Abstract types and dependence in programming languages
The propositions-as-types principle of Curry and Howard exhibits the close relationship between proof theory and programming language theory. This dissertation examines the programming concepts of abstract types and dependence from a logical perspective, giving a reconstruction of the type system and semantics of the programming language Russell in the Curry-Howard framework. It begins by presenting a catalog of type theories for the lambda calculus organized by the propositions as types principle. After establishing the catalog as a reference point, the dissertation attacks the motivating problem - the explanation of Russell. This explanation is first done informally, then a family of dialects of Russell is extracted from the intuition. These dialects are distinguished by the rules they use to decide when two types are equal. The family ranges from a complete semantic theory of computational equality to the primitive, syntactic, criteria of being identical except for the names of bound variables. The dissertation concludes with a discussion of more general applications of the embedding techniques exploited here and a critique of the Russell language design.
- Research Organization:
- Cornell Univ., Ithaca, NY (USA)
- OSTI ID:
- 6854222
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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