RepresentativeIndex

A concrete index value for the Function1[X0, *] (Grate) carrier — the witness that makes a bundle read real instead of forged.

'''Why a witness exists at all.''' A Grate bundle is a function X0 => A; reading it needs an X0, and no rule of the type system produces one. Exactly one site in the library needs that read: the from of the bridge's product (Function1BroadcastOptic, private[eo]), which must turn a written MultiFocus[Function1[X0, *]][Unit, B] back into a T, and whose own carrier stores only Unit. Every other read in the Grate surface is handed its index by the caller (to(s), the .at(i) extension, F.index), and every write walks the index space itself (MultiFocusK.tuple counts 0..size-1, representable tabulates). So this typeclass is the whole index-supply story, and it is consulted in exactly one place.

'''What the choice of index does — and does not — affect.''' Instances are read on a path whose bundle is constant by construction (see that optic's from), where every index yields the same value: this witness changes which value is read only when someone hands from a varying bundle by hand. It never changes .modify / .replace / collect*, and it never changes a grate ∘ iso composition — the kernel rebuilds those per index through broadcastFrom, which needs no index.

'''Supply.''' The shipped instances name the canonical first index of the index types the Grate factories fix: Int for MultiFocusK.tuple (and for apply over a Function1[Int, *]), Boolean, Unit, plus any singleton type via ValueOf. For every other index type the caller supplies one — either a local given (given RepresentativeIndex[Symbol] = RepresentativeIndex.at(Symbol("x"))) or the at smart constructor at the use site. MultiFocusK.representable pins its index to F.Representation, which has no canonical inhabitant — so a grate over one takes its witness from the caller, the same value the read side passes to .at(i) per call.

'''The shipped instances do privilege a value''' (0 for Int, false for Boolean) — the thing MultiFocusK.representable's doc rules out for a constructor index, and rightly: an index that lives on the optic is a claim about the optic. This one is not that. It is the position a read falls back to when nobody is there to name one, it keeps the bridge implicit (so iso.andThen(grate) stays import-free), and it is unobservable on every shipped path — which is why shipping it is a convenience rather than a semantics. The alternative the design note prices out is no shipped instances at all: three composition cells go red and every caller writes a given.

An '''uninhabited''' index type (Function1[Nothing, *]-indexed, a phantom slot) gets no instance, deliberately: there is no index to witness, so the bridge refuses rather than reading a bundle at a value that cannot exist.