Should, in form, is the past tense of shall;however, this does not imply that should cannot be used in present instances. To express an opinion at any instance of time, we use should.
1.He should leave now.
2. I think you should stay back to catch some sleep.
3. She should wait a bit this time.
From the above instances, should is clearly used in expressing one’s opinion. Interestingly,shall can also be used in this way; the only difference being that shall expresses a bit of compulsion/certainty when used as such. The above sentences can be:
1. He shall leave now. [ Leaving is in this case not an opinion, but a must]
2. I think you shall stay back to catch some sleep.[ This is also more of certainty than an opinion where you can decide to do otherwise]
3.She shall wait a bit this time.
Having proven that should can be used in present instances. Let’s us see where it fits perfectly as the past tense of shall. Consider the following sentences:
1. I shall have been done by 4pm.
2. I should have been done by 4pm.
The two sentences are in a future perfect tense– tense used for actions deem to be completed sometime in the future.
In sentence 1, the speaker hopes to finish a particular action by 4pm. This means the action is still ongoing; he is not yet through but hopes to finish at sometime to come. Shall is used here to express a present hope.
In the 2nd sentence, the expected time had past, but the action wasn’t completed- this is now a past hope.And should, not shall, must be used.
So at the point of planning, shall is used to express that present hope, but if the plan fails, it becomes a hope of the past and should is used.
To make things clearer,
shall = present hope ( to be soon actualized)
Should = past hope(failed to actualize)
And since shall expresses a present hope, and should a past hope, it is very logical that should is the past tense of shall.
1. a. I shall have been resting by then.[ I hope to be at rest by a time to come]
b. I should have been resting by now.[ The time has come, but my hope couldn’t actualize]
2. a. We shall have graduated from high school by next year. [ We hope to graduate from school by next year]
b. We should have graduated from school last year.[ The expected year has past, but we couldn’t graduate. So that first hope is now of the past.]