Yoong Liat wrote:May I come in?" (may is present tense)
He asked if he might come in. (might is past tense, so is asked)
In reported speech, the present tense (may) is changed to the past tense (might)
IMO, the above sentence is an example of the uage of 'might' as past tense.
I don't know how many times I've explained it, YL. The backshifting that occurs for Reported Speech is not an actual shift in tense.
The past tense FORM only, not its meaning as a past tense verb, is used to mark the speech as reported; this is done so the listener knows that it's not a direct quote.
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Scenario 1:
Barb: [it's 1PM now] I'm going to go to the movies tonight.
Alice: John, what did Barb say?
John: She said that she was going to go to the movies tonight.
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Scenario 2:
Barb: [it's 1PM now] I'm going to go to the movies tonight. Oh geeze, I just remembered, I can't, I have to babysit.
Alice: John, what did Barb say?
John: She said that she WAS going to go to the movies tonight but that she can't/couldn't. She has to babysit.
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Has Barb gone to the movies? No, she hasn't.
In scenario 1, the speaker backshifts, ie. uses 'was' to mark this as reported speech.
Can 'was going to' describe an actual past tense/past time situation. No, it most definitely can not.
In its usual use, "was going to + verb" describes a situation where the speaker has changed their mind, changing a plan. In scenario 2, we have an example of 'was going to' in its normal use illustrating the speaker's change of plans.
In scenario 1, that same usual meaning is absent. Alice wouldn't think for a second that Barb had changed her mind because that usual meaning is simply not there, that meaning has been stripped and replaced as a marker of reported speech. Alice understands that the use of 'was going to' only marks the speech as reported.
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Contrex: I may try to think this through.
YL: What did Contrex say, JTT?
JTT: He said he may/might try to think this through but given the paucity from him so far, that probably won't happen.
[Contrex hears of this so he applies himself rigorously to this task, in order to prove JTT wrong and he actually gives it some thought. Later he describes his "past tense", finished efforts]
Contrex: I spent 20 minutes pondering this while I was in the shower. I might think this through*.