Is it theoretically possible to do away with the usual forms of taxation? Continuing ... here is how the idea might work in practice.
It requires that all payment transactions go through computers. Basically, the currency that you hold in your account is being devalued because of extra currency being created centrally. Suppose you start with the currency - let's call it the dollar - at its end of year zero value of 1.0. By the end of year one it might be worth say 95% of its year zero value.
Your dollar total is constant (if you don't spend that is..). But when you make a payment of any sort the computerized system applies a scaling factor to compensate for dollar devaluation. So, if you start year one with a thousand dollars, you will still have a thousand dollars in your account, but as they are only worth 950 Year Zero dollars your account will read to you that you have just 950 dollars. Year Zero dollars are now worth 1000/950 = approx 1.05 now-dollars. If you buy something at the end of year one for the advertised price of 100 year zero dollars, the system will actually reduce your account by 105 dollars (and 26 cents :) )
In practice, the exchange rate would change a little bit each day, and not once at the end of the year. It would be a continuous thing. However, as all prices, wages etc are expressed in Year Zero prices there is continuity of price meaning. And given that the government is continually pumping in more currency, the amount in circulation rises and so people's bank account will tend to have more dollars in them as time marches on - though not necessarily more dollars at Year Zero prices of course.
Paper currency could still be viable, but with the proviso that the face value refers to that value of dollars at the time of printing only, and that you would have to ask your phone what that "100 dollar" note is worth in today's dollars.
I think I have invented the future!