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Abstract: this paper will work for any of the different formulations of Martin-Lof's type theory. 2 The construction of the interpretation (Update)
Context of citations to this paper: More
.... 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...
...of defining families of sets by structural recursion. For example, the predicate Z (as used in the type theoretic proof that 0 6= s(n) [29, 43]) with the recursion equations Z(0) Z(s(n) is defined in terms of universes and the rule of N elimination. Martin Lof [27]...
Cited by: More
Propositional Functions and Families of Types - Smith (1989) (Correct)
The Theory of LEGO - A Proof Checker for the Extended Calculus of .. - Pollack (1994) (Correct)
Syntax and Semantics of Dependent Types - Hofmann (1997) (Correct)
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7: Intuitionistic Type Theory (context) - Martin-Lof - 1984
6: Formal Aspects of Computing (context) - Dybjer - 1994
5: Implementing Mathematics with the Nuprl Proof Development System - Constable - 1986
BibTeX entry: (Update)
J. Smith. The independence of peano's fourth axiom from Martin-Lof's type theory without universes. Journal of Symbolic Logic, 53:840--845, 1988. http://citeseer.ist.psu.edu/smith88independence.html More
@misc{ smith88independence,
author = "J. Smith",
title = "The independence of peano's fourth axiom from Martin-Lof's type theory
without universes",
text = "J. Smith. The independence of peano's fourth axiom from Martin-Lof's type
theory without universes. Journal of Symbolic Logic, 53:840--845, 1988.",
year = "1988",
url = "citeseer.ist.psu.edu/smith88independence.html" }
Citations (may not include all citations):236 Intuitionistic Type Theory (context) - Martin-Lof - 1984
141 Constructive Mathematics and Computer Programming (context) - Martin-Lof - 1982 ACM
71 An intuitionistic theory of types: predicative part (context) - Martin-Lof - 1975
14 Grundzuge der Theoretischen Logik (context) - Hilbert, Ackermann - 1928
6 a Nonconstructive Type Theory and Program Derivation (context) - Smith - 1986
4 Die Widerspruchsfreiheit der Stufenlogik (context) - Gentzen - 1936
2 Einige Betrachtungen uber die Begriffe der (context) - Tarski - 1933
The graph only includes citing articles where the year of publication is known.
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Optimized Encodings of Fragments of Type Theory in First Order.. - Tammet, Smith (1994) (Correct)
An Interpretation of Kleene's Slash in Type Theory - Smith (1993) (Correct)
The Strength of the Subset Type in Martin-Lof's Type Theory - Anne Salvesen (1988) (Correct)
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