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Titlebook: Logics of Programs; Brooklyn, June 17-19 Rohit Parikh Conference proceedings 1985 Springer-Verlag Berlin Heidelberg 1985 Computer.Logic.Pro

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Lambda calculus with constrained types, typed case at one extreme and the type-free case at the other. The abstract model theory of the β η type-free case is generalized. We investigate the relation between lambda calculus with constrained types and cartesian closed categories (cccs) at proof-theoretic and model-theoretic levels. We find
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Recursive definitions in type theory,type definitions involving the . function-space constructor (→) to those with only positive occurrences of the defined typed. But we show that arbitrary recursive definitions with respect to the . function-space constructor are sensible. The partial function-space constructor allows us to express re
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Proving termination of Prolog programs, as displayed by Prolog. The first kind of rule takes into account the context of the whole program and is based on a tree oriented operational semantics. The second kind is more compositional, dealing with separate procedures in a context independent way. It is based on a stream oriented semantics.
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The glory of the past, and a complete axiomatic system are presented. A suggested normal form leads to a syntactic classification of safety and liveness formulae. The adequacy of temporal logic to modular verification is examined. Finally we present the notion of . which is proved to fully capture the behavior of probabi
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Continuation semantics in typed lambda-calculi,n untyped lambda-calculi and has used primarily the mechanism of inclusive predicates. Such predicates are easy to understand on atomic values, but they become obscure on functional values. In the case of the typed lambda-calculus, we show that such predicates can be replaced by retractions. The mai
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