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 represent bits and lists as lambda terms, which provides the following 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 which links to more detailed descriptions of the language.

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

Existing solutions may be found at https://rosettacode.org/wiki/Hello_world/Newbie#Binary_Lambda_Calculus

Binary Lambda Calculus

The following self interpreters are taken from the IOCCC entry at https://www.ioccc.org/2012/tromp/hint.html

Bit-wise:

  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

Byte-wise (showing https://www.ioccc.org/2012/tromp/uni8.Blc in hex):

 19468
  05580
   05f00
    bfe5f
     85f3f
      03c2d
     b9fc3f8
    5e9d65e5f
   0decb f0fc3
  9befe   185f7
 0b7fb     00cf6
7bb03       91a1a

C

#ifndef M
#define M 50000
#endif
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
enum {I,O,V,A,L};
long n=44,i,c,T[M]={L,A,8,A,2,  V,0,L,L,V,
    A,30,L,A,2,V,0,L,A,5,A,7,L,V,0,O,
    A,14,L,A,2,V,0,L,A,5,A,2,  V,0,O,O,A},b,s;
long nc = 0, nf = 0, na = 0; // number of cells, number freed, number of allocs
typedef struct _{long t,r; struct _*e,*n;} C;C*e,*f,*l,*S[M];
void x(long l,long u){for(;l<=u;T[n++]=T[l++]);}
long g(){i--||(i=b,c=getchar());return c>>i&1;}
void d(C*l){!l||--l->r||(d(l->e),d(l->n),l->n=f,nf++,f=l);}
long p(long m){if(g()){for(T[n++]=V;g();T[n]++){}n++;}else
          T[m]=n++&&g()?(T[m+1]=p(++n),A):L,p(n);return n-m;}
int main(int t,char **_){char o;
 b=t>1?0:7;T[43]=p(n);i=0;
 for(t=b?10:26;;)switch(T[t]){
  case I: g();i++;assert(n<M-99);if(~c&&b){x(0,6);for(T[n-5]=96;i;T[n++]=!g())
           x(0,9);}x(c<0?7:b,9);T[n++]=!b&&!g();break;
  case O: t=b+t>42?(o=2*o|t&1,28):(putchar
              (b?o:t+8),fflush(stdout),b?12:28);break;
  case V: l=e;for(t=T[t+1];t--;e=e->n){}
                   t=e->t;(e=e->e)&&e->r++;d(l);break;
  case A: t+=2;
          nc++;
          f||(na++,f=calloc(1,sizeof(C)));
          assert(f&&s<M);S[s++]=l=f;f=l->n;
          l->r=1;l->t=t+T[t-1];(l->e=e)&&e->r++;break;
  case L: if(!s--){printf("\n%ld cells\n%ld freed\n%ld allocated\n", nc, nf, na);return 0;};S[s]->n=e;e=S[s];t++;break;
 }
 printf("%ld cells %ld allocated\n", nf, na);
 return T[t+2];
}

JavaScript

#!/usr/local/bin/node --stack-size=8192
let bytemode = process.argv.length <= 2;
var data;
var nchar = 0;
var nbit = 0;
var progchar;

function bit2lam(bit) {
  return function(x0) { return function(x1) { return bit ? x1 : x0 } }
}
function byte2lam(bits,n) {
  return n==0 ? (function(_) { return function(y) { return y } }) // nil
              : (function(z) { return z (bit2lam((bits>>(n-1))&1))
                                        (byte2lam(bits,n-1)) })  // cons bitn bits>n
}
function input(n) {           // input from n'th character onward
  if (n >= data.length)
    return function(z) { { return function(y) { return y } } }     // nil
  let c = data[n];
  return function(z) { return z (bytemode ? byte2lam(c,8) : bit2lam(c&1)) (input(n+1)) } // cons charn chars>n
}
function lam2bit(lambit) {
  return lambit(function(_){return 0})(function(_){return 1})()  // force suspension
}
function lam2byte(lambits, x) {
  return lambits(function(lambit) {
           return function(lamtail) {
             return function(_) { return lam2byte(lamtail, 2*x + lam2bit(lambit)) }
           }
         })(Buffer.from([x]))              // end of byte
}
function output(prog) {
  return prog(function(c) {      // more chars
    process.stdout.write(bytemode ? lam2byte(c,0) : lam2bit(c) ? '1' : '0');
    return function(tail) {
      return function(_) { return output(tail) }
    }
  })(0)                         // end of output
}
function getbit() {
  if (nbit==0) {
    progchar = data[nchar++];
    nbit = bytemode ? 8 : 1;
  }
  return (progchar >> --nbit) & 1;
}
function program() {
  if (getbit()) {               // variable
    var i = 0;
    while (getbit()==1) { i++ }
    return function() { return arguments[i] }
  } else if (getbit()) {        // application
    let p = program();
    let q = program();
    return function(...args) {
      return p(...args)(function(arg) { return q(...args)(arg) }) // suspend argument
    }
  } else {
    let p = program();
    return function(...args) {
      return function(arg) { return p(arg, ...args) }  // extend environment with one more argument
    }
  }
}
process.stdin.on('readable', () => {
  if ((data = process.stdin.read()) != null) {
    prog = program()();
    output(prog(input(nchar)))             // run program with empty env on input
  }
});

Python

#!/usr/local/bin/python3
import os,sys
def bit2lam(bit) :
  return lambda x0: lambda x1: x1 if bit else x0
def byte2lam(bits,n) :
  if (n==0) :
    return lambda _:lambda y: y
  return lambda z: z (bit2lam((bits>>(n-1))&1)) (byte2lam(bits,n-1))
def input(n) :           # input from n'th character onward
  if n >= len(inp) :
    c = os.read(0,1)
    inp.append((lambda _: lambda y: y) if c==b''
          else lambda z: z(byte2lam(c[0],8) if bytemode else bit2lam(c[0]&1))(input(n+1)))
  return inp[n]
def lam2bit(lambit) :
  return lambit(lambda _: 0)(lambda _: 1)(0)  # force suspension
def lam2byte(lambits, x) :
  return lambits(lambda lambit: lambda lamtail: lambda _: lam2byte(lamtail, 2*x+lam2bit(lambit)))(bytes([x]))
def output(prog) :
  return prog(lambda c: os.write(1,lam2byte(c,0) if bytemode else (b'1' if lam2bit(c) else b'0')) and (lambda tail: lambda _ : output(tail)))(0)
def getbit() :
  global nbit, progchar
  if nbit==0 :
    progchar = os.read(0,1)[0]
    nbit = 8 if bytemode else 1
  nbit -= 1
  return (progchar >> nbit) & 1
def program() :
  if getbit() :                # variable
    i = 0
    while (getbit()==1) : i += 1
    return lambda *args : args[i]
  elif getbit() :         # application
    p = program()
    q = program()
    return lambda *args : p(*args)(lambda arg: q(*args)(arg)) # suspend argument
  else :
    p = program()
    return lambda *args: lambda arg: p(arg, *args) # extend environment with one more argument
sys.setrecursionlimit(8192)
inp = []
nbit = progchar = 0
bytemode = len(sys.argv) <= 1
prog = program()(0)
output(prog(input(0)))             # run program with empty env on input

Ruby

#!/usr/bin/ruby
def bit2lam(bit)
  return lambda { |x0| lambda { |x1| bit==0 ? x0 : x1 } }
end
def byte2lam(bits,n)
  return n==0 ? lambda { |_| lambda { |y| y } }
              : lambda { |z| z.call(bit2lam((bits>>(n-1))&1)).call(byte2lam(bits,n-1)) }
end
def input(n)             # input from n'th character onward
  if n >= $inp.length()
    c = STDIN.getbyte
    $inp.append(c==nil ? (lambda { |_| lambda { |y| y } })
                       : lambda { |z| z.call($bytemode ? byte2lam(c,8) : bit2lam(c&1)).call(input(n+1)) } )
  end
  return $inp[n]
end
def lam2bit(lambit)
  return lambit.call(lambda { |_| 0 }).call(lambda { |_| 1 }).call(0)  # force suspension
end
def lam2byte(lambits, x)
  return lambits.call(lambda { |lambit| lambda { |lamtail| lambda { |_| lam2byte(lamtail, 2*x+lam2bit(lambit)) } } }).call(x)
end
def output(prog)
  return prog.call(lambda { |c| putc($bytemode ? lam2byte(c,0) : (lam2bit(c)==0 ? '0' : '1')) and (lambda { |tail| lambda { |_| output(tail) } }) }).call(0)
end
def getbit()
  if ($nbit==0)
    $progchar = STDIN.getbyte
    $nbit = $bytemode ? 8 : 1
  end
  return ($progchar >> $nbit -= 1) & 1
end
def program()
  if getbit()==1                 # variable
    i = 0
    while (getbit()==1) do i += 1 end
    return lambda { |*args| args[i] }
  elsif getbit()==1          # application
    p = program()
    q = program()
    return lambda { |*args| p.call(*args).call(lambda { |arg| q.call(*args).call(arg) }) }  # suspend argument
  else
    p = program()
    return lambda { |*args| lambda { |arg| p.call(arg, *args) } } # extend environment with one more argument
  end
end
$inp = []
$nbit = $progchar = 0
$bytemode = ARGV.length <= 0
$prog = program().call(0)
output($prog.call(input(0)))             # run program with empty env on input