## Blog: Ramón Soto Mathiesen

### References:

• Technology at GDS’s Blog:

### References:

• David Raab’s blog:

### Background

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):

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.

Note: I’m not dishing neither “Yaron Minsky” nor “Richard Feldman” as I have a HUGE respect for both on their work on OCaml and Elm respectively.

### 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:

1. Phantom Types: Are parametrised types whose parameters do not all appear on the right-hand side of its definition. Example: type 'a Foo = Bar.

2. Function Types: Define a function signature as a type. Example for the identity function: type 'a Id = 'a -> 'a.

3. 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:

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).

### Demo:

So lets see how its used:

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 Right wrappers.

### Conclusion:

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.

• Wikipedia:

### Background

As I usually do every Sunday, I skim through Sergeys F# Weekly just to see if there are anything interesting happening in the F# Community.

This week I found Lucas Reis’ blog post really well written, educational and didactic, specially the visualization of final state machine representation.

What seem to tingle a bit my OCD was the implementation of the EventStore:

### Problem by introducing OO data structures into F# (or OCaml)

As Lucas mention, you can just declare a type with () and define it’s members, and then you have a new data structure in F#. As with Lucas EventStore, I will point out the main issue by taking this approach. If we look into MSDN, we can see that ResizeArray is just a type abbreviation for a generic .NET list:

So my example will also made by using the built-in ResizeArray data structure:

We can see that the final reduced sum is a non-deterministic as well as incorrect result:

So why is this happening? Well if you are used to work with the .NET platform, you might as well (if you actually read the documentation on MSDN) have seen the following text on the bottom of almost every Class definition, under the Thread Safety sections:

Public static (Shared in Visual Basic) members of this type are thread safe. Any instance members are not guaranteed to be thread safe.

The main point here is that .NET collections are not immutable and therefore don’t fit well with the functional paradigm that F# is mainly built-on, even though it has support for other paradigms as imperative and OO.

### Build your data structures the right way

Is there a way to solve this self inflicted problem? Yes, we can create constrained types in F#, see Scott Wlaschin Gist in the References below for more information, where you can avoid exposing types from a module. They are accessible from inside the module, but not from code importing the module.

With this in mind, I will create an immutable array like this:

where the 'a iarray is visible from outside, while the single-case union constructor T is marked as private | T of 'a array therefore it can only be accessed from inside the module (and sub modules).

As you can see in the sub (and sub sub) modules, I’m just extracting the standard (and mutable) array type from the single-case union constructor and then using the built-in functions to perform the desired logic.

If you look carefully, I’m never exposing the underlying and mutable array, therefore, as I don’t allow any external piece of code to instantiate my type iarray unless it’s by using the init function, I can therefore argue that my data structure is sound to be used as an immutable F# data structure as the native built-in would be used.

Snippets:

Output:

### Functor modules as in OCaml

In my current implementation of iarray my additions to the array are in linear time, as a new array +1 needs to be allocated on another spot in memory, while my indexed access still is in constant time. So in the case that I was using this data structure for a lot of reads but very few inserts, it would be ideal, but what about if I had a lot of inserts but very few reads? Or what if I had more or less fifty/fifty on reads and writes? Well, in the case that I had a lot of writes and few reads, I would have used a standard built in list as the underlying data structure due to constant addition and linear reads while in the case where I had fifty/fifty reads and writes I would probably go for a balanced tree, logarithmic reads and writes. In all these cases, I would actually have to create new and separated modules for each of the approaches I mention.

Therefore it would be really nice if F# could port the Functor modules from OCaml as it would allow us to change the underlying datastructures inside a module.

I’ve POC an approach where I used records as modules, as you can see in the References, but it’s very hackerish and doesn’t really gets the job done …

### Conclusion:

I think it’s a change of the mindset that you need to do when your are coding with functional programming languages that are multi-paradigm, as you will be able to do things the way you are used to do, in an OO way, but that might not always be the appropriate approach.

### References:

• Sergey Tihon’s Blog:
• Lucas Reis’ Blog:
• MSDN:
• Scott Wlaschin on GitHub Gist:
• Blog: Ramón Soto Mathiesen
• Part I - An introduction to OCaml:

### References:

• Verify F* Online (just copy/paste):