Interesting idea. I feel like it could be productive to categorize operations by their result shape as well:
- Row select: From N rows, produce 0-N rows.
- Column select: From N columns, produce 0-N columns.
- Table add: From MxN and OxP tables, produce max M+OxN+P table.
- Table subtract: From MxN and OxP tables, produce min 0x0 table.
This line of thinking reveals some normally hard-to-see similarities, such as `groupby` and `dedupe` sharing the same underlying mechanism. (i.e., both are "collapsing" row selects.)
- Row select: From N rows, produce 0-N rows.
- Column select: From N columns, produce 0-N columns.
- Table add: From MxN and OxP tables, produce max M+OxN+P table.
- Table subtract: From MxN and OxP tables, produce min 0x0 table.
This line of thinking reveals some normally hard-to-see similarities, such as `groupby` and `dedupe` sharing the same underlying mechanism. (i.e., both are "collapsing" row selects.)