Formal languages still beat natural language for high-specificity tasks

Eitan Wagner, Elisha Rosensweig, and Omri Abend (Hebrew University) have published a position paper at ICML 2026 challenging the notion that natural language could replace formal languages like programming languages. Their argument rests on a fundamental property of natural language: it is optimized for underspecification in open-ended contexts. They introduce a formal framework centered on 'task specificity'—the information-theoretic reduction of uncertainty in an output space given user requirements. Using this framework, they prove a 'specificity crossover theorem' that demonstrates a precise threshold: when task requirements become strict enough, the cost of expressing them in natural language exceeds the cost of direct formal specification.

Through case studies across modalities—image generation (e.g., DALL-E), code synthesis (e.g., GitHub Copilot), and audio production—the researchers show that natural language shines at low-specificity tasks where vagueness is acceptable, but falters when precise constraints are needed. For example, a vague prompt like 'a photo of a cat' works well for image generation, but a specific code requirement like 'sort an array with O(n log n) time complexity' is better expressed formally. The paper concludes that natural and formal languages are complementary tools, advocating for hybrid interfaces that allow users to slide along the specificity spectrum, combining the flexibility of natural language with the precision of formal systems.