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    <p>I have reduced your problem to traits, and I am starting to understand why you are getting into troubles with casts and abstract types. </p> <p>What you are actually missing is ad-hoc polymorphism, which you obtain through the following: - Writing a method with generic signature relying on an implicit of the same generic to delegate the work to - Making the implicit available only for specific value of that generic parameter, which will turn into a "implicit not found" compile time error when you try to do something illegal.</p> <p>Let's now look to the problem in order. The first is that the signature of your method is wrong for two reasons:</p> <ul> <li><p>When replacing a site you want to create a new monomer of the new generic type, much as you do when you add to a collection an object which is a superclass of the existing generic type: you get a new collection whose type parameter is the superclass. You should yield this new Monomer as a result.</p></li> <li><p>You are not sure that the operation will yield a result (in case you can't really replace a state). In such a case the right type it's Option[T]</p> <pre><code>def replaceSiteWithIntersection[A &gt;: StateSiteType &lt;: ReactantStateSite] (thisSite: A, monomer: ReactantMonomer): Option[MonomerClass[A]] </code></pre></li> </ul> <p>If we now look digger in the type errors, we can see that the real type error comes from this method:</p> <pre><code> thisSite.createIntersection </code></pre> <p>The reason is simple: it's signature is not coherent with the rest of your types, because it accepts a ReactantSite but you want to call it passing as parameter one of your stateSites (which is of type Seq[StateSiteType] ) but you have no guarantee that </p> <pre><code>StateSiteType&lt;:&lt;ReactantSite </code></pre> <p>Now let's see how evidences can help you:</p> <pre><code>trait Intersector[T] { def apply(observed: Seq[String]): T } trait StateSite { def name: String } trait ReactantStateSite extends StateSite { def observed: Seq[String] def createIntersection[A](otherSite: ReactantStateSite)(implicit intersector: Intersector[A]): A = { val newStates = observed.intersect(otherSite.observed) intersector(newStates) } } import Monomers._ trait MonomerClass[+StateSiteType &lt;: StateSite] { val stateSites: Seq[StateSiteType] def replaceSiteWithIntersection[A &gt;: StateSiteType &lt;: ReactantStateSite](thisSite: A, otherMonomer: ReactantMonomer)(implicit intersector:Intersector[A], ev: StateSiteType &lt;:&lt; ReactantStateSite): Option[MonomerClass[A]] = { def replaceOrKeep(condition: (StateSiteType) =&gt; Boolean)(f: (StateSiteType) =&gt; A)(implicit ev: StateSiteType&lt;:&lt;A): Seq[A] = { stateSites.map { site =&gt; if (condition(site)) f(site) else site } } val reactantSiteToIntersect:Option[ReactantStateSite] = otherMonomer.stateSites.find(_.name == thisSite.name) reactantSiteToIntersect.map { siteToReplace =&gt; val newSites = replaceOrKeep {_ == thisSite } { item =&gt; thisSite.createIntersection( ev(item) ) } MonomerClass(newSites) } } } object MonomerClass { def apply[A &lt;: StateSite](sites:Seq[A]):MonomerClass[A] = new MonomerClass[A] { val stateSites = sites } } object Monomers{ type Monomer = MonomerClass[StateSite] type ReactantMonomer = MonomerClass[ReactantStateSite] type ProductMonomer = MonomerClass[ProductStateSite] type ProducedMonomer = MonomerClass[ProducedStateSite] } </code></pre> <ol> <li><p>Please note that this pattern can be used with no special imports if you use in a clever way implicit resolving rules (for example you put your insector in the companion object of Intersector trait, so that it will be automatically resolved).</p></li> <li><p>While this pattern works perfectly, there is a limitation connected to the fact that your solution works only for a specific StateSiteType. Scala collections solve a similar problem adding another implicit, which is call CanBuildFrom. In our case we will call it CanReact</p></li> </ol> <p>You will have to make your MonomerClass invariant, which might be a problem though (why do you need covariance, however?)</p> <pre><code>trait CanReact[A, B] { implicit val intersector: Intersector[B] def react(a: A, b: B): B def reactFunction(b:B) : A=&gt;B = react(_:A,b) } object CanReact { implicit def CanReactWithReactantSite[A&lt;:ReactantStateSite](implicit inters: Intersector[A]): CanReact[ReactantStateSite,A] = { new CanReact[ReactantStateSite,A] { val intersector = inters def react(a: ReactantStateSite, b: A) = a.createIntersection(b) } } } trait MonomerClass[StateSiteType &lt;: StateSite] { val stateSites: Seq[StateSiteType] def replaceSiteWithIntersection[A &gt;: StateSiteType &lt;: ReactantStateSite](thisSite: A, otherMonomer: ReactantMonomer)(implicit canReact:CanReact[StateSiteType,A]): Option[MonomerClass[A]] = { def replaceOrKeep(condition: (StateSiteType) =&gt; Boolean)(f: (StateSiteType) =&gt; A)(implicit ev: StateSiteType&lt;:&lt;A): Seq[A] = { stateSites.map { site =&gt; if (condition(site)) f(site) else site } } val reactantSiteToIntersect:Option[ReactantStateSite] = otherMonomer.stateSites.find(_.name == thisSite.name) reactantSiteToIntersect.map { siteToReplace =&gt; val newSites = replaceOrKeep {_ == thisSite } { canReact.reactFunction(thisSite)} MonomerClass(newSites) } } } </code></pre> <p>With such an implementation, whenever you want to make the possibility to replace a site with another site of a different type, all you need is to make available new implicit instances of CanReact with different types. </p> <p>I will conclude with a (I hope) clear explanation of why you should not need covariance. </p> <p>Let's say you have a <code>Consumer[T]</code> and a <code>Producer[T]</code>. </p> <p>You need covariance when you want to provide to the <code>Consumer[T1]</code> a <code>Producer[T2]</code> where <code>T2&lt;:&lt;T1</code> . But if you need to use the value produced by T2 inside T1, you can </p> <pre><code>class ConsumerOfStuff[T &lt;: CanBeContained] { def doWith(stuff: Stuff[T]) = stuff.t.writeSomething } trait CanBeContained { def writeSomething: Unit } class A extends CanBeContained { def writeSomething = println("hello") } class B extends A { override def writeSomething = println("goodbye") } class Stuff[T &lt;: CanBeContained](val t: T) object VarianceTest { val stuff1 = new Stuff(new A) val stuff2 = new Stuff(new B) val consumerOfStuff = new ConsumerOfStuff[A] consumerOfStuff.doWith(stuff2) } </code></pre> <p>This stuff clearly not compiles:</p> <blockquote> <p>error: type mismatch; found : Stuff[B] required: Stuff[A] Note: B &lt;: A, but class Stuff is invariant in type T. You may wish to define T as +T instead. (SLS 4.5) consumerOfStuff.doWith(stuff2).</p> </blockquote> <p>But again, this come from a misinterpretation of usage of variance, as <a href="https://stackoverflow.com/questions/5277526/real-world-examples-of-co-and-contravariance-in-scala">How are co- and contra-variance used in designing business applications?</a> Kris Nuttycombe answer explain. If we refactor like the following</p> <pre><code>class ConsumerOfStuff[T &lt;: CanBeContained] { def doWith[A&lt;:T](stuff: Stuff[A]) = stuff.t.writeSomething } </code></pre> <p>You could see everything compiling fine.</p>
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    1. COA few comments before I try to work through your answer, after which I am sure I will have more comments. The name Graph is a bit of a misnomer; it is kind of like a graph, but the data structure is totally different--each "node" has "sites" with "states" and the edges go between the sites not the nodes. Yeah, I agree the signature on `replaceSiteWithIntersection` is completely wrong. The find and replace throws an exception in the real code if not found. I am eager to try this type-classes solution.
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    2. COIn case you have complex questions like this one I suggest you to always put a Bounty, extra points for answering. People will pay more attention
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    3. COI will certainly do that after the option becomes available later today.
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