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With the growing importance of customer service in contemporary business, recognizing the intents behind service dialogues has become essential for the strategic success of enterprises. However, the nature of dialogue data varies significantly across different scenarios, and implementing an intent parser for a specific domain often involves tedious feature engineering and a heavy workload of data labeling. In this paper, we propose a novel Neural-Bayesian Program Learning model named Dialogue-Intent Parser (DI-Parser), which specializes in intent parsing under data-hungry settings and offers promising performance improvements. DI-Parser effectively utilizes data from multiple sources in a "Learning to Learn" manner and harnesses the "wisdom of the crowd" through few-shot learning capabilities on human-annotated datasets. Experimental results demonstrate that DI-Parser outperforms state-of-the-art deep learning models and offers practical advantages for industrial-scale applications.