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You're replying to a comment by Dave Phillips.
Very interesting read. Thanks.
A brief comment on your section on Prolog functors:
You say that functors in Prolog "refer to two things". This is a bit weird to say. Clearly, the second thing is just a convenience predicate that Prolog provides for analyzing structures/terms.
This convenience predicate isn't some separate notion of a functor any more than the =.. operator is. The fact that the predicate is called 'functor' shouldn't be taken too seriously. It could just as well have been called 'analyze'.
A functor in Prolog is the atom at the beginning of a structure. It is defined by its name and its arity.
(BTW, the =.. operator is used to decompose structures into lists. e.g. f(1, 2) =.. [f, 1, 2]. is a true statement.)
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