A Visual Lambda-Calculator Using Typed Mind-Maps

Abstract

Lambda calculus is an influential and extensivelyused notation for describing computable functions, andMind-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 serveral 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 [1], 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 MindMapping of lambda calculus is interesting and elegant in its own right.

Exploring the Potential of User Modeling Based on Mind Maps

“…If the nodes were to be weighted stronger the deeper they were, the weight of a node (1 by default) was multiplied with a) the absolute depth of the node; b) the natural logarithm of the depth; c) the common logarithm of the depth; or d) the square root of the depth. If the resulting weight was lower than 1, e.g., for ln (2), then the weight was set to 1. If nodes were to receive less weight the deeper they were, then the original weight of 1 was multiplied with the reciprocal of the metrics a) -d).…”

“…Nevertheless, the result is plausible. Most of Docear's users are researchers and therefore they should be interested in books about academic writing, and hence 2 We double-checked all data and the source code, and are quite confident that there are no flaws in the user modeling process. click the corresponding recommendations.…”

“…Mindmaps received attention in various research fields. They have been used to implement a lambda calculator [2], to filter search results from Google [3], to present software requirements [4], to research how knowledgeable business school students are, and there are numerous studies about the effectiveness of mind-maps as a learning tool [5]. In the field of document engineering and text mining, mind maps were created automatically from texts [6], and have been utilized to model XML files [7].…”