An interpretation of Martin-löf's type theory in a type-free theory of propositions

Journal of Symbolic Logic 49 (3):730-753 (1984)
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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