{- CSC324 Fall 2018 Lab 9 -}

module Lab9 where

-- |
-- = Task 1: Fitting some generic functions
-- For each of the functions below, give an implementation
-- of them so that they are *total* (always terminate and don't raise
-- and error), and compile with the given type signatures.

-- Feel free to change the function and parameter names to be more descriptive!


-- Note that (_, _) is the Haskell *tuple* type, which is also generically polymorphic.
f0 :: a -> (a, a)
f0 x = undefined

f1 :: (a -> b -> c) -> a -> b -> c
f1 x y z = undefined

f2 :: (b -> c) -> (a -> b) -> a -> c
f2 g h x = undefined

-- What's special about this one?
f3 :: (a, b) -> (c -> b)
f3 (x, y) = undefined


-- |
-- = Task 2: One new generic type, `Maybe`

-- For your reference, here's the definition of the `Maybe` type built into Haskell:
-- data Maybe = Nothing | Just a

safeHead :: [a] -> Maybe a
safeHead = undefined

safeTail :: [a] -> Maybe [a]
safeTail = undefined

onlyWhen :: (a -> Bool) -> a -> Maybe a
onlyWhen = undefined

try :: (a -> b) -> Maybe a -> Maybe b
try = undefined


-- |
-- = Task 3: Introduction to typeclasses

data Shape
    = Circle Float            -- ^ A circle with the given radius
    | Rectangle Float Float   -- ^ A rectangle with the given width and height
    | Square Float            -- ^ A square with the given side length