Inside the boxes, you might use a (State SymbolTable) monad to carry around the symbol table:

  type SymbolTable = Map String Symbol

Me and a codeveloper are working on a type system in Haskell, where our current code has iterative computation, until it reaches a fixpoint.

Here's the iterative code:

https://github.com/Peaker/lamdu/blob/master/Lamdu/Data/Expre...

If you need to internally carry state, you just use a State monad to thread around the state purely.