This is, in spirit, what Solvespace does--although like the other reply here says with extruded 2D.

From https://solvespace.com/tech.pl

> The core of any parametric CAD program is its geometric constraint solver.

and

> In SolveSpace, constraints are represented as equations in a symbolic algebra system. In general, these equations are solved numerically, by a modified Newton's method.

and from https://en.wikipedia.org/wiki/Geometric_constraint_solving#M...

> symbolic methods have been applied to this type of constraint solving (see Reference 20 on the Wikipedia link).

And your Zen "beginner mind" question got me to thinking, maybe I could use Prolog itself in my CAD system to directly make 3D shapes, since Prolog has been written in Lisp. Although Prolog does have a number of limitations:

https://en.wikipedia.org/wiki/Prolog#Limitations

>> Does any system aspire to be a Prolog for 3D? You sketch a variety of views and a system solves, if possible, for a solid geometry representation?

I'm not aware of any. Maybe slightly related, my plan for a "hole tool" in Solvespace is to add a hole entity to 2D drawings that will automatically create a featured hole when the sketch is extruded. But that's not actually solving anything in a math sense.