Crazy J/QUINE

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QUINE

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Quite obvious if you look at it closely, but some explanation should be given anyway.

The program consists of 3 parts: 

   |                |        |                 |
   | `````````````` | ENGINE |      DATA       |
   |                |        |                 |
   |      2N+2      |    N   |      2N+2       |

ENGINE is a function of length N that accepts pairs of boolean arguments:

  • It accumulates the list of {饾煓,饾煔,饾煕} codes and counts number of pairs given.
  • If {FALSE, FALSE} is given, it adds 饾煕 to the front of the list and two 饾煕's to the end, then it calls itself recursively to accept next pair of boolens.
  • If {FALSE, TRUE} is given, it adds 饾煓 to the front of the list and (饾煕,饾煓) to the end, then it calls itself recursively.
  • If {TRUE, FALSE} is given, it adds 饾煔 to the front of the list and (饾煓,饾煕) to the end, then it calls itself recursively.
  • If (TRUE, TRUE} is given, it adds (2N+2) 饾煔's to the front of the list and two 饾煓's to the end, then the list is printed.

We use alternative boolean implementation (with the shortest possible representation of boolean constants but with longer "if" operator): 

   true = I
   false = J
   COND I I (位 garbage . THEN-BRANCH) (位 garbage . ELSE-BRANCH)

What are 饾煓, 饾煔 and 饾煕? They are Q1, Q2 and Q4 combinators: 

   Q1 = 位 x y z . x (z y)
   Q2 = 位 x y z . y (z x)
   Q4 = 位 x y z . z (y x)

Such a choice allows to do this: 

   value (位 garbage . <print 'i'>)
         (位 garbage . <print '`'>)
         (位 garbage . <print 'j'>)

Okay, that's what ENGINE does. Where's the QUINE?

Let's look at the outputs of this program: 

   PROG:   ```````` <ENGINE> jjjiijii
   OUTPUT: `````````ijjjjiijii

PROG's output consists of 3 parts:

  • Sequence of ` characters. The length of the sequence is the same as the length of DATA section.
  • Decoded DATA in reverse order. "Decoded" means:
    • ij becomes `
    • ji becomes i
    • jj becomes j
   ```````` `ij jj ji ij ii
            ^^^ ~~ ~~ ~~ ~~
            |||_/  /  /  |
            ||____/  /   |
            |_______/   STOP
  • Copy of DATA section.

What DATA should we pass to the ENGINE to make QUINE? It must be encoded ENGINE reversed!


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