Local[F, E] lets you alter the E value that is observed by an F[A] value using ask; the modification can only be observed from within that F[A] value.

Local[F, E] has three external laws:

def askReflectsLocal(f: E => E) = {
  local(f)(ask) <-> ask map f
}

def localPureIsPure[A](a: A, f: E => E) = {
  local(f)(pure(a)) <-> pure(a)
}

def localDistributesOverAp[A, B](fa: F[A], ff: F[A => B], f: E => E) = {
  local(f)(ff ap fa) <-> local(f)(ff) ap local(f)(fa)
}

Local has one internal law:

def scopeIsLocalConst(fa: F[A], e: E) = {
  scope(e)(fa) <-> local(_ => e)(fa)
}