public interface ICache
    {
        T Get<T>(string key);
    }

    public interface IProcessor<T>
    {
        T ProcessInner();
    }

    public class ProcessorA : IProcessor<int>
    {
        public int ProcessInner(){...}
    }

    public class ProcessorA : IProcessor<string>
    {
        public string ProcessInner() {...}
    }

    public class Processor<T>
    {
        public Processor(ICache cache, IProcessor<T> innerProcessor) {...}
        public Process()
        {
            innerProcessor.ProcessInner(cache.GetFromCache<T>());
        }
    }