Author: Mencius Moldbug [moldbug@gmail.com]
Date: 9/15/2008
Version: 10K

1. Introduction

    This file defines one function, "nock." 
    
    nock is in the public domain.
 
2. Data

    A "noun" is either an "atom" or a "cell."  An "atom" is an unsigned 
    integer of any size.  A "cell" is an ordered pair of any two nouns,
    the "head" and "tail."

3. Semantics

    nock maps one noun to another.  It doesn't always terminate.

4. Pseudocode

    nock is defined in a pattern-matching pseudocode, below.

    Brackets enclose cells.  [a b c] is [a [b c]].

5. Definition

5.1 Transformations

      *[a [b c] d] => [*[a b c] *[a d]]
      *[a 0 b]     => /[b a]
      *[a 1 b]     => [b]
      *[a 2 b c d] => *[a 3 [0 1] 3 [1 c d] [1 0] 3 [1 2 3] [1 0] 5 5 b]
      *[a 3 b]     => **[a b]
      *[a 4 b]     => &*[a b]
      *[a 5 b]     => ^*[a b]
      *[a 6 b]     => =*[a b]
      *[a]         => *[a]

5.2 Operators

5.2.1 Goto [*]

      *[a]             -> nock[a]

5.2.2 Deep [&]
    
      &[a b]           -> 0
      &[a]             -> 1
 
5.2.4 Bump [^]

      ^[a b]           -> ^[a b]
      ^[a]             -> (a + 1)

5.2.5 Like [=]

      =[a a]           -> 0
      =[a b]           -> 1
      =[a]             -> =[a]

5.2.6 Snip [/]

      /[1 a]           -> a
      /[2 a b]         -> a
      /[3 a b]         -> b
      /[(a + a) b]     -> /[2 /[a b]]
      /[(a + a + 1) b] -> /[3 /[a b]]
      /[a]             -> /[a]