  In visualization, the process of transforming raw data into visually
comprehensible representations is pivotal. While existing models like the
Information Visualization Reference Model describe the data-to-visual mapping
process, they often overlook a crucial intermediary step: design-specific
transformations. This process, occurring after data transformation but before
visual-data mapping, further derives data, such as groupings, layout, and
statistics, that are essential to properly render the visualization. In this
paper, we advocate for a deeper exploration of design-specific transformations,
highlighting their importance in understanding visualization properties,
particularly in relation to user tasks. We incorporate design-specific
transformations into the Information Visualization Reference Model and propose
a new formalism that encompasses the user task as a function over data. The
resulting formalism offers three key benefits over existing visualization
models: (1) describing task as compositions of functions, (2) enabling analysis
of data transformations for visual-data mapping, and (3) empowering reasoning
about visualization correctness and effectiveness. We further discuss the
potential implications of this model on visualization theory and visualization
experiment design.
