  In the past decade, ALMA observations have revealed that a large fraction of
protoplanetary discs contains rings in the dust continuum. These rings are the
locations where pebbles accumulate, which is beneficial for planetesimal
formation and subsequent planet assembly. We investigate the viability of
planet formation inside ALMA rings in which pebbles are trapped by either a
Gaussian-shape pressure bump or by the strong dust backreaction. Planetesimals
form at the midplane of the ring via streaming instability. By conducting
N-body simulations, we study the growth of these planetesimals by collisional
mergers and pebble accretion. Thanks to the high concentration of pebbles in
the ring, the growth of planetesimals by pebble accretion becomes efficient as
soon as they are born. We find that planet migration plays a decisive role in
the evolution of rings and planets. For discs where planets can migrate inward
from the ring, a steady state is reached where the ring spawns ${\sim}20
M_\oplus$ planetary cores as long as rings are fed with materials from the
outer disc. The ring acts as a long-lived planet factory and it can explain the
'fine-tuned' optical depths of the observed dust rings in the DSHARP large
program. In contrast, in the absence of a planet removal mechanism (migration),
a single massive planet will form and destroy the ring. A wide and massive
planetesimals belt will be left at the location of the planet-forming ring.
Planet formation in rings may explain the mature planetary systems observed
inside debris discs.
