blc is an implementation of the binary lambda calculus.
Binary lambda calculus (BLC) is a minimal, purely functional programming language based on a binary encoding of the untyped lambda calculus with De Bruijn indices.
Lambda terms have the following representation in BLC:
| term | lambda | BLC | --------------|--------|----------------| | abstraction | λM | 00M | | application | MN | 01MN | | variable | i | 1i0 |
Since BLC programs are basically lambda calculus terms, they can be applied to other terms. In order to be applicable to binary (but not BLC-encoded) input, it has to be lambda-encoded first. Bytestrings are lambda-encoded as Church lists of bytes and bytes are lambda-encoded as Church lists of lambda-encoded bits.
Bits 0 and 1 are lambda-encoded as Church booleans:
| bit | lambda | BLC | |-----|-------------|---------| | 0 | λλ2 (true) | 0000110 | | 1 | λλ1 (false) | 000010 |
Example: BLC-encoding steps for a byte representing the ASCII/UTF-8 encoded letter 'a':
| encoding | representation | |----------|----------------| | decimal | 96 | | binary | 01100001 | | lambda | λ1(λλ2)(λ1(λλ1)(λ1(λλ1)(λ1(λλ2)(λ1(λλ2)(λ1(λλ2)(λ1(λλ2)(λ1(λλ1)(λλ1)))))))) | | BLC | 00010110000101100000110000101100000100001011000001000010110000011000010110000011000010110000011000010110000011000010110000010000010000010 |
The library is already usable, but it is still a work in progress.