started a subdir for the book

1 files changed, 50 insertions, 0 deletions

diff --git a/book/examples/chapter6/Bin.gf b/book/examples/chapter6/Bin.gf
new file mode 100644
index 000000000..c181656f8
--- /dev/null
+++ b/book/examples/chapter6/Bin.gf
@@ -0,0 +1,50 @@
+abstract Bin = {
+
+cat Nat ; Bin ; Pos ;
+
+data 
+  Zero : Nat ; 
+  Succ : Nat -> Nat ;
+
+  BZero : Bin ;         -- 0
+  BPos  : Pos -> Bin ;  -- p
+  BOne  : Pos ;         -- 1
+  AZero : Pos -> Pos ;  -- p0
+  AOne  : Pos -> Pos ;  -- p1
+
+fun
+  bin2nat : Bin -> Nat ;
+def
+  bin2nat BZero = Zero ;
+  bin2nat (BPos p) = pos2nat p ;
+fun 
+  pos2nat : Pos -> Nat ;
+def
+  pos2nat BOne = one ;
+  pos2nat (AZero p) = twice (pos2nat p) ;
+  pos2nat (AOne  p) = Succ (twice (pos2nat p)) ;
+fun one : Nat ;
+def one = Succ Zero ;
+fun twice : Nat -> Nat ;
+def 
+  twice Zero = Zero ;
+  twice (Succ n) = Succ (Succ (twice n)) ;
+
+fun
+  nat2bin : Nat -> Bin ;
+def
+  nat2bin Zero = BZero ;
+  nat2bin (Succ n) = bSucc (nat2bin n) ;
+fun
+  bSucc : Bin -> Bin ;
+def
+  bSucc BZero = BPos BOne ;
+  bSucc (BPos p) = BPos (pSucc p) ;
+fun
+  pSucc : Pos -> Pos ;
+def
+  pSucc BOne = AZero BOne ;
+  pSucc (AZero p) = AOne p ;
+  pSucc (AOne p) = AZero (pSucc p) ;
+
+}
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