Leaf answer specifics and countall/2

[bakaq]

@UWN, it seems that "leaf answer" is very related to the concept you want in the specification of countall/2 from the Prolog prologue. However, the sense I've been using "leaf answer" is different from the one of countall/2 (which is lifted from findall/3), because it includes tail falses, and it's therefore implementation specific.

?- use_module(library(iso_ext)).
   true.
?- (true;false).
   % 2 "leaf answers with tail false". This could eventually return just 1
   % with some clever optimizations that notice that they can compile this
   % to just "true".
   true
;  false.
?- countall((true;false), N).
   % Only one "countall/2 answer", which will always be the case no matter
   % what the underlying implementation does.
   N = 1.

From my understanding, countall/2 counts the "successful leaf answers". If countall/2 gives N as a result, there is either N or N + 1 "leaf answers", depending on if there is a tail false or not¹. I'm not sure which of these concepts should be blessed with the nicer term, but here are some options:

1. "Leaf answer" includes tail falses, and "successful leaf answer" doesn't. I prefer this one, but makes the blessed term procedural.
2. "Leaf answer" doesn't include tail false. This is much more logically nice, and makes it so that changes to indexing, search strategy and optimizations don't change the number of leaf answers. But then we will need a name for the more general case which does in fact include the tail false (this concept is needed in the toplevel, embedding API and for profiling code), and I can't really think of a good one.

Footnotes

1. And also ignoring exceptions and things like that. ↩

[UWN]

false is not a leaf answer. There is no answer like

?- something(X).
   X = 1
;  false
;  X = 2.

It may be a complete answer like

?- 1 = 2.
   false.

It terminates an answer. Optionally, indeed. It terminates an answer, like an exception terminates an answer.

[bakaq]

After thinking about it a bit more, I think that we don't actually need a name for the "generalized leaf answer" of option 1. The interface that I made in #2527 works fine with option 2, leaving the procedural "answer finalization" to another level. That will probably also need to be reflected in the embedding API in #2582 anyway.

[UWN]

On the one hand, we are considering Prolog's execution mechanism. But it might make sense to look also to alternative mechanisms. Say, some parallel executions. In that context, a false in between, or an error in between might make sense. Very vaguely speaking.