Step by Step solution about How to resolve the algorithm Balanced ternary step by step in the Haskell programming language

In Haskell programming language, the provided code focuses on the implementation of balanced ternary numbers, a particular type of numeric representation. Here's a detailed explanation:

1. Data Structure:

   • data BalancedTernary = Bt [Int]: This is the data type for balanced ternary numbers, which are represented as lists of integers ([Int]).

2. List Manipulation Functions:

   • zeroTrim: This function removes leading zeros from a list of integers. It takes a list as an argument and returns a trimmed list.
   • listBt: This function converts a list of integers to a balanced ternary number (Bt [Int]).

3. Normalization Function:

   • btNormalize: This function normalizes a balanced ternary number by carrying over digits that exceed the ternary base (3). It converts a list of integers to a normalized balanced ternary number.

4. Conversion Functions:

   • btList: This function extracts the list of integers from a balanced ternary number (Bt [Int]).
   • strBt: This function converts a string of ternary digits ('-' for -1, '0' for 0, and '+' for 1) to a balanced ternary number.
   • intBt: This function converts an integer to a balanced ternary number.
   • btInt: This function converts a balanced ternary number to an integer.

5. Arithmetic Operations:

   • Num instance: The code defines Num instance for balanced ternary numbers, providing implementations for arithmetic operations like addition ((+)), multiplication ((*)), and negation (negate).

6. Signum Function:

   • signum: This function returns the sign of a balanced ternary number. It returns 0 for Bt [0], Bt [1] for positive numbers, and Bt [-1] for negative numbers.

7. Absolute Value Function:

   • abs: This function returns the absolute value of a balanced ternary number. It returns the number itself if it's positive and the negation if it's negative.

8. Integer Conversion:

   • fromInteger: This function converts an integer to a balanced ternary number.

9. Main Function:

   • main: This function provides an example of using the defined functions. It creates three balanced ternary numbers (a, b, c), multiplies a by b - c (r), and prints the intermediate and final results.

data BalancedTernary = Bt [Int]

zeroTrim a = if null s then [0] else s where
	s = fst $ foldl f ([],[]) a
	f (x,y) 0 = (x, y++[0])
	f (x,y) z = (x++y++[z], [])

btList (Bt a) = a

instance Eq BalancedTernary where
	(==) a b = btList a == btList b

btNormalize = listBt . _carry 0 where
	_carry c [] = if c == 0 then [] else [c]
	_carry c (a:as) = r:_carry cc as where
		(cc, r) = f $ (a+c) `quotRem` 3 where
			f (x,  2) = (x + 1, -1)
			f (x, -2) = (x - 1,  1)
			f x = x

listBt = Bt . zeroTrim

instance Show BalancedTernary where
	show = reverse . map (\d->case d of -1->'-'; 0->'0'; 1->'+') . btList

strBt = Bt . zeroTrim.reverse.map (\c -> case c of '-' -> -1; '0' -> 0; '+' -> 1)

intBt :: Integral a => a -> BalancedTernary
intBt = fromIntegral . toInteger

btInt = foldr (\a z -> a + 3 * z) 0 . btList

listAdd a b = take (max (length a) (length b)) $ zipWith (+) (a++[0,0..]) (b++[0,0..])

-- mostly for operators, also small stuff to make GHC happy
instance Num BalancedTernary where
	negate = Bt . map negate . btList
	(+) x y = btNormalize $ listAdd (btList x) (btList y)
	(*) x y = btNormalize $ mul_ (btList x) (btList y) where
		mul_ _ [] = []
                mul_ as b = foldr (\a z -> listAdd (map (a*) b) (0:z)) [] as

	-- we don't need to define binary "-" by hand

	signum (Bt a) = if a == [0] then 0 else Bt [last a]
	abs x = if signum x == Bt [-1] then negate x else x

	fromInteger = btNormalize . f where
		f 0 = []
		f x = fromInteger (rem x 3) : f (quot x 3)


main = let	(a,b,c) = (strBt "+-0++0+", intBt (-436), strBt "+-++-")
		r = a * (b - c)
	in do
		print $ map btInt [a,b,c]
		print $ r
		print $ btInt r