Sea

Sea is a three command simple translation of Underload. Sea was discovered by Orby during October of 2020.

Commands

Sea consists of three commands: (, ), and &. ( and ) are quoting operators as in Underload. & is the sole sufficient concatenative combinator.

Rewrite rules

Expression	Rewritten
(a) &	(K) (S') a
(b) (a) K	a
(d) (c) (b) (a) S'	((d) c) a (d) b

Note that only (, ), and & are Sea commands. K and S' are presented as conceptual aids.

Theory

Notice we can reconstruct S' from (, ), and &

 ()()()()()()()&()&&
 ()()()()()()(K)(S')(K)(S')&
 ()()()()()()(K)(S')(K)(K)(S')S'
 ()()()()()()(K)((S')K)S'(S')K
 ()()()()(())(S')K()K(S')K
 ()()()()S'()K(S')K
 (())()()K(S')K
 (())(S')K
 S'

Once we have S' we can recover K?

See also

• The Theory of Concatenative Combinators