Reversible printing with sort printing and anonymous sort quality variables (combines #22155, #22283, #22310)

[JasonGross]

Written by Claude (Anthropic AI) at the request of and under the supervision of @JasonGross.

This PR stacks three printing features plus one integration commit so that reversible printing knows how to make sort qualities and sort quality variables explicit when they are what keeps a printed term from re-parsing.

It combines:

• Add Set Printing Sorts option #22155 — Set Printing Sorts: like Set Printing Universes but shows only the sort structure. Plain sorts print as usual; hidden sort quality variables are shown with their universe levels anonymized as _ (e.g. Type@{s ; _}), and universe instances of polymorphic references are displayed when they carry sort qualities. (Note: distinct from the pre-existing Printing Sort Qualities flag, which they coexist with.)
• Add Printing Reversible flags: check printed terms reparse to equal terms, escalating printing options when not #22283 — Printing Reversible … flags: after printing a term, the printed form is re-parsed and re-elaborated and compared back to the original; when it does not round-trip, printing options are escalated along a ladder until it does (or a reversible-printing warning is emitted).
• Add Set Printing Sort Quality Variables Anonymously #22310 — Set Printing Sort Quality Variables Anonymously: sort quality variables that have no name print as _ (which re-parses to a fresh quality variable) instead of their raw α-names (which cannot be re-parsed at all). This PR tracks the amended Add Set Printing Sort Quality Variables Anonymously #22310, which also includes the Type@{_ ; u} sort-annotation grammar extension: _ is now accepted as an anonymous sort quality inside a sort (mirroring what universe instances already accepted). The ladder integration relies on this so that the sort in a printed type — not just an instance annotation — round-trips.
• one new commit integrating sort printing and anonymous quality variables into the reversible-printing escalation ladder.

Escalation ladder

The reversible-printing ladder now tries, in order of increasing explicitness (each rung is standalone, not cumulative):

coercions → implicit arguments → sorts → sorts + anonymous quality variables → notations off → universes + anonymous quality variables → universes → universes without notations + anonymous quality variables → universes without notations → parentheses → raw (Printing All + universes + parentheses).

Rationale for trying anonymous quality variables before the non-anonymous form at each rung: an unnamed sort quality variable has no name-based syntax that re-parses — its raw α-name is unparsable — so printing it anonymously as _ is the only reversible form available. With the Type@{_ ; u} grammar extension above, this anonymous form re-parses both in an instance annotation (idT@{_ ; _}) and inside a sort in the type (Type@{_ ; _}), so a bare sort-polymorphic constant round-trips fully with no warning at the sorts + anonymous-quality-variables rung.

The immediately following rung retries with the flag off, because anonymizing a quality variable can itself be what breaks re-parsing (the _ re-parses to a fresh variable, which round-trips only when unification can match it); in that case the more explicit non-anonymous rung, or a later universes rung, is what succeeds. Raw printing stays faithful, with anonymous quality variables off.

Notes

• This PR should not be merged before its dependencies (Add Set Printing Sorts option #22155, Add Printing Reversible flags: check printed terms reparse to equal terms, escalating printing options when not #22283, Add Set Printing Sort Quality Variables Anonymously #22310) and will be rebased onto them once they merge; it is opened as a draft for CI and review of the integration.

🤖 Generated with Claude Code

https://claude.ai/code/session_01L9BGQT7XUuubV6C619DW4b