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Abstract: The advent of proof-carrying code has generated significant interest in reasoning about low-level languages. It is widely believed that low-level languages with jumps must be difficult to reason about because of being inherently non-modular. We argue that this is untrue. We take it seriously that, unlike statements of a high-level language, pieces of low-level code are multiple-entry and multiple-exit. And we define a piece of code as consisting of either a single labelled instruction or a finite union of pieces of code. Thus we obtain a compositional natural semantics and a matching Hoare logic for a basic low-level language with jumps. By their simplicity and intuitiveness, these are comparable to the standard natural semantics and Hoare logic of While. The Hoare logic is sound and complete wrt the semantics and allows for compilation of proofs of the Hoare logic of While. [Copyright &y& Elsevier]

Abstract: In this paper we compare the semantical and syntactical definitions of extensions for open default theories. We prove that, over monadic languages, these definitions are equivalent and do not depend on the cardinality of the underlying infinite world. We also show that, under the domain closure assumption, one free variable open default theories are decidable. [Copyright &y& Elsevier]