Abstract
We present an interpreation of a constructive domain theory in Martin-Löf's type theory. More specifically, we construct a well-pointed Cartesian closed category of semilattices and approximable mappings. This construction is completely formalized and checked using the interactive proof assistant ALF.
We base our work on Martin-Löf's domain interpretation of the theory of expressions underlying type theory. But our emphasis is different from Martin-Löf's, who interprets the program forms of type theory and proves a correspondence between their denotational and operational semantics. We instead show that a theory of domains can be developed within a well-defined fragment of (total) type theory. This is an important step toward constructing a model of all of partial type theory (type theory extended with general recursion) inside total type theory.
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This research was partially supported by ESPRIT Basic Research Action “TYPES”.
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Hedberg, M. A type-theoretic interpretation of constructive domain theory. Journal of Automated Reasoning 16, 369–425 (1996). https://doi.org/10.1007/BF00252182
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DOI: https://doi.org/10.1007/BF00252182