MySQL GTID-set algebra — the dedup correctness core.

A GTID set is the sole authority for replication position (ADR-0001): dedup is set membership, never an ordinal comparison. This module is the one place GTID-set membership and interval math live, so no consumer — the connection's gap gate, the assembler, or a sink — ever hand-rolls them.

String format (MySQL canonical, INCLUSIVE bounds)

A comma-separated list of per-UUID entries; each entry is <uuid>:<interval>[:<interval>...]; an interval is a single number N or an inclusive range N-M with M >= N. "" is the empty set. A UUID is the 36-char hyphenated hex form; GNOs are integers >= 1. Ranges are inclusive: uuid:1-11 is GTIDs 1..11 and uuid:7 is uuid:7-7. Multi-source sets are supported — several UUID entries in one string.

render/1 produces the canonical form: UUIDs lower-cased and ordered lexicographically, intervals within a UUID sorted ascending and coalesced (merged where overlapping or adjacent), single-element intervals rendered as N. Parsing normalises to this form, so parse |> render is idempotent and, for any already canonical string s, s |> parse |> render == s.

Malformed input

parse/1 raises ArgumentError on any string outside the grammar above — a bad UUID, a GNO < 1 or non-numeric, a descending range, an empty entry. A dedup core must never silently coerce a malformed position into a plausible-but- wrong set, so parsing fails closed rather than guessing.

Single GTID shape

member?/2 takes a set and a single GTID as {uuid :: String.t(), gno :: pos_integer()}. The UUID is matched case-insensitively.

Scope

The bounds here are INCLUSIVE and stay inclusive. The COM_BINLOG_DUMP_GTID wire encoding uses an EXCLUSIVE end (uuid:1-11 -> wire end 12); that conversion is Task 3's concern and is deliberately not baked into this module.