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The Independence of Peano's Fourth Axiom from MartinLöf's Type Theory without Universes
 Journal of Symbolic Logic
, 1988
"... this paper will work for any of the different formulations of MartinLof's type theory. 2 The construction of the interpretation ..."
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Cited by 17 (2 self)
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this paper will work for any of the different formulations of MartinLof's type theory. 2 The construction of the interpretation
The Strength of the Subset Type in MartinLöf's Type Theory
 In Third Annual Symposium on Logic in Computer Science
, 1988
"... this paper show that the exact formulation of the rules of type theory is very important for the power of the subset type; it actually turns out that there are propositions involving subsets which are trivially true in naive set theory but which cannot be proved in type theory. We will look at the p ..."
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Cited by 10 (1 self)
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this paper show that the exact formulation of the rules of type theory is very important for the power of the subset type; it actually turns out that there are propositions involving subsets which are trivially true in naive set theory but which cannot be proved in type theory. We will look at the provability of propositions of the form
A New Paradox in Type Theory
 Logic, Methodology and Philosophy of Science IX : Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science
, 1994
"... this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and ..."
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Cited by 7 (0 self)
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this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and the axiom of description in impredicative Type Theories. 1 Minimal and Polymorphic HigherOrder Logic
On Specifications, Subset Types and Interpretation of Propositions in Type Theory
 Programming Methodology Group, University of Goteborg and Chalmers University of Technology
, 1989
"... Introduction Type theory may be used as a programming language with an integrated programming logic. An implementation of the theory should then give an environment allowing you to specify, construct and verify programs interactively. We have used NUPRL [10], which is such an environment for type t ..."
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Introduction Type theory may be used as a programming language with an integrated programming logic. An implementation of the theory should then give an environment allowing you to specify, construct and verify programs interactively. We have used NUPRL [10], which is such an environment for type theory, to develop some examples. NUPRL's logic is based on MartinLof's type theory [7] and provides you with a proof system, a function which extracts programs from proofs, a program evaluator, a library system and a possibility to define your own syntax and proof tactics for (partial) automatization of proofs. The usual way to specify a program in type theory is by identifying the specification with a type and a program satisfying the specification is then an element of this type. For instance a specification of a function which, given a nonempty list, returns any member of that list may be given by the proposition: (#x #<F
A normalization proof for MartinLöf's type theory
, 1996
"... The theory we will be concerned with in this paper is MartinLöf's polymorphic type theory with intensional equality and the universe of small sets. We will give a different proof of normalization for this theory. ..."
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The theory we will be concerned with in this paper is MartinLöf's polymorphic type theory with intensional equality and the universe of small sets. We will give a different proof of normalization for this theory.