# Partial Function composability in Haskell

Below is my solution for the CTFP chapter 4 challenges which essentially involves composing partial functions (that don't have defined outputs for all possible inputs i.e. returning a Maybe).

The challenge is to implement composition, identity(to satisfy category requirements) and try it out with 2 partial functions. As I'm relatively new to Haskell, I was hoping to get a general code review with suggestions on better idioms and testing I could follow. Link to Code

import Test.HUnit

module Main where

-- Given
safeRoot :: Double -> Maybe Double
safeRoot x
| x < 0     = Nothing
| otherwise = Just (sqrt x)

-- Q1: Identity and composition
partialFnId :: a -> Maybe a
partialFnId x = Just x

partialFnCompose :: (b -> Maybe c) -> (a -> Maybe b) -> (a -> Maybe c)
partialFnCompose g f = \x -> case (f x) of
Just value -> g value
Nothing -> Nothing

-- Testing Q1
testPartialFnMeetsCategoryRequirements1 = TestCase $assertEqual "Id should pass through inputs" (Just 3) (partialFnId 3) testPartialFnMeetsCategoryRequirements2 = TestCase$ assertEqual "Composition with identity is noop(1)" (Just 2.0) ((partialFnCompose partialFnId safeRoot) 4)
testPartialFnMeetsCategoryRequirements3 = TestCase $assertEqual "Composition with identity is noop(2)" (Just 2.0) ((partialFnCompose safeRoot partialFnId) 4) -- Q2: Implement safeReciprocal safeReciprocal :: Double -> Maybe Double safeReciprocal x | x == 0 = Nothing | otherwise = Just (1 / x) -- Q3: Implement safeRootReciprocal via composing the above 2. safeRootReciprocal :: Double -> Maybe Double safeRootReciprocal = partialFnCompose safeRoot safeReciprocal -- Testing Q3 testSafeRootReciprocal1 = TestCase$ assertEqual "Provides root of reciprocal for valid inputs" (Just 2.0) (safeRootReciprocal 0.25)
testSafeRootReciprocal2 = TestCase $assertEqual "Provides Nothing on invalid inputs(1)" Nothing (safeRootReciprocal 0.0) testSafeRootReciprocal3 = TestCase$ assertEqual "Provides Nothing on invalid inputs(2)" Nothing (safeRootReciprocal (-0.25))

main = do
runTestTT \$ TestList [testPartialFnMeetsCategoryRequirements1,
testPartialFnMeetsCategoryRequirements2,
testPartialFnMeetsCategoryRequirements3,
testSafeRootReciprocal1,
testSafeRootReciprocal2,
testSafeRootReciprocal3]