I’m surprised to see an application of the Banach fixed-point theorem as an example of something that’s too implicit from the perspective of a computer scientist. After all, real quantities can only be represented in a computer as a sequence of approximations — and that’s exactly what the theorem provides.
I would have expected you to use, say, the Brouwer fixed-point theorem instead, because Brouwer fixed points can’t be computed to arbitrary precision in general.
This comment of mine is a bit cheeky, since there are plenty of theoretical computer scientists who think about characterising terms as fixed points, and logic programming is a whole discipline that is about characterising the problem rather than constructing a solution, but broadly speaking I think it is true among less theoretically-minded folks that “program” means “thing constructed step by step from atomic pieces”.
I’m surprised to see an application of the Banach fixed-point theorem as an example of something that’s too implicit from the perspective of a computer scientist. After all, real quantities can only be represented in a computer as a sequence of approximations — and that’s exactly what the theorem provides.
I would have expected you to use, say, the Brouwer fixed-point theorem instead, because Brouwer fixed points can’t be computed to arbitrary precision in general.
(I come from a mathematical background, fwiw.)
This comment of mine is a bit cheeky, since there are plenty of theoretical computer scientists who think about characterising terms as fixed points, and logic programming is a whole discipline that is about characterising the problem rather than constructing a solution, but broadly speaking I think it is true among less theoretically-minded folks that “program” means “thing constructed step by step from atomic pieces”.