We present a small-step, frame stack style, semantics for sequential Core Erlang, a dynamically typed, impure functional programming language. The semantics and the properties that we prove are machine-checked with the Coq proof assistant. We improve on previous work by including exceptions and exception handling, as well as built-in data types and functions. Based on the semantics, we define multiple concepts of program equivalence (contextual, CIU equivalence, and equivalence based on logical relations) and prove that the definitions are all equivalent. Using this we are able to give a correctness criterion for refactorings by means of contextually equivalent symbolic expression pairs, which is one of the main motivations of this work.

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