-- | Exercise 2 template.
-- Instructions. 
--      1. You are to write your solutions to the exercise in this file. You
--      may add extra functions in this file to implement your solution.
--
--      2. You are to comment your code indicating how you arrived at a
--      solution.
--
--      3. It is best to avoid Prelude and library functions not already
--      imported and develop your own code for your solutions.
--
--      4. Do NOT change the type or name of any of the template functions. 
--
--      5. Do NOT change the name of this file. 
--
--      6. Do NOT change the module name of this file.
--
--      7. To submit this to GradeScope, submit ONLY this file.
--
--      8. Have lots of fun :). Wahoo!!

module Ex2 where

-- This imports the required types and support functions for the questions.
import Ex2Types

import Prelude (Int, Float, Integer, Eq, Ord, Bool (..), Double, String, otherwise, Num, Integral, Fractional, abs, (+), (-), (^), subtract, (*), (/), signum, (==), (/=), (<), (<=), (>), (>=), compare, (||), (&&), not, rem, mod, div, quot, max, min, fromIntegral, toInteger, undefined, error, Show, show, Bounded, minBound, maxBound, seq)
import Debug.Trace

-- 1 
twoTautology :: ((Bool,Bool) -> Bool) -> Bool
-- Provide your answer below
twoTautology _ = undefined


twoEquiv :: ((Bool,Bool)->Bool)->((Bool,Bool)->Bool)->Bool
-- Provide your answer below
twoEquiv _ _ = undefined

--2
badFermat :: Integer
badFermat = undefined


-- 3 
collatzIndex ::  Int -> SF [Int]
-- Provide your answer below
collatzIndex _ = undefined


-- 4
bisection::(Double->Double)->(Double,Double)-> SF Double
-- Provide your answer below
bisection _ _ =  undefined

-- 5
bsort:: (Ord a) => [a] -> [a]
bsort _ = undefined        


qsort:: (Ord a) => [a] -> [a]
qsort _  = undefined

msort:: (Ord a) => [a] -> [a]
msort _  = undefined

-- 6
dimension::Matrix a -> (SF (Int,Int))
dimension _ = undefined

transpose:: Matrix a -> (SF (Matrix a))
transpose _ = undefined

addMat :: DoubleMatrix -> DoubleMatrix -> (SF DoubleMatrix)
addMat _ _  = undefined

multMat :: DoubleMatrix -> DoubleMatrix -> (SF DoubleMatrix)
multMat _ _ = undefined

-- 7
nreverse :: (Ord a) => [a] -> [a]
nreverse _ = undefined

freverse :: (Ord a) => [a] -> [a]
freverse _ = undefined


hreverse :: (Ord a) => [a] -> [a]
hreverse  _ =  undefined

-- 8

all_paths:: Expr f x -> [([f],x)]
all_paths _ = undefined

-- 9
fact :: Integer
fact  = undefined

-- 10
widthRose :: Integral a =>  Rose a -> Int
widthRose _ = undefined

-- 11
is_ordered:: (Ord a) => STree a -> Bool
is_ordered _ = undefined

is_balanced:: STree a -> Bool
is_balanced _ = undefined

strong_balance::  STree a -> STree a
strong_balance _ = undefined