A Step-indexed Semantics of Imperative Objects

Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for which these values are guaranteed to behave like proper elements of the type. Building on work by Ahmed, Appel and others, we introduce a step-indexed semantics for the imperative object calculus of Abadi and Cardelli. Providing a semantic account of this calculus using more `traditional', domain-theoretic approaches has proved challenging due to the combination of dynamically allocated objects, higher-order store, and an expressive type system. Here we show that, using step-indexing, one can interpret a rich type discipline with object types, subtyping, recursive and bounded quantified types in the presence of state

Denotational semantics for a program logic of objects

No description supplie

Denotational semantics for a program logic of objects

No description supplie

Under consideration for publication in Math. Struct. in Comp. Science Denotational Semantics for a Program Logic of Objects †

The object-calculus is an imperative and object-based programming language where every object comes equipped with its own method suite. Consequently, methods need to reside in the store (“higher-order store”) which complicates the semantics. Abadi and Leino defined a program logic for this language enriching object types by method specifications. We present a new soundness proof for their logic using Denotational Semantics. It turns out that denotations of store specifications are predicates defined by mixed-variant recursion. A benefit of our approach is that derivability and validity can be kept distinct. Moreover, it is revealed which of the limitations of Abadi and Leino’s logic are incidental design decisions and which follow inherently from the use of higher-order store. We discuss the implications for the development of other, more expressive, program logics. 1