The three-element linear concatenative basis

Brent Kerby calls out that ‘take’, ‘cat’, and ‘i’ are a linear basis in a concatenative language.

The Theory of Concatenative Combinators » Linear Completeness

[B] [A] take == [A [B]]
[B] [A] cat  == [B A]
    [A] i    == A

This is a valid basis because ‘take’ covers quoting, concatenation, and reording; ‘cat’ covers concatenation; and ‘i’ covers unquoting. (Note that concatenation is covered twice, which is why there is a possible two-instruction basis.)

Categories of instructions in a concatenative basis

The two-element linear concatenative basis

A linear basis for Swanson