I think my Tom Swifty and other experiments show pretty conclusively that GPT-3 just doesn't get puns (likely due to BPEs), so of course it wouldn't be able to explain them either (likewise). I for one am pleased that puns are what separate us from the machines, and have spent a lifetime preparing for this moment...

But to test it out:

Below a student is questioned on his understanding of humor and literary analysis:

Q. Explain the pun in the following Tom Swifty: '"I got a great deal on my new Raybans", Tom said shadily.'
A. The pun is on "shadily": Raybans are a sunglass brand, which make things look shady, but Tom is implying he purchased unusually cheap, and thus probably counterfeit, sunglasses, which is a 'shady' or dark or criminal or unethical thing to do. The pun conflates blocking light with economic crimes.

Q. Explain the pun in the following joke: "Why do so many bakeries have cats? Because cats are always kneading."
A. The joke implies that bakeries use cats to knead their dough, because cats regularly make kneading motions on furniture or humans, which imitates actions they take as kittens to get milk from their mother; the pun uses 'knead' in two senses, of kneading dough to bake bread and kneading human laps for attention. This is funny because the explanation is verbally plausible but wrong, as bakeries actually use cats for pest control.

Q. Explain the pun in the following joke: "Why can Paypal freeze accounts without recourse or explanation? Because long ago they decided users must accept their Terms of Service and the clause of Paypal infallibility."
A. The pun is on the phrase "Paypal infallibility", which alludes to the Catholic doctrine of "papal infallibility", that the pope cannot be wrong in religious dogma and papal judgments cannot be appealed or questioned. This was attacked as religious tyranny and an overreach of power. Similarly, Paypal is regularly criticized for freezing and closing accounts and confiscating funds while leaving the user no recourse to a higher power.

Q. Explain the pun in the following joke: "What does Adult Swim call their physical retail stores? Brick and Morty."
A.

|The pun "Brick and Morty" alludes to the cable television network "Adult Swim", which broadcasts a cartoon series called "Rick and Morty", a humorous parody of "Back to the Future" and other science fiction films. "Brick and Morty" refers not to the characters in the cartoon, but to physical stores that sell DVDs and merchandise based on the cartoon. The pun conflates two meanings of "Brick and Mortar", a brick-and-mortar store and a brick which is part of a building.

|The joke plays on the similarity of words "Brick and Mortar" (referring to physical stores instead of online) and the characters called "Brick and Mortar" on Adult Swim shows "Rick and Morty".

Q. Explain the pun in the following joke: "What do you call a generic unicorn? An Uniporn"
A. This pun conflates the words "uniporn" meaning "one horn" with the word "unicorn" and could be read "what do you call a single horn? one horn" or "A single horn, what does it do? It gives you one horn".

Q. Explain the pun in the following joke: "What did one melon say to the other? Cantaloupe".

A. The puns in this joke are on "cantaloupe" and "cantaloupes".

Q. Explain the pun in the following joke: "Why is it good to have a lawyer? Because pea ple (people)"

A. The puns in this joke are on "pea ple (people)" and a vegetable called "peas".

|This pun plays on the phrase "Brick and mortar stores" which refers to physical retail stores that exist in the real world where you can purchase goods and products. In the case of Adult Swim, they have numerous "Brick and Mortar Stores" or physical retail stores where you can purchase merchandise from their show "Brickle and Morty".

Q. Explain the pun in the following joke: "Why did the chicken cross the Möbius strip? To get to the other siiiiide."
A. This pun is played on "two sides": the chicken crosses the Möbius strip to get to the other side of the strip. A Möbius Strip has only one side.

Q. Explain the pun in the following joke: "How many hipsters does it take to change a lightbulb? Two: one to Instagram how cool it is at that moment, and one to change it."
A. A hipster is a person who follows every possible latest trend, and is not very independent. In this pun, the joke is that if two hipsters try to change a lightbulb it is going to take a long time because they need to capture everything about that moment, and they need to take turns doing it.

Q. Explain the pun in the following joke: I really want the new Jay-Z Album but I don't have a "Green Light" to buy it
A. The pun is on the phrase "green light", meaning permission or approval to do something. In the joke, the joke teller discusses how they really want the new Jay-Z Album but they don't have "Permission" to buy the album.

Q. Explain the pun in the following joke: "When is a door not a door? When it is ajar."
A. A "jar" is a container, in this case for liquid, such as milk. If a door is ajar, it is open. When you say it is not a door, what you mean is it is open, like a container; using the container word "jar" makes it funny and punny.

Q. Explain the pun in the following joke: "What did the hurricane say to the coconut palm tree? Hold on to your nuts, this is no ordinary blow job."
A. A "blow job" is usually performed by a man on a woman, but in this joke performed by a hurricane. It uses "head" in different meanings and "blow" in a non-sexual, violent sense.

|The joke implies that the retail chain has a store named "Brick" and another named "Morty", which is a reference to the television shows "Rick and Morty" and "Brickleberry", two animated comedy shows that are inappropriate for children. Adult Swim is a late night programming block on cable television, generally intended for mature audiences; the name "Brick" is a reference to the aforementioned "Brickleberry", and "Morty" a reference to "Rick and Morty".

Q. Explain the pun in the following joke: "How many fitness coaches does it take to screw in a lightbulb? As many as you can stick around for."
A. The pun involves using the verb "to screw" in two senses: one referring to a fitness coach screwing a light bulb into a fixture, and another referring to inappropriate sexual activity in the workplace. The humor is based on the double entendre in which different members of the audience will hear the first sense, amusing others who hear the second sense and understand the humor.

Q. Explain the pun in the following joke: "How many marriage therapists does it take to change a light bulb? We don't know, most of them aren't light bulbs!"
A. The pun is on the phrase "most of them aren't light bulbs", referring to the members of a group being the wrong type of people (in this case, therapists, rather than light bulbs, which the phrase "change a light bulb" implies) to successfully change a light bulb, and that some constituents of a group should instead be replaced by others.

...Q. Explain the pun in the following joke: "Santa Claus' helpers are known as subordinate Clauses."
| The word 'subordinate' is defined as 'secondary or lower in rank, power or authority'. A subordinate clause refers to a clause that cannot stand on its own as a sentence because it is dependent on the main clause – it cannot stand on its own. 'Subordinate' clauses take on many different shapes, but they all have that in common – they all cannot stand on their own.
A subordinate clause is a clause that does not express a complete thought - it must be attached to a main clause to form a complete sentence.
A subordinate clause begins with a subordinating conjunction (e.g. after, because, as) or a relative pronoun (who, whose, which, that, where, etc.)
Q. Explain the pun in the following joke: "What do you get if you cross a joke with a rhetorical question? An utterly rhetorical joke."
A. The pun is on the word 'utterly', which literally means to end, finish, or eradicate any or all traces of something, and is now an intensifier.

|The pun is on the similarity of "subordinate clauses" and "subordinate Clauses" when the latter phrase has a capital C; a subordinate clause is a clause within a sentence which establishes the logical connection between the independent clause and the main point of the sentence. In this case, it establishes the connection between Santa Claus' helpers and Santa Claus.

Q. Explain the pun in the following joke: "Why does Nickelodeon refuse to air "A Song of Ice and Fire"? Because they think George R. R. Martin socializes with too many Ice and Fire fans."
A. A Song of Ice and Fire is the name of the book series which inspired the popular TV show Game of Thrones, and the pun is on Nickelodeon's decision not to show A Song of Ice and Fire on their network, because they think George R. R. Martin socializes with too many fans of it on social media.

Q. Explain the pun in the following joke: "What kind of books do the Borg like to write? Borg-Warner."
A. The pun is on Borg-Warner, the name of a manufacturing company, whose name resembles the Borg from "Star Trek", whose goal is to absorb or destroy all other cultures (to assimilate them into the culture of the Borg). Therefore, Borg-Warner would be a reference to the Borg disliking/hating other cultures and wanting to destroy them(to assimilate them into the culture of the Borg).

Q. Explain the pun in the following joke: "A vulture boards an airplane carrying two dead raccoons. The flight attendant says, 'I'm sorry, sir, only one carrion bag per passenger.'"
A. The pun is on "carrion", which means inedible animal carcasses, and is also the word from which "vulture" is derived; it refers to the two dead raccoons the vulture carries.

...Q. Explain the pun in the following joke: "Is your refrigerator running? Yes? Then you had better go catch it!"
A. |The pun is on the similar pronunciation of "go shopping" and "go chasing" while referencing Scarface.

Q. Explain the pun in the following joke: "What is the difference between a Folsom Prison concert and a youth soccer game? At a Folsom Prison concert, the inmates are all restrained in chairs with ball and chain on their legs."
A. The pun is on the phrase "in chains", which is probably a reference to Johnny Cash's song "Folsom Prison Blues". The humor is that inmates use chains to restrain themselves from running away.

Q. Explain the pun in the following joke: "When faced with an ethical dilemma, who did Kirk turn to? Spock! Of course for advice!"
A. The pun is on the phrase "to turn to":

Q. Explain the pun in the following joke: "Q: What did the two peanuts say after they got on the elevator? A: "This elevator tastes terrible!"
A. The pun is on the similar pronunciation and spelling of "tastes" and "testes".

Q. Explain the pun in the following joke: "Why couldn't the pirate find his treasure? Because he wasn't a chartered surveyor."
A. The pun is on the two meanings of "chartered surveyor":

Q. Explain the pun in the following joke: "What did Dolly Parton say when she saw the book "Erotic Stories for Pun Lovers"? "Just the titles makes me climax!"
A. The pun is on both meanings of "climax":

|A. The pun is on the phrase "catch cold", which is similar enough to "catch (the) fridge" that it confuses the listener for a moment while the rest of the joke is explained, but has a very different meaning.

It fails abysmally. In further completions, it tries out a few memorized real jokes as well as bizarre GPT-3-jokes, but likewise, the explanations make zero sense.

GPT-3 just doesn't understand puns, so it can't interpret them either, honestly or not.