# Iota and Jot

Paradigms Formal language, Turing tarpit, esoteric Chris Barker Chris Barker 2001; 16 years ago 2001 / 2001; 16 years ago Scheme, JavaScript Scheme interpreter, Web browser (JavaScript) Public domain www.nyu.edu/projects/barker Zot

In formal language theory and computer science, Iota and Jot (from Greek iota ι, Hebrew yodh י, the smallest letters in those two alphabets) are languages, extremely minimalist formal systems, designed to be even simpler than other more popular alternatives, such as the lambda calculus and SKI combinator calculus. Thus, they can also be considered minimalist computer programming languages, or Turing tarpits, esoteric programming languages designed to be as small as possible but still Turing-complete. Both systems use only two symbols and involve only two operations. Both were created by professor of linguistics Chris Barker in 2001. Zot (2002) is a successor to Iota that supports input and output.[1]

## Universal iota

Chris Barker's universal iota combinator ι has the very simple λf.fSK structure defined here, using denotational semantics in terms of the lambda calculus,

${\displaystyle \iota :=\lambda f.((fS)K)}$

(1)

From this, one can recover the usual SKI expressions, thus:

${\displaystyle I\,=\,(\iota \iota ),\;K\,=\,(\iota (\iota (\iota \iota ))),\;S\,=\,(\iota (\iota (\iota (\iota \iota ))))}$

(2)

Because of its minimalism, it has influenced research concerning Chaitin's constant.[2]

## Iota

Iota is the LL(1) language that prefix orders trees of the aforementioned Universal iota ι combinator leafs, consed by function application ε,

iota = "1" | "0" iota iota


so that for example 0011011 denotes ${\displaystyle ((\iota \iota )(\iota \iota ))}$, whereas 0101011 denotes ${\displaystyle (\iota (\iota (\iota \iota )))}$.

## Jot

Jot is the total[disambiguation needed] regular language,

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


where the ${\displaystyle w1}$ denote ${\displaystyle (w\iota )}$ whereas the ${\displaystyle w0}$ denote ${\displaystyle (\iota w)}$ so that 1100 denotes ${\displaystyle (\iota \iota )(\iota \iota )}$ whereas 1000 denotes ${\displaystyle \iota (\iota (\iota \iota )}$ and the ${\displaystyle 0^{*}w}$ reduce to Iw yielding a natural Gödel numbering of all algorithms.

## Zot

The Zot and Positive Zot languages command Iota computations, from inputs to outputs by continuation-passing style, in syntax resembling Jot,

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


where 1 produces the continuation ${\displaystyle \lambda cL.L(\lambda lR.R(\lambda r.c(lr)))}$, and 0 produces the continuation ${\displaystyle \lambda c.c\iota }$, and wi consumes the final input digit i by continuing through the continuation w.