17 (Miui)

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17 is an esolang designed by User:Miui. The intention is to golf the functions described in User:Miui/Oragami without relying on a quantum computer.

Overview

A 17 program meets the following criteria:

• 17 is defined as ι+ι=17.
• The string ιι=µ
• The constant Μ1=µ/µ**µ
• The constant Μ2=34
• The constant Μ3=6
• The string Μ3+Μ3=[511,1023]
• The constant Μ4=[-∞,0,∞]
• The constant Μ5=[0,1]
• The constant π=[6,τ]
• The string Μ5*Μ5=b17
• The string "Pi"='kaE0X7.P3E7ieAtaWlJdrCoCS9b'
• 34 is the result of addition of 17+17
• 34 is the only result of incrementation.
• b17 is the only result of Μ5*Μ5
• The constant Μ91=M(n) = M(M(n + ιιιιιιιιιιι))
• The string ιιιιιιιιιιι=i
• The string Ν91=Nope.
• Ν(n) cannot be incremented.
• The string Dµ30 is divmod(30)

or alternatively stated

1. Μ1 is equivalent to µ over µ to the power of µ and Μ2=34.
2. Μ3 evaluates as an interval
3. Μ4 evaluates as pi, NaN, or ≠Μ
4. "Pi" is a base62 string 'kaE0X7.P3E7ieAtaWlJdrCoCS9b' which evaluates to 3.14159265359 via the Pi function (Pi)Μ
5. b17 can be instantiated to reverse divide by 17 or multiply by 2 operations.
6. Recursion function rounds up if incremented, and rounds down if not.
7. Ν91 is a no-op function where Ν(91) evaluates to the string 'Nope.'
8. Incremental evaluation will append unary data to top of the stack and is a delimiter.
9. Divmod 30 then increment will return 4.

Operations

Commands are increment, evaluate and reference.

• Incrementation commands + or Increment/increment (n) time/s
• Evaluate command %%
• Reference command > or Reference/reference

Pi Function

ι+17=x
x=Μ2%%

This evaluates to 6

π%%

This evaluates to Μ4=≠Μ=0

Μ0+π=π%%

This evaluates to 3.14159265359

b17(Pi)%%

Evaluates to kaE0X7

Pseudocode
 function (Pi) {
      ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
         const  = Pi(base62String, 62).integerValue(314159265359);
         setDecString(big.times(17));
         const bitString = big.toString(2);
     } Μ4/Μ5 %%
 }
Μπ+%%

Evaluates to 9C7.SHLpwP3E7iePEucXNoXI

Recursion Function

Μ91%%

This evaluates to

Μ0(Μ1(2))
Μ1(1)
Μ2(Μ3(4))
Μ4(5)
Μ91
1

Example programs

Hello, World!

H

A program is simply a unary string of ι symbols, so a golfed "Hello, World!" such as

 240518692878%%>

alternatively:

Evaluate two hundred forty billion, five hundred eighteen million, six hundred ninety-two thousand, eight hundred seventy-eight lower-case iotas then reference.

Evaluates to H

Hi.

Example with recursion

240518692878%%>Μ91+%%ι%%>

alternatively:

Evaluate two hundred forty billion, five hundred eighteen million, six hundred ninety-two thousand, eight hundred seventy-eight lower-case iotas then reference.
Evaluate Μ91 and increment 
Then evaluate one lower-case iota and reference.

This evaluates to Hi.

Total

171749209129279056906684150347584115690508718183117419140003836513868923676948104213124479614501542532961169618378310807164456469115301997603135051207200118165996999724813863352366464112524321967365297310337820598626650718994556
%%>

alternatively:

Evaluate seventeen quattuorseptuagintillion, one hundred seventy-four treseptuagintillion, nine hundred twenty duoseptuagintillion, nine hundred twelve unseptuagintillion, nine hundred twenty-seven septuagintillion, nine hundred five 
novemsexagintillion, six hundred ninety octosexagintillion, six hundred sixty-eight septsexagintillion, four hundred fifteen sexsexagintillion, thirty-four quinsexagintillion, seven hundred fifty-eight quattuorsexagintillion, four hundred 
eleven tresexagintillion, five hundred sixty-nine duosexagintillion, fifty unsexagintillion, eight hundred seventy-one sexagintillion, eight hundred eighteen  novemquinquagintillion, three hundred eleven octoquinquagintillion, seven hundred 
forty-one septenquinquagintillion, nine hundred fourteen sexquinquagintillion, three hundred eighty-three quattuorquinquagintillion, six hundred fifty-one trequinquagintillion, three hundred eighty-six duoquinquagintillion, eight hundred 
ninety-two unquinquagintillion, three hundred sixty-seven quinquagintillion, six hundred ninety-four novemquadragintillion, eight hundred ten octoquadragintillion, four hundred twenty-one septenquadragintillion, three hundred twelve 
sexquadragintillion, four hundred forty-seven quinquadragintillion, nine hundred sixty-one quattuorquadragintillion, four hundred fifty trequadragintillion, one hundred fifty-four duoquadragintillion, two hundred fifty-three 
unquadragintillion, two hundred ninety-six quadragintillion, one hundred sixteen novemtrigintillion, nine hundred sixty-one octotrigintillion, eight hundred thirty-seven septentrigintillion, eight hundred thirty-one sextrigintillion, eighty 
quintrigintillion, seven hundred sixteen quattuortrigintillion, four hundred forty-five tretrigintillion, six hundred forty-six duotrigintillion, nine hundred eleven untrigintillion, five hundred thirty trigintillion, one hundred ninety-nine 
novemvigintillion, seven hundred sixty octovigintillion, three hundred thirteen septenvigintillion, five hundred five sexvigintillion, one hundred twenty quinvigintillion, seven hundred twenty quattuorvigintillion, eleven trevigintillion, 
eight hundred sixteen duovigintillion, five hundred ninety-nine unvigintillion, six hundred ninety-nine vigintillion, nine hundred seventy-two novemdecillion, four hundred eighty-one octodecillion, three hundred eighty-six septendecillion, 
three hundred thirty-five sexdecillion, two hundred thirty-six quindecillion, six hundred forty-six quattuordecillion, four hundred eleven tredecillion, two hundred fifty-two duodecillion, four hundred thirty-two undecillion, one hundred 
ninety-six decillion, seven hundred thirty-six nonillion, five hundred twenty-nine octillion, seven hundred thirty-one septillion, thirty-three sextillion, seven hundred eighty-two quintillion, fifty-nine quadrillion, eight hundred sixty-two 
trillion, six hundred sixty-five billion, seventy-one million, eight hundred ninety-nine thousand, four hundred fifty-six lower-case iotas then reference.

Evaluates to Hello, World!

XKCD Random Number

Ν91+Dµ30Μ91++++%%>

alternatively:

Nope. Evaluate divmod(34,5)
Reference

This evaluates to 4.

Computational class

17 is a finite state automata.

See also

Combinatory logic is a significantly more powerful combinatoric language.

External Resources

• https://en.wikipedia.org/wiki/McCarthy_91_function
• https://iannmiui-png.github.io/wiki/17/17interpreter interpreter (W.I.P)
• Tupper's self-referential formula Korean page