With the Reader monad, we also had some special-purpose operations, beyond its general monadic operations. These were `lookup` and `shift`. With the State monad, we'll also have some special-purpose operations. We'll consider two basic ones here. One will be to retrieve what is the current store. This is like the Reader monad's `lookup`, except in this simple implementation there's only a single location for a value to be looked up from. Here's how we'll do it:
- let get_state : store state =
+ let get_store : store state =
fun s -> (s, s);;
This passes through the current store unaltered, and also returns a copy of the store as its value. We can use this operation like this:
- some_existing_state_monad_box >>= fun _ -> get_state >>= (fun cur_store -> ...)
+ some_existing_state_monad_box >>= fun _ -> get_store >>= (fun cur_store -> ...)
The `fun _ ->` part here discards the value wrapped by `some_existing_state_monad_box`. We're only going to pass through, unaltered, whatever *store* is generated by that monadic box. We also wrap that store as *our own value*, which can be retrieved by further operations in the `... >>= ...` chain, such as `(fun cur_store -> ...)`.
The other operation for the State monad will be to update the existing store to a new one. This operation looks like this:
- let set_state (new_store : int) : dummy state =
+ let set_store (new_store : int) : dummy state =
fun s -> (dummy, new_store);;
If we want to stick this in a `... >>= ...` chain, we'll need to prefix it with `fun _ ->` too, like this:
- some_existing_state_monad_box >>= fun _ -> set_state 100 >>= ...
+ some_existing_state_monad_box >>= fun _ -> set_store 100 >>= ...
-In this usage, we don't care what value is wrapped by `some_existing_state_monad_box`. We don't even care what store it generates, since we're going to replace that store with our own new store. A more complex kind of `set_state` operation might insert not just some constant value as the new store, but rather the result of applying some function to the existing store. For example, we might want to increment the current store. Here's how we could do that:
+In this usage, we don't care what value is wrapped by `some_existing_state_monad_box`. We don't even care what store it generates, since we're going to replace that store with our own new store. A more complex kind of `set_store` operation might insert not just some constant value as the new store, but rather the result of applying some function to the existing store. For example, we might want to increment the current store. Here's how we could do that:
- some_existing_state_monad_box >>= fun _ -> get_state >>= (fun cur_store -> set_state (cur_store + 1) >>= ...
+ some_existing_state_monad_box >>= fun _ -> get_store >>= (fun cur_store -> set_store (cur_store + 1) >>= ...
-We can of course define more complex functions that perform the `get_state >>= (fun cur_store -> set_state (cur_store + 1)` as a single operation.
+We can of course define more complex functions that perform the `get_store >>= (fun cur_store -> set_store (cur_store + 1)` as a single operation.
In general, a State monadic **box** (type `'a state`, what appears at the start of a `... >>= ... >>= ...` chain) is an operation that accepts some starting store as input---where the store might be simple as it is here, or much more complex---and returns a value plus a possibly modified store. This can be thought of as a static encoding of some computation on a store, which encoding is used as a box wrapped around a value of type `'a`. (And also it's a burrito.)
We use the `None`/`Some factorial` option type here just as a way to ensure that the contents of `fact_cell` are of the same type both at the start and the end of the block.
+ If you've got a copy of *The Seasoned Schemer*, which we recommended for the seminar, see the discussion at pp. 118-125.
+
* Now would be a good time to go back and review some material from [[week1]], and seeing how much we've learned. There's discussion back then of declarative or functional languages versus languages using imperatival features, like mutation. Mutation is distinguished from shadowing. There's discussion of sequencing, and of what we mean by saying "order matters."
In point 7 of the Rosetta Stone discussion, the contrast between call-by-name and call-by-value evaluation order appears (though we don't yet call it that). We'll be discussing that more in coming weeks. In the [[damn]] example, continuations and other kinds of side-effects (namely, printing) make an appearance. These too will be center-stage in coming weeks.