Author: Mencius Moldbug (moldbug@gmail.com)
Date: 5/25/2008
Version: 11K

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.

    Parentheses 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 7 b c)   => *(a 3 (((1 0) b) c) 1 0 3)
      *(a 8 b c)   => *(a c)

      *(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 Same (=)

      =(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)