You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


by Heiko Seeberger

Inspired by a recent conversation with my former colleague Brendan McAdams and my current coworker Markus Hauck, I decided to put together a quick post about phantom types, a topic perfectly suited for demonstrating the power of the type system of Scala.

Phantom types are called this way, because they never get instantiated. Really? So what are they good for? Simply to encode type constraints, i.e. prevent some code from being compiled in certain situations.

Let’s look at an example: Software developers are known for their vast need of coffee. So let’s define the class Hacker that defines the two methods hackOn and drinkCoffee.

class Hacker { def hackOn : Hacker = { println ( "Hacking, hacking, hacking!" ) new Hacker } def drinkCoffee : Hacker = { println ( "Slurp ..." ) new Hacker } } class Hacker { def hackOn: Hacker = { println("Hacking, hacking, hacking!") new Hacker } def drinkCoffee: Hacker = { println("Slurp ...") new Hacker } }

In the spirit of functional programming and immutable objects, both methods return a new instance of Hacker.

Of course the current implementation doesn’t encode the following constraint which is imposed by the very nature of human beings in general and software developer in particular: After hacking a Hacker can’t continue doing so, but needs to drink some coffee. Put another way, we should not be able to call hackOn again on the Hacker returned by a previous call of hackOn:

scala > val hacker = new Hacker hacker : Hacker = Hacker @ 3fb4f649 scala > hacker. hackOn . hackOn // This should not compile, but it does! Hacking, hacking, hacking ! Hacking, hacking, hacking ! res0 : Hacker = Hacker @ 2ff5659e scala> val hacker = new Hacker hacker: Hacker = Hacker@3fb4f649 scala> hacker.hackOn.hackOn // This should not compile, but it does! Hacking, hacking, hacking! Hacking, hacking, hacking! res0: Hacker = Hacker@2ff5659e

We could solve this problem by introducing two subclasses of Hacker – e.g. ExhaustedHacker and CaffeinatedHacker – which only define the respective methods returning the other subclass. But sometimes this is not a viable option, e.g. if we need subclassing to implement some other concern. Just think of a class hierarchy of animals or such: In this case the former approach would lead to an explosion of classes.

Therefore let’s implement the two states a hacker can be in using type parameters. First we define the possible states in the companion object:

object Hacker { sealed trait State object State { sealed trait Caffeinated extends State sealed trait Decaffeinated extends State } } object Hacker { sealed trait State object State { sealed trait Caffeinated extends State sealed trait Decaffeinated extends State } }

Here we use sealed to prevent the possible states from being extended. Notice that we don’t define any concrete subclasses, hence nobody will ever be able to instantiate State, State.Caffeinated or State.Decaffeinated.

Next we add a type parameter to Hacker and constrain it to a subtype of Hacker.State using an upper bound:

class Hacker [ S <: Hacker. State ] { import Hacker. _ def hackOn : Hacker [ State. Decaffeinated ] = { println ( "Hacking, hacking, hacking!" ) new Hacker } def drinkCoffee : Hacker [ State. Caffeinated ] = { println ( "Slurp ..." ) new Hacker } } class Hacker[S <: Hacker.State] { import Hacker._ def hackOn: Hacker[State.Decaffeinated] = { println("Hacking, hacking, hacking!") new Hacker } def drinkCoffee: Hacker[State.Caffeinated] = { println("Slurp ...") new Hacker } }

Unfortunately we’re not yet there:

scala > val hacker = new Hacker [ Hacker. State . Caffeinated ] hacker : Hacker [ Hacker. State . Caffeinated ] = Hacker @ 33e5ccce scala > hacker. hackOn Hacking, hacking, hacking ! res0 : Hacker [ Hacker. State . Decaffeinated ] = Hacker @ 34340fab scala > hacker. hackOn . hackOn // This should not compile, but it still does! Hacking, hacking, hacking ! Hacking, hacking, hacking ! res1 : Hacker [ Hacker. State . Decaffeinated ] = Hacker @ 3b6eb2ec scala> val hacker = new Hacker[Hacker.State.Caffeinated] hacker: Hacker[Hacker.State.Caffeinated] = Hacker@33e5ccce scala> hacker.hackOn Hacking, hacking, hacking! res0: Hacker[Hacker.State.Decaffeinated] = Hacker@34340fab scala> hacker.hackOn.hackOn // This should not compile, but it still does! Hacking, hacking, hacking! Hacking, hacking, hacking! res1: Hacker[Hacker.State.Decaffeinated] = Hacker@3b6eb2ec

While calling hackOn returns a decaffeinated hacker, we’re still able to call hackOn a second time. This is not a surprise, because we haven’t constrained calling any of the two methods yet.

Type Bounds

Let’s fix that with a neat trick: In order to only allow calling hackOn on an instance of Hacker[State.Caffeinated], we have to make the compiler fail, if the Hacker is parameterized with any other State. Therefore we parameterize hackOn and constrain the parameter with an upper and a lower bound:

def hackOn [ T >: S <: State. Caffeinated ] : Hacker [ State. Decaffeinated ] def hackOn[T >: S <: State.Caffeinated]: Hacker[State.Decaffeinated]

When the compiler tries to infer a type for T, it has to find one that is a supertype of S which represents the hacker’s state and at the same time a subtype of State.Caffeinated. Obviously this cannot work if S is State.Decaffeinated, because neither State.Decaffeinated nor any of its supertypes is a subtype of State.Caffeinated.

So essentially by sandwiching the type parameter T of the method in between the parameter S of the class and the desired state we constrain calling the method to such instances which are parameterized with the desired state. Let’s complete the code for Hacker, thereby making the constructor private and providing factory methods for Hackers in each of the two states:

object Hacker { sealed trait State object State { sealed trait Caffeinated extends State sealed trait Decaffeinated extends State } def caffeinated : Hacker [ State. Caffeinated ] = new Hacker def decaffeinated : Hacker [ State. Decaffeinated ] = new Hacker } class Hacker [ S <: Hacker. State ] private { import Hacker. _ def hackOn [ T >: S <: State. Caffeinated ] : Hacker [ State. Decaffeinated ] = { println ( "Hacking, hacking, hacking!" ) new Hacker } def drinkCoffee [ T >: S <: State. Decaffeinated ] : Hacker [ State. Caffeinated ] = { println ( "Slurp ..." ) new Hacker } } object Hacker { sealed trait State object State { sealed trait Caffeinated extends State sealed trait Decaffeinated extends State } def caffeinated: Hacker[State.Caffeinated] = new Hacker def decaffeinated: Hacker[State.Decaffeinated] = new Hacker } class Hacker[S <: Hacker.State] private { import Hacker._ def hackOn[T >: S <: State.Caffeinated]: Hacker[State.Decaffeinated] = { println("Hacking, hacking, hacking!") new Hacker } def drinkCoffee[T >: S <: State.Decaffeinated]: Hacker[State.Caffeinated] = { println("Slurp ...") new Hacker } }

Now we can only call hackOn on a Hacker[State.Caffeinated], i.e. after calling drinkCoffee and vice versa:

scala > Hacker. caffeinated . hackOn . drinkCoffee . hackOn . drinkCoffee Hacking, hacking, hacking ! Slurp ... Hacking , hacking, hacking ! Slurp ... res0 : Hacker [ Hacker. State . Caffeinated ] = Hacker @ 6b3b6b21 scala > Hacker. caffeinated . hackOn . hackOn < console >: 14 : error : type arguments [ Hacker. State . Decaffeinated ] do not conform to method hackOn 's type parameter bounds [ T >: Hacker. State . Decaffeinated <: Hacker. State . Caffeinated ] scala> Hacker.caffeinated.hackOn.drinkCoffee.hackOn.drinkCoffee Hacking, hacking, hacking! Slurp ... Hacking, hacking, hacking! Slurp ... res0: Hacker[Hacker.State.Caffeinated] = Hacker@6b3b6b21 scala> Hacker.caffeinated.hackOn.hackOn <console>:14: error: type arguments [Hacker.State.Decaffeinated] do not conform to method hackOn's type parameter bounds [T >: Hacker.State.Decaffeinated <: Hacker.State.Caffeinated]

Unfortunately the error messages we get from this sandwiching trick are not immensely helpful: type arguments [Hacker.State.Decaffeinated] do not conform to method hackOn’s type parameter bounds [T >: Hacker.State.Decaffeinated

Implicit Evidence

Therefore we can use another approach: We replace the respective type bounds with an implicit parameter of type S =:= State.Caffeinated or S =:= State.Decaffeinated:

def hackOn ( implicit ev : S =:= State. Caffeinated ) : Hacker [ State. Decaffeinated ] = { println ( "Hacking, hacking, hacking!" ) new Hacker } def drinkCoffee ( implicit ev : S =:= State. Decaffeinated ) : Hacker [ State. Caffeinated ] = { println ( "Slurp ..." ) new Hacker } def hackOn(implicit ev: S =:= State.Caffeinated): Hacker[State.Decaffeinated] = { println("Hacking, hacking, hacking!") new Hacker } def drinkCoffee(implicit ev: S =:= State.Decaffeinated): Hacker[State.Caffeinated] = { println("Slurp ...") new Hacker }

This makes the compiler look for an implicit value of type =:= parameterized with the proper types. Predef defines an implicit method which provides such instances if the left and right hand sides are of the exact same type:

object =:= { implicit def tpEquals [ A ] : A =:= A = singleton _=:= . asInstanceOf [ A =:= A ] } object =:= { implicit def tpEquals[A]: A =:= A = singleton_=:=.asInstanceOf[A =:= A] }

Therefore we get the same effect like before, i.e. we can only call hackOn if Hacker is parameterized with State.Caffeinated and drinkCoffee if Hacker is parameterized with State.Decaffeinated:

scala > Hacker. caffeinated . hackOn . drinkCoffee . hackOn . drinkCoffee Hacking, hacking, hacking ! Slurp ... Hacking , hacking, hacking ! Slurp ... res0 : Hacker [ Hacker. State . Caffeinated ] = Hacker @ 3461511d scala > Hacker. caffeinated . hackOn . hackOn < console >: 14 : error : Cannot prove that Hacker. State . Decaffeinated =:= Hacker. State . Caffeinated . scala> Hacker.caffeinated.hackOn.drinkCoffee.hackOn.drinkCoffee Hacking, hacking, hacking! Slurp ... Hacking, hacking, hacking! Slurp ... res0: Hacker[Hacker.State.Caffeinated] = Hacker@3461511d scala> Hacker.caffeinated.hackOn.hackOn <console>:14: error: Cannot prove that Hacker.State.Decaffeinated =:= Hacker.State.Caffeinated.

As you can see, we get a much better error message than before: Cannot prove that Hacker.State.Decaffeinated =:= Hacker.State.Caffeinated

Conclusion

We have shown that phantom types can be used to encode type constraints. Sometimes these can be implemented in a different way, e.g. via subclassing, but when that’s not possible, they are a powerful tool. Some examples for real world use cases – not saying that the affinity of software developers for coffee isn’t real – are state machines and builders.

If you’re interested in the full source code, check out the project on GitHub. Any questions or feedback are highly appreciated.