started a subdir for the book

book/examples/chapter6/Nat.gf

@@ -0,0 +1,22 @@
+abstract Nat = {
+  cat
+    Prop ;                        -- proposition
+    Nat ;                         -- natural number
+  data
+    Zero : Nat ;                  -- 0
+    Succ : Nat -> Nat ;           -- the successor of x
+  fun
+    Even : Nat -> Prop ;          -- x is even
+    And  : Prop -> Prop -> Prop ; -- A and B
+
+  fun one : Nat ;
+  def one = Succ Zero ;
+
+  fun twice : Nat -> Nat ;
+  def twice x = plus x x ;
+
+  fun plus : Nat -> Nat -> Nat ;
+  def 
+    plus x Zero = x ;
+    plus x (Succ y) = Succ (plus x y) ;
+}