Perhaps the work on binary lambda calculus and Kolmogorov complexity by John Tromp would be interesting to you? http://tromp.github.io/cl/cl.html http://tromp.

Perhaps the work on binary lambda calculus and Kolmogorov complexity by John Tromp would be interesting to you? http://tromp.github.io/cl/cl.html http://tromp.github.io/cl/cl.html "Functional Bits: Lambda Calculus based Algorithmic Information Theory" http://tromp.github.io/cl/LC.pdf http://tromp.github.io/cl/LC.pdf