Scala : sandbox: Scala : add 6-natural

2 files changed, 34 insertions, 0 deletions

diff --git a/Scala/sandbox/0-main.scala b/Scala/sandbox/0-main.scala
index 2092d9d..99ee4ba 100644
--- a/Scala/sandbox/0-main.scala
+++ b/Scala/sandbox/0-main.scala
@@ -8,5 +8,6 @@ object Main  extends App {
     Rationals.run
     IntSet.run
     IntList.run
+    Natural.run
 
 }
diff --git a/Scala/sandbox/6-natural.scala b/Scala/sandbox/6-natural.scala
new file mode 100644
index 0000000..01af1be
--- /dev/null
+++ b/Scala/sandbox/6-natural.scala
@@ -0,0 +1,33 @@
+// Peano numbers
+object Natural
+{
+  abstract class Nat
+  {
+    def isZero: Boolean
+    def predecessor: Nat
+    def successor = new Succ(this)
+    def + (that: Nat): Nat
+    def - (that: Nat): Nat
+  }
+
+
+  object Zero extends Nat
+  {
+    def isZero = true
+    def predecessor = throw new Error("0.predecessor")
+    def + (that: Nat) = that
+    def - (that: Nat) = if (that.isZero) this else throw new Error("negative number")
+  }
+
+  class Succ(n: Nat) extends Nat
+  {
+    def isZero = false
+    def predecessor = n
+    def + (that: Nat) = new Succ(n + that)
+    def - (that: Nat) = if (that.isZero) this else n - that.predecessor
+  }
+
+  def run = {
+    println("Natural")
+  }
+}