Shortest meta-circular description of a universal computational structure? (opens in new tab)

I think a meta-circular interpreter for Prolog would fit this description nicely. Prolog excels at writing interpreters in general, and in particular admits exceptionally short meta-circular meta-interpreters, i.e., interpreters written in Prolog that can interpret pure Prolog code, including their own source code.

An example of such a meta-circular Prolog interpreter is:

    mi([]).
    mi([G0|Gs0]) :-
            clause(G0, Rs, Gs0),
            mi(Rs).

It can interpret pure Prolog code, a Turing-complete subset of first-order predicate logic. For example, given the following clauses:

    clause(natnum(0), Rs, Rs).
    clause(natnum(s(X)), [natnum(X)|Rs], Rs).

It yields:

    ?- mi([natnum(X)]).
       X = 0
    ;  X = s(0)
    ;  X = s(s(0))
    ;  X = s(s(s(0)))
    ;  X = s(s(s(s(0))))
    ;  ... .

The meta-interpreter's own code can also be represented in this way:

    clause(mi([]), Rs, Rs).
    clause(mi([G0|Gs0]), [clause(G0,Rs,Gs0),mi(Rs)|Ls], Ls).

    clause(clause(Head, Rs0, Rs), Ls, Ls) :- clause(Head, Rs0, Rs).

And now it can interpret its own source code, interpreting any given program, arbitrarily deeply nested. For example:

    ?- mi([mi([mi([natnum(X)])])]).
       X = 0
    ;  X = s(0)
    ;  X = s(s(0))
    ;  X = s(s(s(0)))
    ;  ... .

Tested with Scryer Prolog.

paging John Tromp, paging John Tromp...

To quell AGI hysteria I've posed a simple Algorithmic Information Theoretic IQ Test question: What is the shortest program you can come up with that outputs this string: 0000000001000100001100100001010011000111010000100101010010110110001101011100111110000100011001010011101001010110110101111100011001110101101111100111011111011111

Yann LeCun responded: "I can construct a computer for which the shortest program that generates this bit string has length 1."

To which I posed this question: "Why do mathematicians spend centuries asking for their minimum set of axioms but, not even Wolfram's acolytes ask for the shortest meta-circular description of a universal computational structure?"