This is a new applied development of trace theory to compilation. Trace theory allows to commute independent program instructions, but overlooks the differences between control and data dependencies. Control(C)-dependences, unlike data-dependences, are determined by the Control Flow Graph, modelled as a local DFA. To ensure semantic equivalence, partial commutation must preserve C-dependences. New properties are proved for C-dependences and corresponding traces. Any local language is star-connected with respect to C-dependences, hence this trace language family is recognizable. Local languages unambiguously represent traces. Within the family of local languages with the same C-dependences, we construct the language such that instructions are maximally anticipated. This language differs from the Foata-Cartier normal form. Future directions for application of trace theory to program optimization are outlined.