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The C/C++ memory model provides an interface and execution model for programmers of concurrent (shared-variable) code. It provides a range of mechanisms that abstract from underlying hardware memory models -- that govern how multicore architectures handle concurrent accesses to main memory -- as well as abstracting from compiler transformations. The C standard describes the memory model in terms of cross-thread relationships between events, and has been influenced by several research works that are similarly based. In this paper we provide a thread-local definition of the fundamental principles of the C memory model, which, for concise concurrent code, serves as a basis for relatively straightforward reasoning about the effects of the C ordering mechanisms. We argue that this definition is more practical from a programming perspective and is amenable to analysis by already established techniques for concurrent code. The key aspect is that the memory model definition is separate to other considerations of a rich programming language such as C, in particular, expression evaluation and optimisations, though we show how to reason about those considerations in the presence of C concurrency. A major simplification of our framework compared to the description in the C standard and related work in the literature is separating out considerations around the "lack of multicopy atomicity", a concept that is in any case irrelevant to developers of code for x86, Arm, RISC-V or SPARC architectures. We show how the framework is convenient for reasoning about well-structured code, and for formally addressing unintuitive behaviours such as "out-of-thin-air" writes.