Our interest is in constructing interactive systems involving a human-expert interacting with a machine learning engine on data analysis tasks. This is of relevance when addressing complex problems arising in areas of science, the environment, medicine and so on, which are not immediately amenable to the usual methods of statistical or mathematical modelling. In such situations, it is possible that harnessing human expertise and creativity to modern machine-learning capabilities of identifying patterns by constructing new internal representations of the data may provide some insight to possible solutions. In this paper, we examine the implementation of an abstract protocol developed for interaction between agents, each capable of constructing predictions and explanations. The \PXP protocol, described in [12] is motivated by the notion of ''two-way intelligibility'' and is specified using a pair of communicating finite-state machines. While the formalisation allows the authors to prove several properties about the protocol, no implementation was presented. Here, we address this shortcoming for the case in which one of the agents acts as a ''generator'' using a large language model (LLM) and the other is an agent that acts as a ''tester'' using either a human-expert, or a proxy for a human-expert (for example, a database compiled using human-expertise). We believe these use-cases will be a widely applicable form of interaction for problems of the kind mentioned above. We present an algorithmic description of general-purpose implementation, and conduct preliminary experiments on its use in two different areas (radiology and drug-discovery). The experimental results provide early evidence in support of the protocol's capability of capturing one- and two-way intelligibility in human-LLM in the manner proposed in [12].