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Would you please to explain the differences?
For example, this would be the exception to throw if the caller attempted to use some object before it had been properly initialized.
For example, this will be the exception to throw if the caller attempted to use some object before it had been properly initialized.
Would is conditional and will is not. In the usage listed in your example, I don't see any practical difference that a listener or reader might register. I think that the first sentence is more correct, because if indicates the condition under which that particular exception is to be thrown. If the word if were replaced with the word when, I would favor the second sentence. You will not be misunderstood or thought to be using English oddly with either sentence.
Would also has some common, colloquial uses that are not conditional in modern English (at least in the United States version of it), but in my experience these are generally verbal hedging. For example, I initially typed "I would say that the first sentence is more correct...", but that is confusing given this specific question and I can't think of a single grammar-based argument for why that's an acceptable construction.
The uses of will and would are distinguished succinctly in When should I use would / would have / will / will have?.
In the context of your example, would is used when you are describing a condition - something which would happen if something else happened first. Will is used when you are stating an intention or predicting the future - ie when the condition has already happened.
In your example there is a condition, so would is correct : "If the caller attempted to use some object, then ... would be the result."
However, I think there may be bigger problems with your sentence than the choice between would and will. The meaning of the sentence is far from clear. Perhaps the context would provide enough explanation. Otherwise, your concern about which word is correct is misplaced. Clear communication is much more important than using correct grammar.
In common practice, would and will are used interchangeably. English as a first language is not taught as thoroughly as when it is a second language. Considerable laxity is tolerated, especially in spoken English.
