The programming language for HTML5 is Javascript. Web browsers can't interprete any other programming languages. When you want to create a HTML application in Scala, you will need a transcompiler which turns your Scala code into Javascript.
I found a project with that goal via Google, but I have no idea if it's usable yet: http://scalagwt.github.com/
By the way: I am currently developing a client/server application with the client in Javascript and the server in Java. There is surprisingly few duplicate code, as long as you follow a strict separation of concerns between client and server (the server does all the game logic, the clients job is taking user input and displaying the game state as told by the server).