Combine Stateful Computations Using A State Monad

Instructor: [00:00] One of the most powerful features of state is the ability to combine stateful computations that depend on a fixed-type state. State is defined as a product type, with a fixed-type state S on the left and a variable-type resultant A on the right. While the type can vary for A, it is imperative that the state S never change its type and remain fixed.

[00:21] With these constraints in mind, let's dive into what combining stateful computations could possibly look like. We start by creating a function called compute. We'll define compute as a function that takes a number and returns a state number of number with number in the state and the resultant, which we'll abbreviate to just number.

[00:42] To implement, we'll take in a given number N as input, but we now need a way to get this number into a state. As we need to be able to use any stateful computation, it seems we'll need a way to somehow get N into our resultant.

[00:56] Turns out we're in luck. State provides a construction helper named of, which is defined as a function that takes any type A and provides a state S of A, putting our value in the resultant.

[01:08] We can now use of to return our required state by passing it N. Let's see what we've got so far by using this log function to peek in on what we get back when we call it with 10. We see our type ready to run with a state of 2, which will get us back a pair 10, 2.

[01:26] Looks like our resultant is populated with 10 as expected. Running with exitWith retrieves our state of 2, while aboutWith pulls our resultant right for modification.

[01:37] Modification, you say, how do we even? One way to modify the resultant is to use map to lift a given function over our resultant. We now need some function to lift and apply. I believe this curried add function will do just nicely, providing the result of two numbers under addition. Before we can lift it, we need it in scope.

[01:59] We can lean on some destructuring sugar here and pluck add off of our convenient helper's object, which we'll require in here at the top of our file. Now, we need to get our function to work on the resultant. By passing it to map after partially applying the number 2 and saving it, we see we get back our 12.

[02:18] What if we wanted to add a given state to the resultant? If we run with 5, we would get back 15 instead of this constant 12. With no access to the state, it looks like map is not going to cut the mustard.

[02:31] To consider both a state and a resultant, a state instance provides a means through a method called chain. When defined on a state S of A, it expects a function that will take an A and return a new state S of B, giving us back a state S of B. As it may not be clear how this could solve our problem, let's take it for a spin and see what's up.

[02:53] We just replace our call to map with a call to chain, passing it a function that will take the resultant X as input. We now need to return another state to match our expected signature. We'll reach for the get helper available on the state constructor.

[03:08] Get allows us to lift a function that will be applied to the current state and will deposit the result in the resultant. In our case, we just lift add with a partially applied X. Now, we get 15 in our resultant when evaluated with 5. As we vary the state, we see our resultant varies, as well.

[03:27] This function doesn't really tell the story and may make future us scratch our head a bit. Let's remedy that by creating a function called add state. Creating this separate function will allow us to give this discrete transaction a name. We'll define add state as a function that takes a given number and gives us back a state number of number, or just number.

[03:49] To implement, we'll take a given number N and return the result of calling get with N partially applied to add. We can replace this hot mess with an easier-to-read add state. Give it a save, and we still get 12.

[04:04] Just like before, our computations reflect changes in our state. While the resultant varies, our state remains the same for any other computations we might want to chain.

[04:15] Reading from state is only half of it. To take full advantage of state, we need to be able to modify the state portion, as well. To derive an inkling of how we would chain in something like this, let's create another function called ink state, which will increment the state by one.

[04:31] We'll define ink state as a function that goes from unit to our state number. To handle the increment, it just so happens we have this handy ink function we can use to do our dirty work for us. We just bring it into scope like we did with add. We can implement by first taking in nothing. Instead of using get, we'll reach for modify, lifting our ink function.

[04:55] Now, modify needs to be plucked off the constructor and brought into scope. We're pretty much done. We just chain it in to get our state incremented. When we give it a save, we see our state is now three, but I have some bad news.

[05:12] A quick peek on the resultant shows we've lost our calculation and now have a unit. That's because modify returns a state S of unit. Looks like we have a little something we need to address.

[05:24] First, we need the previous resultant. Let's allow a number N as input to our function. Now that we have our N, we need to get it into the resultant, but we can't just pass it into map, as map expects a function.

[05:37] There's a special combinator named constant that we can enlist. That will give us back a function that always returns a pointed value. We just pull it in from crocks, jump down to our mapping, passing in constant with our N partially applied. Give it a save and it looks like we're back in business.

[05:56] What about the state? A quick call to exitWith shows that we're still good there. With our state incremented, and our resultant populated as expected, we can just keep chaining to our hearts' desire, with the type talking care of all of our state management for us, no matter how complicated our computations become.