Learn BINARY-LAMBDA-CALCULUS with Real Code Examples

BLC represents programs as lambda calculus expressions encoded in binary.

It is Turing-complete but extremely low-level and minimalistic.

Designed for studying program-size complexity and algorithmic information theory.

Programs are interpreted by BLC interpreters that parse the binary lambda expressions.

Demonstrates the connection between computation, minimal representation, and compression.

Lambda abstraction and application

Binary encoding of terms

No built-in standard library

Evaluation via normal-order reduction

Self-contained minimal programs

Lambda abstraction: λx.E represents anonymous functions

Function application: (F G) applies F to G

Binary encoding: 0 for λ, 1 for application structure

Reduction strategies: normal-order evaluation

No mutable state or side effects

Single binary-encoded source file

Optional text-based lambda source for readability

Interpreter executable or script

No dependencies or modules required

Output directed via interpreter

Write lambda expressions to implement desired function

Encode expressions in binary according to BLC specification

Test program using BLC interpreter

Optimize encoding for minimal program size

Analyze output and correctness

Beginner: small arithmetic functions

Intermediate: combinator-based programs

Advanced: implementing data structures in lambda calculus

Expert: optimizing minimal-size BLC programs

Architect: research-level analysis of algorithmic complexity

BLC vs Brainfuck: Both minimal; BLC functional, Brainfuck imperative

BLC vs Lambda Calculus: BLC is binary encoding of lambda calculus

BLC vs Python: Python practical; BLC theoretical/minimal

BLC vs LOLCODE: LOLCODE humorous; BLC formal and minimal

BLC vs C: C compiled; BLC interpreted and functional

2003 - Concept of Binary Lambda Calculus introduced by Granlund et al.

2004 - First interpreter implementations released

2005 - Initial combinator examples published

2007 - Binary encodings refined for compactness

2010 - Research papers on program-size complexity using BLC

2012 - Extended functional benchmarks implemented

2015 - Minimal self-contained programs demonstrated

2018 - Interpreters updated for modern platforms

2020 - Community experimentation in esoteric programming

Future - Ongoing research in algorithmic information theory

BLC - Binary Lambda Calculus

Lambda abstraction - anonymous function λx.E

Application - applying one function to another (F G)

Combinator - function with no free variables

Binary encoding - compact representation of lambda terms