This work develops a method for robot program synthesis. Currently, the programming task is one of the major hurdles of robotic application. Progress towards automatic synthesis of robot programs will ease industrial robot application. The proposed system provides a means towards automated (guided by knowledge) conversion of a user's request, expressed in natural language, to the appropriate conceptual model of the required task. This model incorporates the information necessary for understanding, planning, and sensory-guided performance of the required robotic task. First, we state the problem of robotic assembly and recognize its hierarchic structure as the structure of a system that builds a predesigned assembly. Next, we present and analyze the requirements of the robotic assembly domain. This analysis enables us to draw conclusions concerning the most suitable methodology for the development of a support system for assembly program synthesis and interpretation. It is the conceptual graph-based approach. Then we present the algorithm of the proposed conceptual graph-based system and show how the system synthesizes robotic assembly operations, such as valid assembly sequences and sequences of special treatments for the assembled components (including the determination of the required resources). Finally, a case study illustrates the approach developed here on a large family of multi-axisymmetric components. We also present illustrative examples of working sessions with the current implementation of the system.