Invent the Questions, Compile the Consequences: Learning Executable Structure from Terminal Feedback

Can terminal feedback reveal not only a computation's outcome, but also the structure needed to execute and revise it? We study replayable tool systems with hidden states, unknown action targets, and no intermediate observations. Under explicit projective and identifiability conditions, we recover action-aligned coordinates, call laws, and functional dependencies from experiments that each return a scalar. Our central construction uses measured action relations to align state decoding and tool dynamics in one representation. For type-A actions, we recover matrix multiplication from a noisy measured Lie bracket and extract this representation using a spectrally separated anchor. The calibration has explicit perturbation bounds and polynomial complexity in dimension and conditioning parameters, without initialization near the unknown solution. Complementary reset constructions expose local information without assuming independent state control. For one-dimensional records, suitable reset conditions identify bounded-degree complete maps without requiring an open set of jointly reachable states. When stage outputs are retained as final records, additional local-law conditions permit recovery of local laws and minimum parent sets without expanding the composed program. After acquisition and initialization, the learned interface evaluates unseen legal sequences of learned tools and propagates argument edits within a fixed schedule without further terminal queries. Finite-noise guarantees account for discovery, conditioning, and error amplification during execution. Together, these results show how the execution interface itself can be learned from terminal feedback under explicit structural conditions.