Prolog meta-interpreters and single sided unification

Question

I tried this vanilla interpreter:

solve(true) :- !, true.
solve(X is E) :- !, X is E.
solve((A,B)) :- !, solve(A), solve(B).
solve(H) :- clause(H,B), solve(B).

Can we use it to meta-interpret some code? I tried this code,
requires SWI-Prolog 8.3.19, which runs fine normally:

sumlist([X|Y], R) => sumlist(Y, H), R is X+H.
sumlist([], R) => R is 0.

?- sumlist([1,2,3],X).
X = 6.

?- sumlist(X,Y).
ERROR: No rule matches sumlist(_21604,_21606)

But meta-interpretation goes wrong. The reason is that clause/2
doesn’t know about rules that use single sided unification:

?- clause(sumlist(A,B),C).
A = [_22728|_22730],
C =  (sumlist(_22730, _22736), B is _22728+_22736) ;
A = [],
C =  (B is 0).

?- solve(sumlist([1,2,3],X)).
X = 6.

?- solve(sumlist(X,Y)).
SWI-Prolog wurde unerwartet beendet.

Is there a solution for meta-interpreters and single sided unification?

Answer 1

One way out of the dilemma and stay inside the ISO core standard, is to translate single sided unfication to a combination of nonvar/1, (=)/2 and (==)/2, like here:

?- clause(sumlist(X,Y),Z), write((sumlist(X,Y):-Z)), nl, fail; true.
sumlist(_A, _B) :- nonvar(_A), _A = [_C|_D], sumlist(_D, _E), _B is _C+_E
sumlist(_A, _B) :- nonvar(_A), _A = [], _B is 0

Of course we need to add the built-ins nonvar/1, (=)/2 and (==)/2 as well to the meta interpreter:

solve(true) :- !.
solve(X is E) :- !, X is E.
solve(nonvar(X)) :- !, nonvar(X).
solve(X == Y) :- !, X == Y.
solve(X = Y) :- !, X = Y.
solve((A, B)) :- !, solve(A), solve(B).
solve(H) :- clause(H, B), solve(B).

Meta-interpreting sumlist/2 now works fine:

?- solve(sumlist([1,2,3],X)).
X = 6

?- solve(sumlist(X,Y)).
No

But the translator might challenge a Prolog system concering clause indexing. It moves away the functors from the head into the body. So the Prolog system would need some body front indexing as pioneered by YAP and found in Jekejeke Prolog.

Open Source:

Yet Another Pattern Matcher
https://gist.github.com/jburse/a3517410a28b759ef44f72584f89aaf8#file-picat3-pl

Vanilla Interpreter, Expansion Solution
https://gist.github.com/jburse/a3517410a28b759ef44f72584f89aaf8#file-vanilla4-pl