Should we tax clearly unhealthy foods , and subsidize clearly healthy ones?

In my opinion foods with large amounts of procced fructose, (sugars) alcohol and fried carbs are CLEARLY unhealthy. (Not that other unhealthy foods don't exist but I am talking about foods that are clearly and without controversy are unhealthy.) And high water content vegetable's (not including potato's and the like) and legumes (beans) are clearly healthy.

The cost to the economy of unhealthy foods (both thru healthcare costs and productivity losses) is greater then the all of the profits company's make on unhealthy foods.

Now some may argue that government interference with the free market is an attack on freedom. To this I say 1. that the in the preamble of the constitution It mentions the right to life BEFORE the right to liberty or the pursuit of happiness. 2 we already subsidize and tax lots of other stuff for less compelling reasons. 3. Companies can't sell their products without  public investment (roads bridges police etc.). Therefore it is only fair that company's payback the public the FULL economic cost of there products.