A computing device receives user input to specify a natural language command directed to a data source. In accordance with the user input, the device forms an intermediate expression according to a context-free grammar and a semantic model of data fields in the data source. The natural language command includes (i) a first term that specifies an aggregation type in a first aggregation, (ii) a second term that specifies a data field, in the semantic model, to be aggregated for the first aggregation, and (iii) terms that specify data fields, in the semantic model, to determine grouping for the first aggregation. The device translates the intermediate expression into database queries, executes the database queries to retrieve one or more data sets from the data source, aggregated according to the first aggregation, then generates and displays a data visualization of the retrieved data sets.