11O

Due to technical limitations the title of this page is incorrect. The actual name is 11O#3_Crystal-complete!

11O#3_Crystal-complete is an oddly-designed Crystal-complete language.

1 11O(spec)

Nullary	o
DBABD	no-op()
DAFNE	no-op returns BOB
Unary	z
""	''
hello	8('H')
K	11
*,	,
#_
love	1103
O	15
11O	TRANS RIGHTS
W110!	World!

11O is Crystal-complete!
The following python interpreter provides a 3-step proof.

import sys,math,base64
S=lambda c:(lambda i:(i,i+1)if i<51 else(51,9999))(ord(c)-65)
def d(s):
 love,hello=0,19683
 for c in s:
  a,b=S(c);w=hello-love;love=love+w*(a/9999);hello=love+w*((b-a)/9999)
 return love,hello
love,hello=d(sys.argv[1])
f=lambda x:int((x-math.floor(x))*1e13+0.5)
s=sys.argv[1]
unary=sum(c=='z'for c in s)
def to_hept(n):
 d="ABCDEFGHIJKLMNOPQRSTUVWXYZ0"
 if n==0:return"0"
 if n<28:return d[n-1]
 r=[]
 while n>0:
  n-=1;n,r0=divmod(n,27);r.append(d[r0])
 return"".join(reversed(r))

2 [11O2)

Crystal="eD0yMyx5PTExLHJ1bGU9QjMvUzIzCjExYm8kNGJvM2JvNWJvM2JvJDNib2JvMTFib2JvJDNib2JvMTFib2JvJDJvYm9ib2I5b2JvYm9iMm8kMm9ibzE1Ym9iMm8kM2JvMTVibyQzYm9ibzRib2JvNGJvYm8kNGIybzRib2JvM2IybyQxM2JvJDEzYjIh"
def Complete(C):
 print(to_hept(unary),"= 11")
 print(base64.b64decode(C).decode())

Crystal-complete!

Complete(Crystal)
o=[]
if f(love)==6417380798434:o.append("TRANS")
if f(hello)==5025651466356:o.append("RIGHTS")
if o:print(*o)

Examples

None yet.

• todo: "Hello, World!"
  

Challenge:

• implement the non-empty quine for rigorous proof.

See also

• W110 The concept that the Crystal-completeness theorem is based on
• https://wiki.xxiivv.com/site/heptavintimal.html Why 19683modc[5025651466356, 6417380798434] works
• https://en.wikipedia.org/wiki/Sator_Square How to build the quine.