I do not think of a rate of interest but of  many own rates of 
interests to use Keynes' term
Each is itself a function over time of expected price minus current 
price divided by current price
Standard inflation measures changes in goods prices
Inflation  is not an unambigous measure. There can also be various 
asset price inflation indexes. (Alchian and Kessel I believed 
discussed this years ago in a good but little known paper.)
It is a measure of prices of a set of assets compared to price of money.
If it changes  it means that own rates of interest on that group of 
assets  differ from money rates of interest.

David Colander