Talk given at Papers We Love SG #006

1. Binary Lambda Calclus and
Combinatory Logic
Presented by Melvin Zhang
by John Tromp in Randomness and Complexity,
From Leibniz to Chaitin (2007)

2. Algorithmic Information Theory
Ray Solomonoff

3. http://jonisalonen.com/2013/lets-draw-the-mandelbrot-set/

4. for (int row = 0; row < height; row++) {
for (int col = 0; col < width; col++) {
double c_re = (col - width/2)*4.0/width;
double c_im = (row - height/2)*4.0/width;
double x = 0, y = 0;
double r2;
int iter = 0;
while (x*x+y*y < 4 && iter < max) {
double x_new = x*x-y*y+c_re;
y = 2*x*y+c_im;
x = x_new;
iter++;
}
if (iter < max) pixel(col, row, colors[iter]);
else pixel(col, row, black);
}
}
http://jonisalonen.com/2013/lets-draw-the-mandelbrot-set/

5. https://www.cs.auckland.ac.nz/ chaitin/inv.html
“So I’ve done that using LISP because LISP is simple
enough, LISP is in the intersection between theoretical
and practical programming. Lambda calculus is even
simpler and more elegant than LISP, but it’s unusable.”
– An Invitation to Algorithmic Information Theory
Gregory Chaitin

6. http://www.mathrix.org/liquid/archives/the-history-of-the-chaitin-leibniz-medallion

7. λ-calculus
Alonzo Church

8. Combinatory Logic
Haskell Curry

9. Binary λ-calculus
John Tromp

10. Futher readings:
• John’s LC and CL Playground
https://tromp.github.io/cl/cl.html
• Understanding ioccc.org/2012/tromp
https://github.com/melvinzhang/binary-lambda-calculus
• Church’s Thesis and Functional Programming
Turner, 2006
• Meta Math!: The Quest for Omega
Chaitin, 2005