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This article presents Proteus, a core calculus that models dynamic software updating, a service for fixing bugs and adding features to a running program. Proteus permits a program's type structure to change dynamically but guarantees the updated program remains type-correct by ensuring a property we call con-freeness. We show how con-freeness can be enforced dynamically, and how it can be approximated via a novel static analysis. This analysis can be used to assess the implications of a program's structure on future updates in order to make update success more predictable. We have implemented Proteus for C, and briefly discuss our implementation which we have tested on several well-known programs.