module Calculator.Prim.Function
    ( Function (..)
    , mkFunc
    , mkFuncEither
    , oneArg
    , partial
    , testFunc
    ) where

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-- | Represents a function, where rank == No. of arguments
data Function = Function {
      arity :: Int
    , apply :: [Double] -> Either [String] Double
    }

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-- | Make a @Function@ out of an arity and another function
mkFunc :: Int -> ([Double] -> Double) -> Function
mkFunc a f = mkFuncEither a (Right . f)

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-- | Make a @Function@ with an arity using an error giving function
mkFuncEither :: Int -> ([Double] -> Either [String] Double) -> Function
mkFuncEither a f = Function { arity = a , apply = g }
    where g xs = if length xs == a
                 then f xs
                 else Left [ "Invalid no. of arguments"
                           , "Required: " ++ show a
                           , "Provided: " ++ show (length xs)
                           ]

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-- | Make a @Function@ out of a single argument function
oneArg :: (Double -> Double) -> Function
oneArg f = mkFunc 1 (\ [x] -> f x)

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-- | Partially apply a function, thus creating a one-argument function.
-- To be used for parametrized functions, e.g getting g(x) = f(x,1,2)
-- this retains the free-variable 'x'
partial :: Function -> [Double] -> Double -> Maybe Double
partial f xs x = case apply f (x:xs) of
                   Left _  -> Nothing
                   Right v -> Just v

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-- | Test a @Function@ with some value t, useful for sanity checking
-- while adding a @Function@ to a @Bindings@
testFunc :: Function -> Double -> Maybe [String]
testFunc f t = case apply f (replicate (arity f) t) of
                 Left ms -> Just ms
                 Right _ -> Nothing

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