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A lambda calculus model of Martin-Löf's theory of types with explicit substitution (1997)  (Make Corrections)  
Daniel Fridlender



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Abstract: This paper presents a proof-irrelevant model of Martin-Lof's theory of types with explicit substitution; that is, a model in the style of [Smi88], in which types are interpreted as truth values and objects (or proofs) are irrelevant. The fundamental difference here is the need to cope with a formal system which in addition to types has sets and substitutions. This difference leads us to a whole reformulation of the model which consists in defining an interpretation in terms of the untyped... (Update)

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BibTeX entry:   (Update)

@misc{ fridlender-lambda,
  author = "Daniel Fridlender",
  title = "A lambda calculus model of Martin-Löf's theory of types with explicit substitution",
  url = "citeseer.ist.psu.edu/fridlender97lambda.html" }
Citations (may not include all citations):
236   Intuitionistic Type Theory (context) - Martin-Lof - 1984
89   The Lambda Calculus (context) - Barendregt - 1981
79   Pattern matching with dependent types (context) - Coquand - 1992
39   A Non-Type-Theoretic Semantics for Type-Theoretic Language (context) - Allen - 1987
35   Formal Aspects of Computing (context) - Dybjer - 1994
33   Generalized algebraic theories and contextual categories (context) - Cartmell - 1986
25   truth and set (context) - Aczel, the et al. - 1980
21   Programming in MartinL of's Type Theory (context) - Nordstrom, Petersson et al. - 1990
19   Programming with proofs: a second order type theory (context) - Parigot - 1988
17   record types and subtyping in type theory (context) - Tasistro - 1997
15   Syntax and semantics of dependent types - Hofmann - 1997
10   The Independence of Peano's Fourth Axiom from Martin-Lof's T.. - Smith - 1988
8   Internal type theory - Dybjer - 1996
1   Higman lemma in type theory (context) - Fridlender - 1997
1   A general formulation of simultaenous inductive-recursive de.. (context) - Dybjer - 1997
1   A Type Theoretical Analysis of Some Aspects of Programming L.. (context) - Gaspes - 1997

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