Optic

Flip the direction of an optic — only defined when the carrier admits both Accessor[F] and ReverseAccessor[F] (i.e. iso-shaped carriers).

True iff at least one focus satisfies p. Short-circuits on the first hit when the carrier's ForgetfulFold[F] is short-circuit-aware. The default Monoid[Boolean] cats exposes is conjunction (&&); we instantiate a disjunction monoid inline so a single match can win without consulting the rest.

foldMap over the focus — the primary consumption path for Fold and any other carrier with a ForgetfulFold[F] instance. Combines every focus through Monoid[M].

Total read — extract the focus, available when the carrier always hits (Accessor[F]: Tuple2 for Lens, Direct for Iso / Getter). readOnly wraps the same read as a concrete Getter, the one-way view of a writable optic.

Partial read — Some(focus) on hit, None on miss. Available when the carrier may miss (PartialAccessor[F]: Either for Prism, Affine for Optional / AffineFold).

First focus visible through the optic, if any. Available on any carrier admitting ForgetfulFold[F] — Forget[F] (Fold), MultiFocus[F] (Traversal), Affine (Optional / AffineFold), Either (Prism), Tuple2 (Lens). For 0-or-1-focus carriers this is the same Option you'd get from .getOption; for multi-focus carriers it picks the first focus the underlying Foldable enumerates.

Implemented via foldMap under a custom "first-Some" Monoid[Option[A]] — the same shape Monocle's Fold.headOption uses. The custom monoid short-circuits via _.orElse(_), so on a Foldable[F] whose foldMap is itself short-circuit-aware (e.g. LazyList) the walk stops at the first focus.

Number of foci visible through the optic. O(n) in the focus count via Foldable.foldMap under Monoid[Int]. Distinct from Foldable.size only in that it routes through the carrier's ForgetfulFold[F] — same end result, available wherever foldMap is.

Modify (A => B) or replace (by constant B) the focus in-place. Available for every carrier with a ForgetfulFunctor[F] instance — i.e. every current optic family.

Effectful modify over any Applicative[G]; unlike modifyF this variant also exposes all, which collects every visited focus via Applicative[List].

Effectful modify over any Functor[G] — generalises modify to monadic / effectful A => G[B] transformations.

Overwrite a T-shaped value at the focus — available when the carrier can witness T => F[X, B] (e.g. Direct, where F[X, B] = B). transfer lifts a C => B into this same shape with an extra C argument.

Construct a T directly from an A, running f: A => B at the focus — available for carriers with a ForgetfulApplicative[F] instance (today: Direct).

Total read — extract the focus, available when the carrier always hits (Accessor[F]: Tuple2 for Lens, Direct for Iso / Getter). readOnly wraps the same read as a concrete Getter, the one-way view of a writable optic.

Modify (A => B) or replace (by constant B) the focus in-place. Available for every carrier with a ForgetfulFunctor[F] instance — i.e. every current optic family.

Flip the direction of an optic — only defined when the carrier admits both Accessor[F] and ReverseAccessor[F] (i.e. iso-shaped carriers).

Build the "no context" reverse — takes a fresh B and produces the corresponding T. Available when the carrier has a ReverseAccessor[F] instance (today: Either and Direct).

Overwrite a T-shaped value at the focus — available when the carrier can witness T => F[X, B] (e.g. Direct, where F[X, B] = B). transfer lifts a C => B into this same shape with an extra C argument.

Generalised place: transform a D at the focus via D => B rather than replacing unconditionally.

Profunctor over (B, A) — dimap on the inner focus pair. Requires a ForgetfulFunctor[F] so the carrier can map its focus in place.

Profunctor over (S, T) — dimap on the outer parameter pair, letting callers pre-compose the source side and post-compose the result side of a fixed-focus optic.

The identity optic — S is its own focus and modification has no effect. Carrier is data.Direct (no leftover). Returns the concrete BijectionIso (not an anonymous Optic) so id.andThen(x) picks up the fused compose members like any other Iso.