic.. (context) - auchli - 1970
4 From lambda calculus to cartesian closed categories (context) - Lambek - 1980
3 The semantics of evidence (context) - Constable - 1985 ACM
3 Lambda denability in the full type hierarchy (context) - Plotkin - 1980
2 Introduction or Combinators and Lambda Calculus (context) - Hindley, Seldin - 1986
2 Semantical analysis of specication logic (context) - Tennant - 1985
1 invariance and lambda-denability (context) - Statman - 1982
1 Intuitionistic propositional calculus and denably non-empty .. (context) - auchli - 1965
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