Case Studies on Algorithm Discovery from Proofs: The Delete Function on Lists and Binary Trees using Multisets

The proof based synthesis of element deletion algorithms for [sorted] lists and [sorted] binary trees, in a multitype context (basic ordered elements, multisets, lists, and trees) is performed and the necessary theory is developed. This constitutes a case study in theory exploration and automated synthesis of algorithms based on natural style proofs, which allows to investigate the heuristics of theory construction on multiple types, as well as the natural style inferences and strategies for constructing human readable proofs. The experiments are realised in the frame of the Theorema system.