The rise of large language models (LLMs) has introduced a new type of programming: natural language programming. Users write prompts, which are instructions in natural language, to direct LLMs to perform tasks such as natural language processing, code generation, reasoning, etc. An emerging area of research enables interoperability between prompts and programs. We present a novel programming abstraction, shared program state, that removes the manual work required to enable interoperability between prompts and program states. With shared program state, programmers can write prompts that directly access program variables, compute with program objects, and implement control flow in the program. We present a schema for specifying natural function interfaces that extend programming systems to support programs with prompts and leverage this schema to specify shared program state as a natural function interface. We implement shared program state in the Nightjar programming system. Nightjar enables programmers to write Python programs containing prompts that share the Python program state. We show that Nightjar programs achieve comparable or higher task accuracy than manually written implementations (+4-19%), while decreasing the lines of code by 39.6% on average. The tradeoff is that Nightjar may incur runtime overhead (0.4-4.3x manual implementations).