1. A method comprising, by a computer system: receiving a data-transformation request in relation to a visualization of a first dataset, wherein the visualization represents columns of data, wherein the data-transformation request expresses at least one transformation of the first dataset without using Structured Query Language (SQL) syntax, wherein the visualization is characterized by a first SQL statement maintained by the computer system, wherein the columns of the visualization are mapped to constituent parts of the first SQL statement in which the columns are referenced; automatically determining a second SQL statement configured to return a second dataset, wherein the second dataset implements the at least one transformation of the first dataset, the automatically determining comprising: looking up an identifier of the at least one transformation in a repository; responsive to a determination that there exists, in the repository for the identifier, an applicable SQL generation rule other than a default rule, automatically building the second SQL statement based, at least in part, on the mapping of the visualization to the constituent parts of the first SQL statement, using SQL syntax specified by the applicable SQL generation rule; and responsive to a determination that there does not exist, in the repository for the identifier, an applicable SQL generation rule other than the default rule, automatically building the second SQL statement based, at least in part, on the mapping of the visualization to the constituent parts of the first SQL statement, using SQL syntax specified by the default rule, the building comprising including the first SQL statement as a subquery in a clause of the second SQL statement; causing the second SQL statement to be executed on one or more databases; receiving the second dataset in response to the causing; and updating the visualization to reflect the second dataset.