Re:There's a mathematician in your compiler
by thaumasiotes on Tuesday March 31, 2020 @09:43AM
(#22737437)
>> my understanding is if you deduce something true from an assumption it means nothing.
> Your understanding is not complete.
> If you start from a set of assumptions and perform a series of logical deductions to reach a conclusion, you have proven that given the assumptions are true, the conclusion is true. You have a proof of correctness under the assumptions.
04091948 is completely correct here.
If you assume P and prove Q, then you've proven that P implies Q.
If you assume P and prove True, then you've proven that P implies True. This is the same thing as proving nothing, since everything implies True.
Re:There's a mathematician in your compiler
by QuesnayJr on Tuesday March 31, 2020 @09:48AM
(#22737472)
It's the article that has it backwards. You can deduce true from any premise. In terms of the Curry-Howard isomorphism, I can write a program from any input to the one-element type by throwing away the input and returning the one element.
I think the previous comment was alluding to "resolution", where you prove a statement true by assuming it is false, and then deriving a contradiction. That only works in classical logic, though.
Your understanding is not complete.
If you start from a set of assumptions and perform a series of logical deductions to reach a conclusion, you have proven that given the assumptions are true, the conclusion is true. You have a proof of correctness under the assumptions.
If you can go on to demonstrate your conclusion is false (say, with a single counterexample) then it will prove that at least one of your original assumptions is false. You now have some provably reliable knowledge .