Universal Lambda Machine

One of the foundational mathematical constructs behind computer science is the universal Machine, as a machine that can emulate the behaviour of any other machine, given a description of it. Alan Turing introduced the idea of a universal Turing machine in 1936–1937. The lambda calculus is an even older, and in many ways simpler, model of computation. That simplicity is reflected in the Binary Lambda Calculus (BLC for short), which describes lambda terms with binary tokens 00 for lambda, 01 for application, and 1^n0 for variable n, which binds to the n'th enclosing lambda. BLC also specifies a way to encode bits and lists as lambda terms which provide for a simple I/O convention. The lambda universal machine parses the binary encoding of a lambda term from the start of its input, applies that term to the remainder of input, and outputs the result interpreted as a list of bits or bytes. BLC as a programming language has its own entry on Rosetta Code at https://rosettacode.org/wiki/Category:Binary_Lambda_Calculus

Task Simulate the universal lambda machine Or in other words, write a BLC interpreter. Support either bit-mode or byte-mode or preferably both, with byte-mode as the default, and a -b command line flag for bit mode.

To test your universal lambda machine, you should execute the following BLC programs.

For bit-mode, one should reproduce the BLC Rosetta Code solutions of

producing as much output as possible before running out of stack/heap space).

https://rosettacode.org/wiki/100_doors#Binary_Lambda_Calculus

Also, the 342 bit program

010100011010000000011000010110011110000010010111110111100001010110000000011000011111000000101111110110010111111011001011110100111010111100010000001011100101010001101000000000010110000101011111101111100000010101111011111011111100001011000000101111111010110111000000111111000010110111101110011110100000010110000011011000100000101111000111001110

should produce output

For byte-mode, one should reproduce the BLC Rosetta Code solutions of