This document contains Haskell code implementing various functions using fold techniques, including summing a list, digit extraction, and performing big integer arithmetic. Each function has associated examples and placeholders for implementation that need to be filled in. The focus is on utilizing higher-order functions to achieve the desired operations.

1. {-
Do not change the skeleton code! The point of this
assignment is to figure out how the functions can
be written this way (using fold). You may only
replace the `error "TBD:..."` parts.
For this assignment, you may use the following library functions:
map
foldl'
foldr
length
append (or ++)
zip
-}
module Warmup where
import Prelude hiding (replicate, sum, reverse)
import Data.List (foldl')
foldLeft :: (a -> b -> a) -> a -> [b] -> a
foldLeft = foldl'
foldRight :: (b -> a -> a) -> a -> [b] -> a
foldRight = foldr
-- | Sum the elements of a list
--

2. -- >>> sumList [1, 2, 3, 4]
-- 10
--
-- >>> sumList [1, -2, 3, 5]
-- 7
--
-- >>> sumList [1, 3, 5, 7, 9, 11]
-- 36
sumList :: [Int] -> Int
sumList xs = error "TBD:sumList"
-- | `digitsOfInt n` should return `[]` if `n` is not positive,
-- and otherwise returns the list of digits of `n` in the
-- order in which they appear in `n`.
--
-- >>> digitsOfInt 3124
-- [3, 1, 2, 4]
--
-- >>> digitsOfInt 352663
-- [3, 5, 2, 6, 6, 3]
digitsOfInt :: Int -> [Int]
digitsOfInt 0 = []
digitsOfInt n = error "TBD:digitsOfInt"

3. -- | `digits n` retruns the list of digits of `n`
--
-- >>> digits 31243
-- [3,1,2,4,3]
--
-- digits (-23422)
-- [2, 3, 4, 2, 2]
digits :: Int -> [Int]
digits n = digitsOfInt (abs n)
-- | From http://mathworld.wolfram.com/AdditivePersistence.html
-- Consider the process of taking a number, adding its digits,
-- then adding the digits of the number derived from it, etc.,
-- until the remaining number has only one digit.
-- The number of additions required to obtain a single digit
-- from a number n is called the additive persistence of n,
-- and the digit obtained is called the digital root of n.
-- For example, the sequence obtained from the starting number
-- 9876 is (9876, 30, 3), so 9876 has
-- an additive persistence of 2 and
-- a digital root of 3.
--

4. -- NOTE: assume additivePersistence & digitalRoot are only called with positive numbers
-- >>> additivePersistence 9876
-- 2
additivePersistence :: Int -> Int
additivePersistence n = error "TBD"
-- | digitalRoot n is the digit obtained at the end of the sequence
-- computing the additivePersistence
--
-- >>> digitalRoot 9876
-- 3
digitalRoot :: Int -> Int
digitalRoot n = error "TBD"
-- | listReverse [x1,x2,...,xn] returns [xn,...,x2,x1]
--
-- >>> listReverse []
-- []
--
-- >>> listReverse [1,2,3,4]
-- [4,3,2,1]
--
-- >>> listReverse ["i", "want", "to", "ride", "my", "bicycle"]
-- ["bicycle", "my", "ride", "to", "want", "i"]

5. listReverse :: [a] -> [a]
listReverse xs = error "TBD"
-- | In Haskell, a `String` is a simply a list of `Char`, that is:
--
-- >>> ['h', 'a', 's', 'k', 'e', 'l', 'l']
-- "haskell"
--
-- >>> palindrome "malayalam"
-- True
--
-- >>> palindrome "myxomatosis"
-- False
palindrome :: String -> Bool
palindrome w = error "TBD"
-- | sqSum [x1, ... , xn] should return (x1^2 + ... + xn^2)
--
-- >>> sqSum []
-- 0
--
-- >>> sqSum [1,2,3,4]
-- 30
--

6. -- >>> sqSum [(-1), (-2), (-3), (-4)]
-- 30
sqSum :: [Int] -> Int
sqSum xs = foldLeft f base xs
where
f a x = error "TBD: sqSum f"
base = error "TBD: sqSum base"
-- | `pipe [f1,...,fn] x` should return `f1(f2(...(fn x)))`
--
-- >>> pipe [] 3
-- 3
--
-- >>> pipe [(x -> x+x), (x -> x + 3)] 3
-- 12
--
-- >>> pipe [(x -> x * 4), (x -> x + x)] 3
-- 24
pipe :: [(a -> a)] -> (a -> a)
pipe fs = foldLeft f base fs
where
f a x = error "TBD"
base = error "TBD"

7. -- | `sepConcat sep [s1,...,sn]` returns `s1 ++ sep ++ s2 ++ ... ++ sep ++ sn`
--
-- >>> sepConcat "---" []
-- ""
--
-- >>> sepConcat ", " ["foo", "bar", "baz"]
-- "foo, bar, baz"
--
-- >>> sepConcat "#" ["a","b","c","d","e"]
-- "a#b#c#d#e"
sepConcat :: String -> [String] -> String
sepConcat sep [] = ""
sepConcat sep (h:t) = foldLeft f base l
where
f a x = error "TBD"
base = error "TBD"
l = error "TBD"
intString :: Int -> String
intString = show
-- | `stringOfList pp [x1,...,xn]` uses the element-wise printer `pp` to
-- convert the element-list into a string:
--

8. -- >>> stringOfList intString [1, 2, 3, 4, 5, 6]
-- "[1, 2, 3, 4, 5, 6]"
--
-- >>> stringOfList (x -> x) ["foo"]
-- "[foo]"
--
-- >>> stringOfList (stringOfList show) [[1, 2, 3], [4, 5], [6], []]
-- "[[1, 2, 3], [4, 5], [6], []]"
stringOfList :: (a -> String) -> [a] -> String
stringOfList f xs = error "TBD"
-- | `clone x n` returns a `[x,x,...,x]` containing `n` copies of `x`
--
-- >>> clone 3 5
-- [3,3,3,3,3]
--
-- >>> clone "foo" 2
-- ["foo", "foo"]
clone :: a -> Int -> [a]
clone x n = error "TBD"
type BigInt = [Int]
-- | `padZero l1 l2` returns a pair (l1', l2') which are just the input lists,
-- padded with extra `0` on the left such that the lengths of `l1'` and `l2'`
-- are equal.

9. --
-- >>> padZero [9,9] [1,0,0,2]
-- [0,0,9,9] [1,0,0,2]
--
-- >>> padZero [1,0,0,2] [9,9]
-- [1,0,0,2] [0,0,9,9]
padZero :: BigInt -> BigInt -> (BigInt, BigInt)
padZero l1 l2 = error "TBD"
-- | `removeZero ds` strips out all leading `0` from the left-side of `ds`.
--
-- >>> removeZero [0,0,0,1,0,0,2]
-- [1,0,0,2]
--
-- >>> removeZero [9,9]
-- [9,9]
--
-- >>> removeZero [0,0,0,0]
-- []
removeZero :: BigInt -> BigInt
removeZero ds = error "TBD"
-- | `bigAdd n1 n2` returns the `BigInt` representing the sum of `n1` and `n2`.
--

10. -- >>> bigAdd [9, 9] [1, 0, 0, 2]
-- [1, 1, 0, 1]
--
-- >>> bigAdd [9, 9, 9, 9] [9, 9, 9]
-- [1, 0, 9, 9, 8]
bigAdd :: BigInt -> BigInt -> BigInt
bigAdd l1 l2 = removeZero res
where
(l1', l2') = padZero l1 l2
(_ , res) = foldRight f base args
f (x1, x2) (carry, sum) = error "TBD"
base = error "TBD"
args = error "TBD"
-- | `mulByDigit i n` returns the result of multiplying
-- the digit `i` (between 0..9) with `BigInt` `n`.
--
-- >>> mulByDigit 9 [9,9,9,9]
-- [8,9,9,9,1]
mulByDigit :: Int -> BigInt -> BigInt
mulByDigit i l = error "TBD"
-- | `bigMul n1 n2` returns the `BigInt` representing the product of `n1` and `n2`.
--

11. -- >>> bigMul [9,9,9,9] [9,9,9,9]
-- [9,9,9,8,0,0,0,1]
--
-- >>> bigMul [9,9,9,9,9] [9,9,9,9,9]
-- [9,9,9,9,8,0,0,0,0,1]
bigMul :: BigInt -> BigInt -> BigInt
bigMul l1 l2 = res
where
(_, res) = foldRight f base args
f x (z, p) = error "TBD"
base = error "TBD"
args = error "TBD"