The binary lambda calculus is defined as the following sequence of bytes:
e : 00 e (Lam)
| 01 e e (App)
| [1] 0 (Var)
The var rule encodes DeBruijn indices with the following pattern:
0 = 10
1 = 110
2 = 1110
3 = 11110
For example the SKI calculus can be expressed in Python as the following lambda expressions:
I = lambda x: x
K = lambda x: lambda y: x
S = lambda x: lambda y: lambda z: x(z)(y(z)) # (x z)(y z)Or in the binary lambda calculus as:
I = 0010
K = 000010110
S = 00000010110111001011011101101110
The smallest eval machine for the binary lambda caluclus is the following program:
01010001
10100000
00010101
10000000
00011110
00010111
11100111
10000101
11001111
000000111
10000101101
1011100111110
000111110000101
11101001 11010010
11001110 00011011
00001011 11100001
11110000 11100110
11110111 11001111
01110110 00011001
00011010 00011010