term Q = λ1((λ11)(λλλλλ14(3(55)2)))1 concatenates two copies of its input, proving that
KS(xx) ≤ ℓ(x) + 66Applying it to its own encoding gives a 132 bit quine:
U(blc(Q) blc(Q) : Nil) = blc(Q) blc(Q)
#lambdacalculus
https://tromp.github.io/cl/Binary_lambda_calculus.html
C-c-c-conjecturing, and dealing with recursion in Emacs (more excursus)
Another blog post, this one not tagged as part of the lambda-calculus series because it doesn't directly deal with lambda-calculus, but it follows on from Part 2, dealing with issues of recursion, and building up towards the #YCombinator and other #lambdacalculus issues.
Some fun things evaluating the efficiency of implementing different functions in #Elisp (with metrics!), and some fun images/visualisations of an interesting function.
I’m not putting this in the lambda-calculus series, though it touches on issues from the last post in the series, but specifically issues of recursion. I was curious to go back and recall how The Little Schemer dealt with problems of recursion (and the Y Combinator (which we still haven’t got properly to yet, but we will, I promise)). In Chapter 9 of The Little Schemer (“and Again, and Again, and Again,…"), it starts off by querying the reader if they want caviar and how to find it in a list, and then essentially gets (from caviar and grits) into issues around the halting problem.
In the spirit of (not-that-radical, unfortunately) openness (inspired by none other than @TodePond,) let me share a thing I've been quietly working on for the last couple of months: #Lamber, my pure #LambdaCalculus -compiling #FunctionalProgramming language inspired by #Lua and #haskell