Iota

Iota is a Turing tarpit designed by Chris Barker, based in combinatory logic. It uses only two symbols, * and i, but not every combination of them is syntactically correct; e.g. *i*ii is correct but *iii is not, as opposed to its "sister language" Jot in which every string of symbols is valid.

Iota can be defined as follows:

*ix     --> **xsk
**kxy   --> x
***sxyz --> **xz*yz

Or, if you prefer:

i = λx.xsk
k = λxy.x
s = λxyz.xz(yz)

*xy where x and y are functions denotes the function (xy). These can be "nested", such that (for example) *x*yz denotes x(yz).

Only the i function and the * operator can actually appear in a program's source code.

See also

• Jot, Iota's "sister language" from the same article
• Binary combinatory logic
• Lambda calculus

External resources

• Iota and Jot: the simplest languages?