A Couple of Meta-Interpreters in Prolog

The three or so times I've needed to build a metainterpreter, I have always referred back to your page for help, so thanks for taking the time to make it! It's greatly appreciated!

any favorite websites / book about this topic ?

thanks for writing this

Your "Power of Prolog" book/site has been a great help to me just this last week or so. I had developed a simple type inference algorithm for a stack-based language called Joy, using knowledge of unification gained from studying a Python implementation of miniKanren. At some point I realized that, if I wanted to do anything "fancy" with my types like propagating constraints or something, I should switch to Prolog (or Kanren.)

> Prolog has powerful built-in mechanisms that can be used in interpreters, and in addition to that, Prolog variables on the object-level (the program to be interpreted) are also variables on the meta-level (the interpreter). As a consequence, Prolog's implicit mechanisms can be absorbed in interpreters: They need not be encoded explicitly.

Brother, you're not kidding! I reimplemented the semantics of Joy in Prolog and when I had boiled off the cruft included due to my ignorance an inexperience with the language the resulting interpreter was very elegant. Several pages of Python became about a half-page of Prolog.

Not only that, but when I went to implement the type inferencer I realized I had just reimplemented the interpreter, only it was more elegant. In Prolog, the interpreter and the type inferencer are the same thing. (I feel foolish for not catching on and using Prolog, et. al. sooner.)

For what it's worth, here's the Joy-in-Prolog code (the library of functions is incomplete but the thun() relation works.):

    /*

    Interpreter

    thun(Expression, InputStack, OutputStack)

    Copyright © 2018 Simon Forman

    This file is part of Thun.

    Thun is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    Thun is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with Thun.  If not see <http://www.gnu.org/licenses/>.

    */
    :- use_module(library(clpfd)).

    thun([], S, S).
    thun( [Func|E], Si, So) :- func(Func, Si, S), thun(E, S, So).
    thun([Combo|E], Si, So) :- combo(Combo, Si, S, E, Eo), thun(Eo, S, So).
    thun(  [Lit|E], Si, So) :- thun(E, [Lit|Si], So).

    combo(i,          [P|S], S, Ei, Eo) :- append(P, Ei, Eo).
    combo(dip,     [P, X|S], S, Ei, Eo) :- append(P, [X|Ei], Eo).
    combo(dipd, [P, X, Y|S], S, Ei, Eo) :- append(P, [Y, X|Ei], Eo).

    combo(branch, [T, _,  true|S], S, Ei, Eo) :- append(T, Ei, Eo).
    combo(branch, [_, F, false|S], S, Ei, Eo) :- append(F, Ei, Eo).

    combo(loop, [B,  true|S], S, Ei, Eo) :- append(B, [B, loop|Ei], Eo).
    combo(loop, [_, false|S], S, E,  E ).

    func(cons, [A, B|S], [[B|A]|S]).
    func(swap, [A, B|S],  [B, A|S]).
    func(dup,     [A|S],  [A, A|S]).
    func(pop,     [_|S],        S ).
    func(+,    [A, B|S],     [C|S]) :- C #= A + B.
    func(-,    [A, B|S],     [C|S]) :- C #= B - A.
    func(*,    [A, B|S],     [C|S]) :- C #= A * B.
    func(nullary,   [P|S],   [X|S]) :- thun(P, S, [X|_]).
    func(concat, [A, B|S],   [C|S]) :- append(B, A, C).

    func(>,    [A, B|S],  [true|S]) :- B #> A.  /* Is this really necessary? */
    func(>,    [A, B|S], [false|S]) :- A #>= B.
    func(<,    [A, B|S],  [true|S]) :- B #< A.
    func(<,    [A, B|S], [false|S]) :- B #>= A.

    func(Name, Si, So) :- define(Name, Body), thun(Body, Si, So).

    define(swons, [swap, cons]).
    define(x, [dup, i]).
    define(sqr, [dup, *]).
    define(ifte, [[nullary], dipd, swap, branch]).
    define(while, [swap, [nullary], cons, dup, dipd, concat, loop]).

And an example run:

    ?- thun([[], 3, sqr, swons], [], So).
    So = [[9]] .

And, showing the ridiculous power of Prolog:

    ?- thun([sqr, swons], Si, So).
    Si = [_8302, _8308|_8310],
    So = [[_8332|_8308]|_8310],
    _8302^2#=_8332,
    _8332 in 0..sup .

That is:

     ?- thun([sqr, swons], Si, So).
    Si = [A, X|...],
    So = [[B|X]|...],
    A^2 #= B,
    B in 0..sup .

Which says, correctly, that "sqr swons" expects a number A and a list X on the stack, and returns just the list X with the square of A cons'd onto it.

Now, as if that weren't messed up enough:

    ?- thun([sqr, swons], Si, [[9]]).
    Si = [_10164, []],
    _10164 in -3\/3 .

Like I said, I feel kinda stupid for not using Prolog sooner.

Can you explain to me what you use Prolog for and why you chose it over something more popular? What are the pros/cons in your mind?

Everytime I get started, I eventually stop when I realize I'm not an alien named Spock :). In all seriousness, it is very challenging to me, so kudos to you. My bucket list has Forth, APL, Lisp, Smalltalk, and Prolog on it.

Sorry to be rude, but could you ask/beg Prof Muggleton to write a book on ILP and/or meta-interpretive learning? Something like an expanded version of his outline webpage (https://www.doc.ic.ac.uk/~shm/ilp_theory.html).

My go-to for trying to understand ILP theory is Nienhuys-Cheng and de Wolf, _Foundations of Inductive Logic Programming_ and De Raedt's _Logical and Relational Learning_ is a more up-to-date overview, but I feel like there's room for a more modern textbook. This new MIL stuff seems to be be an important unifying idea that also connects back to abductive logic programming, if I understand correctly.

Just a request; no offence intended!