This seems a topic that keeps showing up again and again. After every MF#K Meetup last Tuesday of every month we always go out for a couple of beers and speak heavily in favor of the language that we like the most. There are people who seem to need types to code, I will include myself in this group, while others seem to do fine with languages without types as for example Clojure, Erlang, Elixir, … My former workmate, Brandon Lucas, keeps trolling on how you can’t model a state-machine with types, and until I wrote this post, I would totally agree.
What you normally see in blog post when this topic is explained is something similar to this (I will draw some ASCII art to give a better understanding):
1 2 3 4 5 6 7 8 9 10 11 12 module WhatYouNormallySee = type State = On | Off // Bug due to lack of testing // Note: ALWAYS use FsCheck, F# implementation of Haskells QuickCheck let transition = function | On -> On | Off -> On let transitionFixed = function | On -> Off | Off -> On
What is represented here is a state machine for a light switch. The state is defined as a sum type (algebraic data type) of the two values it can be. But, then when you need to perform the state transition, you would see how people fallback to a function to handle this logic.
In my example, I have deliberately introduced a bug in the
transition function just to prove why this approach is problematic.
This is one of the misconceptions that you hear people talking about when they make the transition to functional programming languages. They think just because they have modeled the domain with a few sum and product types (algebraic data types) it’s all good and you can then claim absolute sentences like: “Make illegal states unrepresentable” and “Making Impossible States Impossible” and therefore you probably don’t need to test that part of the code, which is obviously a wrong misconception of what the authors tries to point out.
We need to be very thoughtful (and mostly careful) when we make those kind of statements, specially due to the audiences that might receive (conceive) these messages.
Use the type system instead of functions
So how can we move the logic from the function into the type domain by using the type system?
Well firstly we will need to introduce the following three simple concepts:
Phantom Types: Are parametrised types whose parameters do not all appear on the right-hand side of its definition. Example:
type 'a Foo = Bar.
Function Types: Define a function signature as a type. Example for the identity function:
type 'a Id = 'a -> 'a.
Not accessible Sum Type Case Constructors: By hiding the underlying case constructors for a given sum type, you can ensure that only specific parts of the code can instantiate your type. Example:
type FooBar = private | Foo of int | Bar of float
Lets see how I use them to re-model the light switch state machine:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 module Light = type 'a Switch = private | State and TurnedOn = On Switch and TurnedOff = Off Switch and On = On and Off = Off and TurnOn = TurnedOff -> TurnedOn and TurnOff = TurnedOn -> TurnedOff module Switch = let private initHelper = State let private turnHelper = fun _ -> State let initOn : TurnedOn = initHelper let initOff : TurnedOff = initHelper let turnOn : TurnOn = turnHelper let turnOff : TurnOff = turnHelper module Output = // Expensive call cos of .NET Type Reflection let state (x:'a Switch) = match typedefof<'a> with | t when t = typedefof<On> -> "on" | t when t = typedefof<Off> -> "off" | _________________________ -> "invalid type"
We combine the concepts 1. and 3. to define the State type, which we limit to only two states: TurnedOn and TurnedOff, which also requires to introduce two type terms: On and Off.
Finally, we just need to expand our domain with the transition types, which we can use concept 2. to create two transition states: TurnOn and TurnOff, which will subsequently require to have the opposite state as input parameter.
That’s it. Now our domain model contains all the logic while our functions just are pure interfaces with no logic whatsoever, see both helper functions, for the initXXX and turnXXX functions. The functions just return the internal State type, which gets tagged by the type definitions. Pretty nifty right?
And we can be sure that no invalid State is created because we ensured that it
can’t be instantiated from outside the module (and sub modules). So even though
type 'a Switch is a generic type, we have limited only to the two
states mentioned before.
The only minor issue is that type abbreviation (alias) in F# are erased at compile time and therefore not available at runtime, as Marcus Griep points out in the following tweet, therefore it’s a bit more difficult to output the currently state (see in next coding blocks how this can be overcome).
So lets see how its used:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 open Light let on = Switch.initOff |> Switch.turnOn let off = on |> Switch.turnOff let error = off // |> Switch.turnOff (* error FS0001: Type mismatch. Expecting a TurnedOff -> 'a but given a TurnOff The type 'Off' does not match the type 'On' *) // on = off (* error FS0001: Type mismatch. Expecting a TurnedOn but given a TurnedOff The type 'On' does not match the type 'Off' *) on |> Output.state off |> Output.state
Produces the following output:
A bit more complex example where we just want to automate the switch to turn
on/off a couple of times in a row. To be able to do this, we introduce the
Either sum type for better readability, but the built-in
Choice<'a,'b> F# type could be used as well. This construct will
also allow us to make a better output printer than the one that is based on
.NET Reflection as we have a guarantee of which types go in to the Left and
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 // You can disable this warning by using '--mlcompatibility' or '--nowarn:62' #nowarn "62" module Util = type ('a,'b) Either = Right of 'a | Left of 'b open Util open Light let blinking : (TurnedOn,TurnedOff) Either -> (TurnedOn,TurnedOff) Either = function | Right on -> on |> Switch.turnOff |> Left | Left off -> off |> Switch.turnOn |> Right // Or just "on" or "off" as we have the certainty of the types and it's a lot // cheaper than .NET Reflection let sprint : (TurnedOn,TurnedOff) Either -> string = function | Right s -> s |> Output.state // or just "on" | Left s -> s |> Output.state // or just "off" let foldHelper = function | [ ] -> fun _ -> [ ] | x::xs -> fun _ -> blinking x :: x :: xs ([ Left off ], [ 1 .. 15 ]) ||> List.fold foldHelper |> List.map sprint |> List.iter (printf "%s ")
I hope I can convince others that it is possible to model a state machine exclusively by using the type system, while keeping the logic out of the function layer. It uses a few type tricks that are present in F# but probably also in other ML alike languages.
Note: Don’t forget to ALWAYS use FsCheck, F# implementation of Haskells QuickCheck, even if you use this kind of approach. We are all human and therefore can fail. If you just remember this last part, You would make me a happy person.