Iota and Jot

Iota and its successor Jot (from Greek iota, Hebrew yodh, the smallest letters in those two alphabets) are extremely minimalist formal systems, designed to be even simpler than other more popular alternatives, such as the lambda calculus and SKI combinator calculus. They can therefore also be considered minimalist computer programming languages, or Turing tarpits, esoteric programming languages that are designed to be as small as possible but still Turing-complete. Both systems use only two symbols and involve only two operations. Zot is a successor to Iota that includes input and output.

Iota's universal combinator has a very simple structure (defined here using denotational semantics in terms of the lambda calculus):

$U=\lambda f.((fS)K)$

From this, one can recover the usual SKI basis combinators as follows:

$I\,=\,(UU),\;K\,=\,(U(U(UU))),\;S\,=\,(U(U(U(UU))))$

Because of its minimalism, it has influenced research concerning Chaitin's constant.

Iota

Iota is the LL(1) Polish notation of trees of the aforementioned $U$ combinator leafs consed by function application $\$$

  iota = "U" | "$" iota iota

so that for example $\$\$UU\$UU$ denotes $((UU)(UU))$, whereas $\$U\$U\$UU$ denotes $(U(U(UU)))$.

Jot

Jot is the regular language

   jot = "" | jot "0" | jot "1"

where the $w1$ denote $\lambda xy.w(xy)$ whereas the $w0$ denote $w(SK)$ and the $0^{*}w$ reduce to $Iw$.

Zot

The Zot and Positive Zot languages command Iota computations from input to output in continuation-passing style and syntax resembling Jot

   zot = pot | "" 
   pot = iot | pot iot
   iot = "0" | "1"

where $1$ produces the continuation $\lambda cL.L(\lambda lR.R(\lambda r.c(lr)))$ and $0$ produces the continuation $\lambda c.c(\lambda f.fSK)$ and $ci$ consumes the final input digit $i$ continuing through continuation $c$.

See also

• Lambda calculus
• Combinatory logic
• Binary combinatory logic
• SKI combinator calculus

External links

• Barker, Chris. "Iota and Jot: the simplest languages?". The Esoteric Programming Languages Webring. Archived from the original on 7 May 2016. Retrieved 13 August 2004.
• https://esolangs.org/wiki/Iota
• https://esolangs.org/wiki/Jot
• https://esolangs.org/wiki/Zot