Computing with Trees Not Numbers
9 by xiaodai | 3 comments on Hacker News.
I came across this meetup page (https://ift.tt/2Xln6Eh) where one of the topics is "Computing with Trees not Numbers". The description look intriguing as well. It talk about tree calculus. Has that been around for long? I can't find much about it on the internet Full Description: Tree calculus is a calculus of combinations with a single ternary operator (for building nodes) that has three reduction rules, according to whether its first argument is a leaf, stem or fork. Its normal forms are the unlabeled binary trees, which provide a better basis for computation than the natural numbers: there is no need to encode and decode programs as numbers, as the binary trees are simultaneously functions to be applied and structures to be traversed. There are compositional, reduction-preserving embeddings of the traditional models of computation into tree calculus. Also, it supports self-interpretation without the need for quotation to convert programs to trees. Tree calculus supports a type system that satisfies subject reduction.
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