Add sums, vectors and arithmetic encodings.

Also define pretty printing of terms.

1 files changed, 26 insertions, 0 deletions

diff --git a/src/Encoded/Bool.idr b/src/Encoded/Bool.idr
index d185856..11bb894 100644
--- a/src/Encoded/Bool.idr
+++ b/src/Encoded/Bool.idr
@@ -1,5 +1,6 @@
 module Encoded.Bool
 
+import Term.Semantics
 import Term.Syntax
 
 export
@@ -7,6 +8,15 @@ B : Ty
 B = N
 
 export
+Show (TypeOf B) where
+  show 0 = "true"
+  show (S k) = "false"
+
+export
+toBool : TypeOf B -> Bool
+toBool = (== 0)
+
+export
 True : Term B ctx
 True = Lit 0
   
@@ -20,3 +30,19 @@ if' = Abs' (\b =>
   Rec b
     (Abs $ Const $ Var Here)
     (Const $ Const $ Abs $ Var Here))
+
+export
+and : Term (B ~> B ~> B) ctx
+and = Abs' (\b => App if' [<b, Id, Const False])
+
+export
+or : Term (B ~> B ~> B) ctx
+or = Abs' (\b => App if' [<b, Const True, Id])
+
+export
+not : Term (B ~> B) ctx
+not = Abs' (\b => App if' [<b, False, True])
+
+export
+isZero : Term (N ~> B) ctx
+isZero = Id