Analysis of execution traces plays a fundamental role in many program analysis approaches. Execution traces are frequently parametric, i.e., they contain events with parameter bindings. Each parametric trace usually consists of many trace slices merged together, each slice corresponding to a parameter binding. Several techniques have been proposed to analyze parametric traces, but they have limitations: some in the specification formalism, others in the type of traces they support; moreover, they share common notions, intuitions, even techniques and algorithms, suggesting that a fundamental understanding of parametric trace analysis is needed. This foundational paper gives the first solution to parametric trace analysis that is unrestricted by the type of parametric properties or traces that can be analyzed. First, a general purpose parametric trace slicing technique is discussed, which takes each event in the parametric trace and distributes it to its corresponding trace slices. Thi...