## state monad tree

It's time for some deeper insights. We once again consider a data type for trees with values only in leaf positions. • Why not exploit monadic structure during the proof? Construct a state monad computation from a function. The State type. In Haskell, all state information usually must be passed to functions explicitly as arguments. State represents the nodes in the next level of the tree. It assumes that -- it has access to the current counter value implicitly. Here is a picture of this tree. The return function leaves the state unchanged, while >>= uses the final state of the first computation as the initial state of the second. Tree numbering is used as an example of using the State Monad in the Hackage page for Control.Monad.State.Lazy. We managed to manipulate state -- the symbol table -- in a purely functional way. This just gets the ball -- rolling, with `0` as the initial counter value. The great thing about it is that now all this additional information is visible to the compiler and the type checker. Copy link Quote reply halfAbee commented Apr 16, 2015. Here's a type that contains nothing but a function: And here are our return and bind functions in their cleaned up form: Now that the paperwork is done, we can start using the do notation. -- Accumulator function for folding over each level. The field leftWidth records the width of the array of String necessary to print the left child subtree. State is defined as a function that takes in some state value, and returns the next state, along with another value. Check this out: When you execute a lambda, you simply replace it with its body and replace the formal parameter with the actual argument. That's all taken care of now. We called the new evaluate only to immediately execute the resulting action? In OO programming, side effects are somewhat tamed with data hiding. I also showed you how to deal with mutable state by passing it as an additional parameter into and out of a function. If the algorithm is pure, then an idiomatic F# equivalent would be a function. Monad instances. Values in the State monad are represented as transition functions from an initial state to a (value,newState) pair and a new type definition is provided to describe this construct: State s a is the type of a value of type a inside the State monad with state of type s. The type constructor State s is an instance of the Monad class. Recall the action that returns the next fresh integer. For this, we will traverse the tree in a depth first traversal and calculate the positions starting from the root, going downward to the leaves. Let me call this function act for action. How can we turn this value into an evaluator? 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.) > import Control.Monad.State Let's define a simple tree type: > data Tree a = Leaf a | Tree [Tree a] deriving (Eq,Show) Sometimes we want to apply a function to every element of the tree. Now we can test our implementation of the glue code in one place, or still better, use the library code. And it does it without any need for synchronization (other than reference counting inside shared pointers). I was wondering if there was something that could be done with a state monad that would let me push my hash set state through the tree as I am traversing the tree. Let us make a remark about the method we will use in this post. Bartosz Milewski This just gets the ball -- rolling, with `0` as the initial counter value. from leaves to root). After we have reformatted our tree into lists of levels of type [[(String, Position)]], we need to convert each level into a string. 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.) Also note that since we have converted empty nodes of type Tree a to non-empty nodes, we have for empty nodes that WidthInfo {nodeWidth = 0, leftWidth = 0, rightWidth = 0}, however we will simply convert empty nodes to empty nodes. By calling state with a function. Ah right, the state monad is the triplet represented by S

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