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An Interpretation of Martin-Löf's Type Theory in a Type-Free Theory of Propositions

Jan Smith
The Journal of Symbolic Logic
Vol. 49, No. 3 (Sep., 1984), pp. 730-753
DOI: 10.2307/2274128
Stable URL: http://www.jstor.org/stable/2274128
Page Count: 24
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An Interpretation of Martin-Löf's Type Theory in a Type-Free Theory of Propositions
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Abstract

We present a formal theory of propositions and combinator terms, and in this theory we give an interpretation of Martin-Löf's type theory. The construction of the interpretation is inspired by the semantics for type theory, but it can also be viewed as a formalized realizability interpretation.

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