Scala - Prefix Unary Operators

Question

I've recently given Scala a second chance, and started with the project I always implement (in functional or pseudo-functional languages): an automated reasoner for propositional logic (and later predicate logic).

Now, I've tried to get the notation of propositional logic in the language itself as pretty as possible, and I've gotten this far - with an implicit conversion (String -> Atom):

("A" and "B") implies "C"

The functions "and" and "implies" (and "or" and "equivalent") are simple methods that call the relevant case class constructor. However, when implementing "not", I get stuck with either of the two following notations:

("A" and "B").not
Not("A" and "B")

Is there a way to trick Scala into accepting the desired:

not("A" and "B")

Preferrably without renaming the class "Not" to "not", because I might like to call it "¬" or something else, in th future.

Answer 1

You can define not as a method on a singleton object, like this:

object Logic {
  def not(x:Expr) = Not(x)
}
import Logic._
not("A" and "B")

(Where Expr is supposed to be the common superclass of And, Or, Not and Atom)

Edit: Here's an example of how this could be used with only a single import:

object Logic {
  abstract class Expr {
    def and(e: Expr) = Conjunction(this, e)
    def or(e: Expr) = Disjunction(this, e)
    def implies(e: Expr) = Implication(this, e)
  }
  case class Conjunction(e1: Expr, e2: Expr) extends Expr
  case class Disjunction(e1: Expr, e2: Expr) extends Expr
  case class Implication(e1: Expr, e2: Expr) extends Expr
  case class Negation(e: Expr) extends Expr
  case class Atom(name: String) extends Expr

  def not(e: Expr) = Negation(e)
  implicit def string2atom(str: String) = Atom(str)
}

// use site
import Logic._
not("A" and "B") implies (not("A") or not("B"))

Answer 2

I noticed on this answer to another question that it appears that one can prefix the operator name with unary_ to achive what you are trying to do. (See unary_!.)

Edit: this article confirms the syntax.

Answer 3

Why Not instead of not? There's nothing to stop you from doing this:

object not {
  def apply(expr: T) = ...
}

And then use not("A" and "B").