Large Language Models (LLMs) can solve previously intractable tasks given only natural-language instructions and a few examples, but they remain difficult to steer precisely and lack a key capability for building reliable software at scale: the modular composition of computations under enforceable contracts. As a result, they are often embedded in larger software pipelines that use domain-specific knowledge to decompose tasks and improve reliability through validation and search. Yet the complexity of writing, tuning, and maintaining such pipelines has so far limited their sophistication. We propose oracular programming: a foundational paradigm for integrating traditional, explicit computations with inductive oracles such as LLMs. It rests on two directing principles: the full separation of core and search logic (allowing the latter to freely evolve without breaking the former), and the treatment of few-shot examples as grounded and evolvable program components. Within this paradigm, programmers express high-level problem-solving strategies as programs with unresolved choice points. These choice points are resolved at runtime by LLMs, which generalize from user-provided examples of correct and incorrect decisions. An oracular program is composed of three orthogonal components: a strategy that consists of a nondeterministic program with choice points that can be reified into a search tree, a policy that specifies how to navigate this tree with the help of LLM oracles, and a set of demonstrations that describe successful and unsuccessful tree navigation scenarios across diverse problem instances. Each component is expressed in a dedicated programming language. We address the key programming language design challenges of modularly composing oracular programs and enforcing consistency between their components as they evolve.

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