AbstractWe present a denotational semantics for a fully functional subset of the Handel-C hardware compilation language (Celoxica Ltd., Handel-C Language Reference Manual, v3.0, 2002,http://www.celoxica.com), based on the concept of typed assertion traces. We motivate the choice of semantic domains by illustrating the complexities of the behaviour of the language, paying particular attention to the prialt (priority-alternation) construct of Handel-C. We then define the typed assertion traces over an abstract notion of actions, and demonstrate key properties of the key semantic operations on these. The denotational semantics is then given using traces with actions instantiated as state-transformers.