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How can I use elisp to search for headlines that return true against a predicate function? In particular, I already have an elisp function within-intervalp which checks whether a number num is within the range specified by property :INTERVAL: (at point). So for example if I have

* Parent
** Child1
:PROPERTIES:
:INTERVAL: [2,3]
:END:
*** Subchild1
:PROPERTIES:
:INTERVAL: [2,4]
:END:
** Child2
:PROPERTIES:
:INTERVAL: [5,7]
:END:
** Child3
:PROPERTIES:
:INTERVAL: [7,9]
:END:

and I run (within-intervalp 2.5), I'd like to see Child1 and Subchild1 pop up in a search. Is this possible?

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You can use org-element-map to collect headlines that meet some criteria.

Something like this:

 (org-element-map (org-element-parse-buffer) 'headline
         (lambda (hl)
           (goto-char (org-element-property :begin hl))
           (when (within-intervalp 2.5)
         hl)))

should return a list of headlines meeting your criteria. You can then map over the list to return candidates for ivy/helm or some other selection engine.

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