The field rightWidth is similar, but corresponds to the right child subtree. There is a perfectly good monad built on this assumption: it's called the reader monad (see the exercise at the end of this tutorial). If you want to create a new monadic State, use the function state: Instead of extracting an action from State, which you can't do, and acting with it on some state, you call the function runState which does it for you: The Monad instance declaration for State looks something like this: Notice that State s is not a type but a type constructor: it needs one more type variable to become a type. That's it. This function will be much more simple than what we will need to print the tree in a top to bottom manner. But we don't have any state yet. The generic monad is defined in the Control.Monad.State.Lazy and, mush like our definition takes two arguments: one for state and one for the result. Getting the current state in the RState monad requires recursion: the current state comes from the future (the continuation), ... Cont (Tree r) a. ContT. Labeling the tree by using the State Monad With the help of the State Monad we get a very similar function: /// labels a tree by using the state monad /// (uses F#’s sugared syntax) Our continuation is supposed to be returning an Evaluator, not a pair (Double, SymTab). We make a DSL, taking advantage of the free monad structure to do all the plumbing. The continuation is a function that returns an evaluator. Still, hidden dependencies make composition fragile. That is, the root will be at the left and the leaf nodes will be on the right. Check this out: When you execute a lambda, you simply replace it with its body and replace the formal parameter with the actual argument. We can use do-notation and the standard monad functions with our DSL. Let us use our generic state monad to rewrite the tree labeling function from above. It's probably not a good first tutorial, but it contains things I'd wish I'd known immediately after reading my first tutorial. There are two ways of encoding a two-argument function and, in Haskell, they are equivalent. The compiler may help with flagging explicit mismatches, but it can't check the implicit ones. In OO programming, side effects are somewhat tamed with data hiding. Bind must therefore define a lambda of the signature s -> (b, s) and pass it to state. You call a function (procedure) whose effects can be: Some of the effects are visible in the signature of the function (types of input and output parameters), others are implicit. This traversal is depth first. (Some functors can be turned into monads themselves, but if that's the case, you don't need to create a free monad.) The standard monad libraries de ne a number of \bread and butter" monads, in-cluding the State, Reader, Writer, List and Maybe monads. Going back to our program, we'll try follow the same procedure we used to derive the Either monad. State monad is defined by a new type State, which is parameterized by two type variables. state monad in LINQ. Note that the actual type definition of the generic transformer is hidden from us, so we must use only the publicly exported functions: get, put and apply (in addition to the monadic functions we get for free.) • Usual approach: expand deﬁnitions of return and bind, perform equational reasoning. The fact that m must be a parameterised type, rather than just a type, is inferred from its use in the types for the two functions. Let us use our generic state monad to rewrite the tree labeling function from above. data Tree a = L a | Tree a :+: Tree a. Symbol table passing is what "actions" are supposed to do; evaluate should only construct the tracks for the symbol-table train. So to compute the positions we will use the following function: Now we combine these positions with the original strings into a single tree. The reader monad hides this process. • Why not exploit monadic structure during the proof? For instance, in C you use a combination of functions and side effects. let state, tree = monad 0: printTree tree: Console.WriteLine() Console.WriteLine("DONE") Console.ReadLine() |> ignore: 0 // return an integer exit code: This comment has been minimized. Ah right, the state monad is the triplet represented by S

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