Embodiments described herein provide a program synthesis framework that generates code programs through a multi-turn conversation between a user and a system. Specifically, the description to solve a target problem is factorized into multiple steps, each of which includes a description in natural language (prompt) to be input into the generation model as a user utterance. The model in turn synthesizes functionally correct subprograms following the current user utterance and considering descriptions and synthesized subprograms at previous steps. The subprograms generated at the multiple steps are then combined to form an output of program in response to the target problem.