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POHow do I use a runtime factory object for a semiring implementation in Scala?
 

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  1. POHow do I use a runtime factory object for a semiring implementation in Scala?
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    <p>I am attempting to model algebraic semirings in Scala. I'm running into type conversion problems that make it appear that it is not possible to do what I want to do in Scala. I'm hoping someone can direct me to the aspect of Scala's typing system that I have misunderstood.</p> <p>(Please bear with the long setup for this question. I've pared it down as much as I can.)</p> <p>A semiring is a set of items over which is defined binary addition (+) and multiplication (*) operators and their identity elements, called zero and one, respectively. For example the Integer Semiring is defined over the integers where + and * are the standard operations from arithmetic and zero and one are the integers 0 and 1. A more exotic example is the Boolean Semiring, which is defined over the values True and False, where + is logical OR, * is logical AND, zero is False, and one is True.</p> <p>To model this I define a trait that specifies the appropriate binary operators.</p> <pre><code>trait SemiringElement { /** * The element type */ type E /** * The type returned by the the addition and multiplication operators */ type R &lt;: SemiringElement val value: E def +(that: R): R def *(that: R): R override def toString = value.toString } </code></pre> <p>Case classes instantiate elements of particular semirings. For example, the Boolean Semiring would look like this.</p> <pre><code>case class BooleanSemiringElement(init: Boolean) extends SemiringElement { type E = Boolean type R = BooleanSemiringElement val value = init def +(that: BooleanSemiringElement#R) = BooleanSemiringElement(value || that.value) def *(that: BooleanSemiringElement#R) = BooleanSemiringElement(value &amp;&amp; that.value) } </code></pre> <p>I additionally have a Semiring trait which specifies zero and one elements.</p> <pre><code>trait Semiring { type E &lt;: SemiringElement /** * The addition identity */ val zero: E /** * The multiplication identity */ val one: E } </code></pre> <p>Specific semiring objects return zero and one elements of the appropriate type.</p> <pre><code>object BooleanSemiring extends Semiring { type E = BooleanSemiringElement val zero = BooleanSemiringElement(false) val one = BooleanSemiringElement(true) } </code></pre> <p>The Semiring objects are essentially factory singletons that know how to return identity elements of the appropriate type.</p> <p>I want to be able to write algorithms that work with semiring elements in general. I use the Semiring factory objects in order to be able to specify a particular semiring at runtime rather than compile time. For example, say I have an object that maintains a map between strings and semiring elements.</p> <pre><code>class ElementMap(s: Semiring) { val m = mutable.Map[String, SemiringElement]() } </code></pre> <p>If I instantiate this with a call like so:</p> <pre><code>val x = new ElementMap(BooleanSemiring) </code></pre> <p>I would like x.m to be a String->BooleanSemiringElement map. The problem is what I have is actually a String->SemiringElement map.</p> <pre><code>scala&gt; val x = new ElementMap(BooleanSemiring) x: ElementMap = ElementMap@46cf97b scala&gt; x.m res2: scala.collection.mutable.Map[String,SemiringElement] = Map() scala&gt; x.m("one") = BooleanSemiring.one scala&gt; x.m("one") + BooleanSemiring.one &lt;console&gt;:12: error: type mismatch; found : BooleanSemiring.one.type (with underlying type BooleanSemiring.BooleanSemiringElement) required: _1.R where val _1: SemiringElement x.m("one") + BooleanSemiring.one ^ </code></pre> <p>If I was willing to specify the type at compile time rather than runtime I could make the element type a generic like so:</p> <pre><code>class ElementMap[BooleanSemiring]... </code></pre> <p>but then I'd need a factory method to create all the different kinds of ElementMap objects. Putting the factory smarts inside a Semiring trait makes more sense architecturally. What I want to be able to say is something like this:</p> <pre><code>class ElementMap(s: Semiring) { val m = mutable.Map[String, s.E]() } </code></pre> <p>that is: create a map from strings to the element type E returned by the Semiring object supplied to the constructor. I can't figure out how to do this. I've tried various syntactic tricks and implicit conversions to no avail.</p> <p>Is there a way write an ElementMap that is configured with a Semiring constructor parameter at runtime, or am I taking the wrong approach? I'm new to Scala and trying to do things in a Scala-esque manner. I feel like I've painted myself into a corner here, but I'm not sure exactly where the misstep lies.</p>
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