Piping an interactive session to a file

Question

I have made a toy interactive console program that is basically an interpreter:

$ myprogram
> this is user input
this is program output

Answer 1

The simpler form could be

tee >(myprogram) | tee -a file.log

If you want to prevent input being shown again to the screen:

tee -a file.log | myprogram | tee -a file.log