MIBBLLII

MIBBLLII Isn't brainfuck But Looks Like It Is is a programming language made by Nathan van Doorn. It is based on the wikipedia:B,C,K,W system. It maps input (expressed as a church list of church booleans corresponding to the bits of the input, ending with an infinite stream of church trues) to output (expressed as a similar list, presumably finite).

Combinators

Expression	Evaluates as
+ a b c	a [ b c ]
- a b c	a c b
. a b	a
, a b	a b b
> a	a
< a b c	a c [ b c ]

[ and ] are used to group combinators for evaluation order.

Proof of Turing Completeness

SKI combinator calculus is Turing-complete, and all the operators in SKI exist in MIBBLLII as <, ., and >. It is still Turing-complete without < or >, as the following shows.

<       +[+,][++-]
>       ,.

See also

• I hate your bf-derivative really I do
• Combinatory logic