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This report is a presentation of a formal semantics for the C programming language. The semantics has been defined operationally in a structured semantics style and covers the bulk of the core of the language.

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Security folklore holds that a security mechanism based on stack inspection is incompatible with a global tail call optimization policy; that an implementation of such a language must allocate memory for a source-code tail call, and a program that uses only tail calls (and no other memory allocating construct) may nevertheless exhaust the available memory. In this article, we prove this widely held belief wrong. We exhibit an abstract machine for a language with security stack inspection whose space consumption function is equivalent to that of the canonical tail call optimizing abstract machine. Our machine is surprisingly simple and suggests that tail calls are as easy to implement in a security setting as they are in a conventional one.

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Modularity is an important pragmatic aspect of semantic descriptions. In denotational semantics, the issue of modularity has received much attention, and appropriate abstractions have been introduced, so that definitions of semantic functions may be independent of the details of how computations are modelled. In structural operational semantics (SOS), however, this issue has largely been neglected, and SOS descriptions of programming languages typically exhibit rather poor modularity -- for instance, extending the described language may entail a complete reformulation of the description of the original constructs. A propos

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Call-by-push-value is a ”semantic machine code”, providing a set of simple primitives from which both the call-by-value and call-by-name paradigms are built. We present its operational semantics as a stack machine, suggesting a term judgement of stacks. We then see that CBPV, incorporating these stack terms, has a simple categorical semantics based on an adjunction between values and stacks. There are no coherence requirements. We describe this semantics incrementally. First, we introduce locally indexed categories and the opGrothendieck construction, and use these to give the basic structure for interpreting the three judgements: values, stacks and computations. Then we look at the universal property required to interpret each type constructor. We define a model to be a strong adjunction with countable coproducts, countable products and exponentials. We see a wide range of instances of this structure: we give examples for divergence, storage, erratic choice, continuations, possible worlds and games (with or without a bracketing condition), in each case resolving the strong monad from the literature into a strong adjunction. And we give ways of constructing models from other models. Finally, we see that call-by-value and call-by-name are interpreted within the Kleisli and co-Kleisli parts, respectively, of a call-by-push-value adjunction.