A Visual Lambda-Calculator Using Typed Mind-Maps

Lambda calculus is an influential and extensively-used notation for describing computable functions, and mind-mapping is widely used as an expression of radiant thinking via a powerful graphical technique. In this paper, we introduce a completely visual representation based on typed mind maps to represent steps of calculation for a pure untyped lambda calculator, VLM. This visual representation has several advantages over traditional textual and visual calculators. VLM uses typed mind maps for both the lambda calculator input and ouput. Although VLM is designed as a computable typed mind maps node of our Typed Mind Maps API project, it can also be applied to learning and teaching the concepts of lambda calculus as a visualization of traditional textual rewrite steps. Moreover, the lambda calculus queries and the results of queries are both represented as FreeMind files, and that allows them to be organized and deployed easily. However, the Mind-Mapping of lambda calculus is interesting and elegant in its own right.