How can I chain implicits in Scala?

Scala has a restriction on automatic conversions to add a method, which is that it won't apply more than one conversion in trying to find methods. For example:

class A(val n: Int)
class B(val m: Int, val n: Int)
class C(val m: Int, val n: Int, val o: Int) {
  def total = m + n + o
}

// This demonstrates implicit conversion chaining restrictions
object T1 { // to make it easy to test on REPL
  implicit def toA(n: Int): A = new A(n)
  implicit def aToB(a: A): B = new B(a.n, a.n)
  implicit def bToC(b: B): C = new C(b.m, b.n, b.m + b.n)

  // won't work
  println(5.total)
  println(new A(5).total)

  // works
  println(new B(5, 5).total)
  println(new C(5, 5, 10).total)
}

EDIT: View bounds ('<%') are deprecated since Scala 2.11 https://issues.scala-lang.org/browse/SI-7629 (You can use type classes instead)

However, if an implicit definition requires an implicit parameter itself(View bound), Scala will look for additional implicit values for as long as needed. Continue from the last example:

// def m[A <% B](m: A) is the same thing as
// def m[A](m: A)(implicit ev: A => B)

object T2 {
  implicit def toA(n: Int): A = new A(n)
  implicit def aToB[A1 <% A](a: A1): B = new B(a.n, a.n)
  implicit def bToC[B1 <% B](b: B1): C = new C(b.m, b.n, b.m + b.n)

  // works
  println(5.total)
  println(new A(5).total)
  println(new B(5, 5).total)
  println(new C(5, 5, 10).total)
}

"Magic!", you might say. Not so. Here is how the compiler would translate each one:

object T1Translated {
  implicit def toA(n: Int): A = new A(n)
  implicit def aToB(a: A): B = new B(a.n, a.n)
  implicit def bToC(b: B): C = new C(b.m, b.n, b.m + b.n)

  // Scala won't do this
  println(bToC(aToB(toA(5))).total)
  println(bToC(aToB(new A(5))).total)

  // Just this
  println(bToC(new B(5, 5)).total)

  // No implicits required
  println(new C(5, 5, 10).total)
}

object T2Translated {
  implicit def toA(n: Int): A = new A(n)
  implicit def aToB[A1 <% A](a: A1): B = new B(a.n, a.n)
  implicit def bToC[B1 <% B](b: B1): C = new C(b.m, b.n, b.m + b.n)

  // Scala does this
  println(bToC(5)(x => aToB(x)(y => toA(y))).total)
  println(bToC(new A(5))(x => aToB(x)(identity)).total)      
  println(bToC(new B(5, 5))(identity).total)

  // no implicits required
  println(new C(5, 5, 10).total)
}

So, while bToC is being used as an implicit conversion, aToB and toA are being passed as implicit parameters, instead of being chained as implicit conversions.

EDIT

Related question of interest:

A discussion on types, origin and precedence of implicits

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Note that you can build circles with implicit parameters, too. Those are, however, detected by the compiler, as exhibited by this:

class Wrap {
  class A(implicit b : B)
  class B(implicit c : C)
  class C(implicit a : A)

  implicit def c = new C
  implicit def b = new B
  implicit def a = new A
}

The error(s) given to the user are not as clear as they could be, though; it just complains could not find implicit value for parameter for all three construction site. That might obscure the underlying problem in less obvious cases.

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Here's a code that also accumulates the path.

import scala.language.implicitConversions

// Vertices
case class A(l: List[Char])
case class B(l: List[Char])
case class C(l: List[Char])
case class D(l: List[Char])
case class E(l: List[Char])

// Edges
implicit def ad[A1 <% A](x: A1) = D(x.l :+ 'A')
implicit def bc[B1 <% B](x: B1) = C(x.l :+ 'B')
implicit def ce[C1 <% C](x: C1) = E(x.l :+ 'C')
implicit def ea[E1 <% E](x: E1) = A(x.l :+ 'E')

def pathFrom(end:D) = end

pathFrom(B(Nil))   // res0: D = D(List(B, C, E, A))

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