BaCO3 (s) + C (s) + H2O (l) → Ba(OH)2 (aq) + 2 CO (g)
This is an oxidation-reduction (redox) reaction:
C0 - 2 e- → CII (oxidation)
CIV + 2 e- → CII (reduction)
C is a reducing agent, BaCO3 is an oxidizing agent (synproportionation (comproportionation)).