Dependency injection, inject with parameters

You can either provide a delegate to manually instantiate your cache provider or directly provide an instance:

services.AddSingleton<ICacheProvider>(provider => new RedisCacheProvider("myPrettyLocalhost:6379"));

services.AddSingleton<ICacheProvider>(new RedisCacheProvider("myPrettyLocalhost:6379"));

Please note that the container will not explicitly dispose of manually instantiated types, even if they implement IDisposable. See the ASP.NET Core doc about Disposal of Services for more info.

If the constructur also has dependencies that should be resolved by DI you can use that:

public class RedisCacheProvider : ICacheProvider
{
    private readonly string _connectionString;
    private readonly IMyInterface _myImplementation;

    public RedisCacheProvider(string connectionString, IMyInterface myImplementation)
    {
        _connectionString = connectionString;
        _myImplementation = myImplementation;
    }
    //interface methods implementation...
}

Startup.cs:

services.AddSingleton<IMyInterface, MyInterface>();
services.AddSingleton<ICacheProvider>(provider => 
    RedisCacheProvider("myPrettyLocalhost:6379", provider.GetService<IMyInterface>()));

You can use :

 services.AddSingleton<ICacheProvider>(x =>
      ActivatorUtilities.CreateInstance<RedisCacheProvider>(x, "myPrettyLocalhost:6379"));

Dependency Injection : ActivatorUtilities will inject any dependencies to your class.

Here is the link to the MS docs: Microsoft.Extensions.DependencyInjection.ActivatorUtilities.CreateInstance

Also: See @poke's answer here for more information. Basically it pulls from the provided services and any other params you pass, like a composit constructor.