Iota and Jot
minimalistic Turing-complete programming languages based on combinatory logic
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 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.
Note that this article uses Backus–Naur form to describe syntax.
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,
From this, one can recover the usual SKI expressions, thus:
Because of its minimalism, it has influenced research concerning Chaitin's constant.
Iota
Iota is the LL(1) language that uses prefix notation to denote trees constructed from the aforementioned universal iota ι combinator (at leaves), and function application (denoted 0),
so that for example 0011011 denotes
(
(
ι
ι
)
(
ι
ι
)
)
{\displaystyle ((\iota \iota )(\iota \iota ))}
, whereas 0101011 denotes
(
ι
(
ι
(
ι
ι
)
)
)
{\displaystyle (\iota (\iota (\iota \iota )))}
.
Jot
Jot is the regular language consisting of all sequences of 0 and 1,
The semantics is given by translation to SKI expressions.
The empty string denotes
I
{\displaystyle I}
,
w
0
{\displaystyle w0}
denotes
(
(
[
w
]
S
)
K
)
{\displaystyle (([w]S)K)}
,
where
[
w
]
{\displaystyle [w]}
is the translation of
w
{\displaystyle w}
,
and
w
1
{\displaystyle w1}
denotes
(
S
(
K
[
w
]
)
)
{\displaystyle (S(K[w]))}
.
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