Composer

Transitive derivation via Tuple2 as the intermediate carrier: given F → Tuple2 and Tuple2 → G, derive F → G. Fires cleanly for Direct-origin chains to any target with a Composer[Tuple2, _] direct (Affine / ModifyF / MultiFocus[F] / MultiFocus[PSVec]).

Express an Iso (or Getter) as a Prism — always takes the Right branch; Nothing in the Left slot so the miss branch is uninhabited.

Express an Iso (or Getter) as a Prism — always takes the Right branch; Nothing in the Left slot so the miss branch is uninhabited.

Express a Direct optic (a Getter, Review, or Iso) as a Forget[F]-carrier optic — lift the single focus into F via pure on the read side, and pick the single B back out of the F[B] on the build side. Powers Getter.andThen(Fold), Optic.cross against a Fold, and the build side of review.andThen(unfold) chains (optics.Unfold is Forget[F]'s build-only citizen, so from is reachable via assocForgetMonad.composeFrom on a Monad[F] chain).

The singleton pick is sound on every reachable path: the only F[B] ever fed to a lifted Direct optic's from is ForgetPull.monadicPull's pure(b). A hand-routed call with cardinality ≠ 1 throws, mirroring the other pickSingletonOrThrow bridges. Requires Applicative[F] for pure and Foldable[F] for the pick.

Express an Iso (or Getter) as a Lens — the Lens's leftover is Unit because the bijection doesn't need any.

Express an Iso (or Getter) as a Lens — the Lens's leftover is Unit because the bijection doesn't need any.