Language models have shown remarkable proficiency in code generation; nevertheless, ensuring type correctness remains a challenge. Although traditional methods, such as constrained decoding, alleviate this problem by externally rejecting untypable code, the model itself does not effectively learn type reasoning internally, which ultimately limits its overall performance. This paper introduces TyFlow, a novel system that internalizes type reasoning within code generation to guide the model to learn the type system. The core of our approach is a novel type-guided program synthesis system that maintains an isomorphism between type derivation trees and synthesis derivation trees, enabling a new code representation based on synthesis decision sequences rather than traditional text-based token sequences. By offloading the complexity of type system learning to the representation itself, models can redirect their computational resources toward higher-level program semantics. Our evaluation shows that TyFlow not only eliminates type errors but also significantly improves functional correctness, highlighting the importance of aligning LMs with type systems internally.