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A Variable Typed Logic of Effects
 Information and Computation
, 1993
"... In this paper we introduce a variable typed logic of effects inspired by the variable type systems of Feferman for purely functional languages. VTLoE (Variable Typed Logic of Effects) is introduced in two stages. The first stage is the firstorder theory of individuals built on assertions of equalit ..."
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Cited by 48 (12 self)
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In this paper we introduce a variable typed logic of effects inspired by the variable type systems of Feferman for purely functional languages. VTLoE (Variable Typed Logic of Effects) is introduced in two stages. The first stage is the firstorder theory of individuals built on assertions of equality (operational equivalence `a la Plotkin), and contextual assertions. The second stage extends the logic to include classes and class membership. The logic we present provides an expressive language for defining and studying properties of programs including program equivalences, in a uniform framework. The logic combines the features and benefits of equational calculi as well as program and specification logics. In addition to the usual firstorder formula constructions, we add contextual assertions. Contextual assertions generalize Hoare's triples in that they can be nested, used as assumptions, and their free variables may be quantified. They are similar in spirit to program modalities in ...
Hybrid PartialTotal Type Theory
, 1995
"... In this paper a hybrid type theory HTT is defined which combines the programming language notion of partial type with the logical notion of total type into a single theory. A new partial type constructor A is added to the type theory: objects in A may diverge, but if they converge, they must be memb ..."
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Cited by 5 (0 self)
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In this paper a hybrid type theory HTT is defined which combines the programming language notion of partial type with the logical notion of total type into a single theory. A new partial type constructor A is added to the type theory: objects in A may diverge, but if they converge, they must be members of A. A fixed point typing rule is given to allow for typing of fixed points. The underlying theory is based on ideas from Feferman's Class Theory and Martin Lof's Intuitionistic Type Theory. The extraction paradigm of constructive type theory is extended to allow direct extraction of arbitrary fixed points. Important features of general programming logics such as LCF are preserved, including the typing of all partial functions, a partial ordering ! ΒΈ on computations, and a fixed point induction principle. The resulting theory is thus intended as a generalpurpose programming logic. Rules are presented and soundness of the theory established. Keywords: Constructive Type Theory, Logics...
Reasoning with Continuations III: A Complete Calculus of Control
, 1992
"... [Anybody taye in the first paragraph? Thanks!] The central result of this paper is an extension of the lambda(v)Ccalculus for a complete set of control operators and a correspondence theorem between the new theory and the lambda/beta/etacalculus. Technically, the theorem shows that the two calcul ..."
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[Anybody taye in the first paragraph? Thanks!] The central result of this paper is an extension of the lambda(v)Ccalculus for a complete set of control operators and a correspondence theorem between the new theory and the lambda/beta/etacalculus. Technically, the theorem shows that the two calculi prove the same equations with respect to the wellknown continuationpassing style translation (and its inverse), which is the standard tool for defining control operators via translation into a functional language. As a corollary, the calculus proves all program equivalences between terms over the pure language extended with control operators. We believe that this work has important consequences for the directstyle compilation of programming languages with control operators.