Status: implemented

or(a, b, …) admits every value any of its members admits. never is the empty union, or(), and admits nothing.

const shape = or(
    { kind: 'circle', r: number },
    { kind: 'square', side: number },
)
const id = or(string, number)

or is a lazy constructor: it captures its members in a thunk and does no flattening, deduplication or subset analysis. That algebra is the data form's: toData merges members kind by kind, absorbs a constant into its whole kind (or(42, number) is all numbers), drops a member another covers, and orders what is left canonically. So two spellings of one set have one data form, and equal says so: or(true, false) and boolean are equal, and subset(toData(42))(toData(number)) holds.

never is what an empty rest is: rest(c, never) is the closed c (open containers). A union with option is how a member is made optional.

The demo on this page runs the Two spellings, one set lesson: pick or(true, false) or boolean, and the comparison under the graph reports equal → true; the TypeScript type and the JSON Schema of the two are the same. The lesson is defined in sample.f.mjs, and the module page's demo lists it among all the others.

• TypeScript: union types and never
• JSON Schema: anyOf, and { "not": {} } for never (reference)

or and never in module.f.mjs; normalization, equal, cmp and subset in data, which documents them (data/README.md).