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module Helper where
import Control.Monad.State
import Text.Parsec hiding ( State )
data Error = SyntaxError ParseError | UndeclaredFunction String | DuplicateFunction String | InvalidIndex Int | FatalError String
instance Show Error where
show (SyntaxError err) = show err
show (UndeclaredFunction err) = "ERROR: undeclared function " <> show err
show (DuplicateFunction err) = "ERROR: duplicate function " <> show err
show (InvalidIndex err) = "ERROR: invalid index " <> show err
show (FatalError err) = show err
type Failable = Either Error
data Expression = Bruijn Int | Variable String | Abstraction Expression | Application Expression Expression
deriving (Ord, Eq)
data Instruction = Define String Expression | Evaluate Expression | Comment String | Load String | Test Expression Expression
deriving (Show)
instance Show Expression where
show (Bruijn x ) = show x
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]
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