1 · A column = a measure over an anchor, made and reduced by operators
A measure is a thing the data can report — revenue, orders. An anchor is the coordinates you report it at — by store, by day — the "per what" of the number. Between them sit the operators: the verbs of the algebra. A reducer collapses many rows into one (summed, counted, a median, the last value); a mapper reshapes a column without collapsing it. Put a measure, its anchor, and the operators together and you have a column: the atom of a Columna answer. The askable space isn't the list of measures — it's measures times operators, filtered by what's legal. Most wrong numbers come from a hidden anchor — the same revenue "averaged" per order, per line-item, and per customer are three different numbers.
2 · Population (universe) — what it's about
Every measure is defined over a population — the exact set of rows it speaks about. Columna names populations as universes (here: transactions, the sales rows; and store_days, one row per store per day it was open). Two measures from different populations aren't automatically comparable, and a rate that spans two of them has no single "per what" until you say which.
3 · The pair — result and disclosure
An answer is never just a number. It's a pair: the result, and a disclosure that travels with it — the assumption, the caveat, the population it was taken over. The disclosure isn't an error; it's the number being honest about what it took to produce it.
4 · The four moods
How the pair reads is the mood:
- serve — fully specified; it just answers.
- disclose — it answers, with the assumption attached.
- clarify — the question has several legitimate readings; which did you mean?
- refuse — the data can't answer that, and here's the reason.
"It depends," said precisely, is often the most correct answer there is.
5 · The legal cone — what may be asked
For each measure, Columna knows every grain it may lawfully be asked at, and every direction that's barred — with the reason. An end-of-period inventory level may be rolled up across stores into a region, but not summed across days: the stock on the 3rd isn't separate from the stock on the 4th, so adding them double-counts. A catalog tells you what exists; the legal cone tells you what may be asked of it — that's what the "what's in this manifold?" panel shows.
6 · Pin — resolving ambiguity
When a question could be taken over more than one population, you pin it — written ON UNIVERSE <name>. Pinning is how a clarify becomes an answer: you choose the reading, and the grammar holds you to what's actually defined there (which is why pinning the wrong population earns an honest refuse).