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

  • Jan Smith (a1)
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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[1]Aczel, P.. The strength of Martin-Löf's intuitionistic type theory with one universe, Proceedings of the symposium on mathematical logic (Oulu, 1974), Report No. 2, Department of Philosophy, University of Helsinki, Helsinki, 1977, pp. 132.
[2]Aczel, P., Frege structures and the notions of proposition, truth and set, The Kleene Symposium, North-Holland, Amsterdam, 1980, pp. 3159.
[3]Beeson, M., Recursive models for constructive set theories, Annals of Mathematical Logic, vol. 23 (1983), pp. 127178.
[4]Martin-Löf, P.. An intuitionistic theory of types, Logic Colloquium '73, North-Holland, Amsterdam, 1975, pp. 73118.
[5]Martin-Löf, P., Constructive mathematics and computer programming, Logic, Methodology and Philosophy of Science VI, North-Holland, Amsterdam, 1982, pp. 153175.
[6]Smith, J.. On the relation between a type theoretic and a logical formulation of the theory of constructions, Dissertation, Department of Mathematics, University of Göteborg, Göteborg, 1978.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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