Balanced ternary something

I don't even know anymore. What's happening? Quite confusing.

1 files changed, 27 insertions, 1 deletions

diff --git a/src/Helper.hs b/src/Helper.hs
index a8e393e..5e02a94 100644
--- a/src/Helper.hs
+++ b/src/Helper.hs
@@ -18,9 +18,35 @@ data Instruction = Define String Expression | Evaluate Expression | Comment Stri
   deriving (Show)
 instance Show Expression where
   show (Bruijn      x        ) = show x
-  show (Variable    var      ) = show var
+  show (Variable    var      ) = var
   show (Abstraction exp      ) = "[" <> show exp <> "]"
   show (Application exp1 exp2) = "(" <> show exp1 <> " " <> show exp2 <> ")"
 
 type Environment = [(String, Expression)]
 type Program = State Environment
+
+-- Dec to Bal3 in Bruijn encoding: reversed application with 1=>0; 0=>1; T=>2; end=>3
+-- e.g. 0=0=[[[[3]]]]; 2=1T=[[[[2 (0 3)]]]] -5=T11=[[[[0 (0 (2 3))]]]]
+decimalToTernary :: Integer -> Expression
+decimalToTernary n =
+  Abstraction $ Abstraction $ Abstraction $ Abstraction $ gen n
+ where -- TODO: Consider switching 0 and 1 for better readability
+  fix 0 = 1
+  fix 1 = 0
+  fix 2 = 2
+  gen 0 = Bruijn 3
+  gen n = Application (Bruijn $ fix $ mod n 3) (gen $ div (n + 1) 3)
+
+ternaryToDecimal :: Expression -> Integer
+ternaryToDecimal exp = sum $ zipWith (*) (resolve exp) (iterate (* 3) 1)
+ where
+  multiplier (Bruijn 0) = 1
+  multiplier (Bruijn 1) = 0
+  multiplier (Bruijn 2) = (-1)
+  resolve' (Application x@(Bruijn _) (Bruijn 3)) = [multiplier x]
+  resolve' (Application fst@(Bruijn _) rst@(Application _ _)) =
+    (multiplier fst) : (resolve' rst)
+  resolve' _ = [0]
+  resolve (Abstraction (Abstraction (Abstraction (Abstraction n)))) =
+    resolve' n
+  resolve _ = [0]