this post and then this post. It might pay to skim those two posts first.
Post: Here are some concluding thoughts.
The prophecy of Yonah came up in the course of discussing what allows us to determine a false vs. true prophet. Yonah had delivered this prophecy to the people of Nineveh (Jonah 3:4): עוֹד אַרְבָּעִים יוֹם, וְנִינְוֵה נֶהְפָּכֶת, "Yet forty days, and Nineveh shall be overthrown". Yet they repented, and the prophecy did not come to pass. This was a public negative prophecy. If so, how can we make this work with the rules of determining a false prophet described in parashat Shofetim?
An insight I think I might have heard a year or two from my father. The prophecy was indeed fulfilled. There is ambiguity in the word נֶהְפָּכֶת, and the people themselves overturned the city. They went from bad to good, and took extreme measures to develop and express their contrition. So, the prophecy could have been fulfilled by either act of God or act of man.
Somewhat related to this, there are several Biblical texts which must go into a developed theory of how one determines a false prophet. The pasuk in Shofetim, for certain. But, also the prophecy to Yirmeyahu in the potter's house (and the parallel in Yechezkel) about Hashem 'repenting' of delivered prophecy. Also, the competing prophecies of Yirmeyahu and Chananiah ben Azzur, and Hashem's needing to reassure Yaakov before he met with his brother, even though he had received previous assurance. And, of course, the prophecy of Yonah. One can explain each of these pesukim in different ways, but one must account for each of them.
The Rambam accounted for each of these in his introduction to his perush hamishnayos as well as in Mishneh Torah, in the laws of determining a false prophet. Namely, private prophecy can be taken back, and public negative prophecy can be taken back, and so testing a prophet is only based on public positive prophecy. (Now go to each source and see how his theory satisfies each constraint imposed by a separate pasuk.) But his interpretations are not necessarily binding. We saw another Rishon, Rabbi Yosef Ibn Caspi, account for each of these pesukim in another, legitimate, manner. Namely, that one can only test a prophet where the positive or negative prophecy contains an explicit condition, and the condition is fulfilled. (See the second post.) And I, as well, suggested ways in which this can work out, such as that this refers to neutral signs and wonders appointed by the prophet to establish himself as a prophet, prior to any prophecy of weal or woe. (See the first post.)
What do I think of Ibn Caspi's approach? Well, he started all this by rejecting the Rambam for not fitting into the plain text of the pasuk in Shofetim. That is, the pasuk never mentioned that there was a distinction between positive and negative prophecy which failed to come true. As such, this is a deviation from peshat and a possible bal tosif. But then, he imposes his own distinction which is not explicitly mentioned in the pasuk. If we are already imposing distinctions, why not revert to the Rambam's distinction? After all, if the pasuk just means test the prophet to see if it does not materialize, in cases where it is possible to test him -- and a specific philosophical approach combined with constraints imposed by interpretations of other pesukim defines where it is possible to test him -- then say as well that it is obviously impossible to test him based on negative prophecy, since we know that Hashem can retract it, and indeed, the most obvious purpose of the prophecy is to issue a threat in order to inspire teshuva.
Ibn Caspi would have an answer ready, that his constraint is more readable into the pasuk. He would be right, since the pasuk says וְלֹא-יִהְיֶה הַדָּבָר וְלֹא יָבֹא, and we cannot know for certain by prophecy with 'absolute' wording that it did not come to pass, because perhaps there was an implied condition. But there is still some measure of forcing into the words of the pasuk, and I believe that we could do the same with the Rambam's interpretation.
Ibn Caspi is not only constrained by peshat considerations of the local and remote pesukim, but by his philosophical theological beliefs as well. Even though Hashem speaks about 'repenting', ונחמתי, in Yirmeyahu 18:8, this cannot mean actual reconsideration, since Hashem knows everything in advance and is unchanging. It must be a change from the receiving end, which is falsely perceived by humans, with their limited perception, as change. And thus is born this distinction between conditional and absolutely worded prophecy, in which absolutely worded prophecy is often actually just implicitly conditional, and so when it is 'retracted' it is just a change of circumstance and an imposition of the implicit condition. Don't accept this philosophical approach to God, and suddenly this unstated caveat is not so obvious in the pasul.
I can see and appreciate Ibn Caspi's distinction. Yet I could have also imagined a distinction in ability to test a false prophet in the opposite direction. With an explicit condition, perhaps the people privately repented sufficiently. Or if it a condition which certainly perceptible, then indeed the prophet can be tested. But the pasuk was speaking about absolutely worded prophecy, in which case we should take him at his word and assume he is a false prophet if it fails to materialize.
This would possibly clash with other textual evidence, such as the repentance of Nineveh. But then, one just needs to use one's sechel. The people all accepted the prophecy as true, and directly addressed Hashem for mercy. When the public reaction was like this, then it is obviously assumed by the people that Hashem can and does retract, in His mercy. In other words, there is a ready teretz for him which is not a stretch at all, given the people's response and assumptions up to that point. This is not the same as a blustering false prophet, who boldly makes predictions, and the predictions just don't come true. Don't start taking all sorts of kvetches, and give him the benefit of the doubt, because of some misdirected sense of dan lekaf zechut, but rather, as the pasuk tells us, בְּזָדוֹן דִּבְּרוֹ הַנָּבִיא, לֹא תָגוּר מִמֶּנּוּ, you shall not fear him.
What do I think about the foreign psukim, outside of parashat Shofetim? In terms of Yirmeyahu in the house of the potter, nothing indicates to me that this was public or even private prophecy. It can just be Hashem's initial 'intention', from which He withdrew. (Except of course Ibn Caspi would say Hashem is unchanging. So say that this was Hashem's attitude towards the person, according to the scales of justice if imposed at that precise time.) In terms of Yirmeyahu vs. Chananiah, I am not sure that we are speaking of judging a prophet in accordance with the laws of Shofetim at all! Rather, Yirmeyahu is speaking rational words to the false prophet and to the hamon am, that Chananiah's positive prophecy is so out of the ordinary (compared with the words of most other prophets) that only time will tell, and they should treat Chananiah's prophecy with a healthy dose skepticism until it actually materializes. Note that Yirmeyahu does not speak of knowing that the prophet was false, but rather the reverse, knowing that the prophet was speaking the truth. And so, neither Yirmeyahu nor Chaninia was being 'tested' in this sense.
In terms of Yonah, it is quite possibly allegory. But if we take it historically, then I don't think anyone ever raised the possibility of Yonah being a false prophet. Yonah complains, sure, in the last perek -- אָנָּה ה הֲלוֹא-זֶה דְבָרִי עַד-הֱיוֹתִי עַל-אַדְמָתִי--עַל-כֵּן קִדַּמְתִּי, לִבְרֹחַ תַּרְשִׁישָׁה: כִּי יָדַעְתִּי, כִּי אַתָּה אֵל-חַנּוּן וְרַחוּם, אֶרֶךְ אַפַּיִם וְרַב-חֶסֶד, וְנִחָם עַל-הָרָעָה. That does not mean that Yonah's reluctance was that people would consider him a false prophet. Rather, I would understand it as that he was reluctant because he thought it was pointless, since the evildoers were not going to be punished anyway. (Chazal understand it as a reluctance because of the negative comparison to Klal Yisrael, who did not do teshuva in response to such negative prophecies.) Sure, if someone were interested in trying him as a false prophet, they could bring him to Beis Din. But no one was interested in this, and applying a little bit of seichel, in terms of the plausibility of Hashem's retraction, given the circumstances, would likely go a long was in an actual court case.
(And ignoring the halacha, the pasuk in Shofetim never actually said to execute him, just not to fear / heed him. And וּמֵת הַנָּבִיא הַהוּא need not be human imposition of the death penalty. The 'proof' might be in the contest between Yirmeyahu and Chaninah, where subsequently, Yirmeyahu predicts for the false prophet Chanania a death at the hands of Heaven within a year. And that prophecy comes true.)