Small hydrocarbons, such as C2H, C3H and C3H2 are more abundant in photo-dissociation regions (PDRs) than expected based on gas-phase chemical models. To explore the hydrocarbon chemistry further, we observed a key intermediate species, the hydrocarbon ion l-C3H+, in the Horsehead PDR with the Plateau de Bure Interferometer at high-angular resolution (6''). We compare with previous observations of C2H and c-C3H2 at similar angular resolution and new gas-phase chemical model predictions to constrain the dominant formation mechanisms of small hydrocarbons in low-UV flux PDRs. We find that, at the peak of the HCO emission (PDR position), the measured l-C3H+, C2H and c-C3H2 abundances are consistent with current gas-phase model predictions. However, in the first PDR layers, at the 7.7 mum PAH band emission peak, which are more exposed to the radiation field and where the density is lower, the C2H and c-C3H2 abundances are underestimated by an order of magnitude. At this position, the l-C3H+ abundance is also underpredicted by the model but only by a factor of a few. In addition, contrary to the model predictions, l-C3H+ peaks further out in the PDR than the other hydrocarbons, C2H and c-C3H2. This cannot be explained by an excitation effect. Current gas-phase photochemical models thus cannot explain the observed abundances of hydrocarbons, in particular in the first PDR layers. Our observations are consistent with a top-down hydrocarbon chemistry, in which large polyatomic molecules or small carbonaceous grains are photo-destroyed into smaller hydrocarbon molecules/precursors.< Réduire