NLP tasks are typically defined extensionally through datasets containing example instantiations (e.g., pairs of image i and text t), but motivated intensionally through capabilities invoked in verbal descriptions of the task (e.g., "t is a description of i, for which the content of i needs to be recognised and understood"). We present Pento-DIARef, a diagnostic dataset in a visual domain of puzzle pieces where referring expressions are generated by a well-known symbolic algorithm (the "Incremental Algorithm"), which itself is motivated by appeal to a hypothesised capability (eliminating distractors through application of Gricean maxims). Our question then is whether the extensional description (the dataset) is sufficient for a neural model to pick up the underlying regularity and exhibit this capability given the simple task definition of producing expressions from visual inputs. We find that a model supported by a vision detection step and a targeted data generation scheme achieves an almost perfect BLEU@1 score and sentence accuracy, whereas simpler baselines do not.