Logic locking “hides” the functionality of a digital circuit to protect it from counterfeiting, piracy, and malicious design modifications. The original design is transformed into a “locked” design such that the circuit reveals its correct functionality only when it is “unlocked” with a secret sequence of bits—the key bit-string. However, strong attacks, especially the SAT attack that uses a SAT solver to recover the key bit-string, have been profoundly effective at breaking the locked circuit and recovering the circuit functionality. We lift logic locking to Higher Order Logic Locking (HOLL) by hiding a higher-order relation, instead of a key of independent values, challenging the attacker to discover this key relation to recreate the circuit functionality. Our technique uses program synthesis to construct the locked design and synthesize a corresponding key relation. HOLL has low overhead and existing attacks for logic locking do not apply as the entity to be recovered is no more a value. To evaluate our proposal, we propose a new attack (SynthAttack) that uses an inductive synthesis algorithm guided by an operational circuit as an input-output oracle to recover the hidden functionality. SynthAttack is inspired by the SAT attack, and similar to the SAT attack, it is verifiably correct, i.e., if the correct functionality is revealed, a verification check guarantees the same. Our empirical analysis shows that SynthAttack can break HOLL for small circuits and small key relations, but it is ineffective for real-life designs.