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Kim B. Bruce

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4 papers
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4

I&C Journal 1999 Journal Article

Comparing Object Encodings

  • Kim B. Bruce
  • Luca Cardelli
  • Benjamin C. Pierce

Recent years have seen the development of several foundational models for statically typed object-oriented programming. But despite their intuitive similarity, differences in the technical machinery used to formulate the various proposals have made them difficult to compare. Using the typed lambda-calculus F ω <: as a common basis, we now offer a detailed comparison of four models: (1) a recursive-record encoding similar to the ones used by Cardelli, Reddy, Cook, and others; (2) Hofmann, Pierce, and Turner's existential encoding; (3) Bruce's model based on existential and recursive types; and (4) Abadi, Cardelli, and Viswanathan's type-theoretic encoding of a calculus of primitive objects.

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I&C Journal 1990 Journal Article

The semantics of second-order lambda calculus

  • Kim B. Bruce
  • Albert R. Meyer
  • John C. Mitchell

In the second-order (polymorphic) typed lambda calculus, lambda abstraction over type variables leads to terms denoting polymorphic functions. Straightforward cardinality considerations show that a naive set-theoretic interpretation of the calculus is impossible. We give two definitions of semantic models for this language and prove them equivalent. Our syntactical “environment model” definition and a more algebraic “combinatory model” definition for the polymorphic calculus correspond to analogous model definitions for untyped lambda calculus. Soundness and completeness theorems are proved using the environment model definition. We verify that some specific interpretations of the calculus proposed in the literature indeed yield models in our sense.

Details DOI
v2026.09.13