ex3.md

1. Types of expresions:

   • ['a','b','c'] :: [Char]
   • ('a,b'c') :: (Char, Char, Char)
   • [(False, '0'), (True, '1')] :: [(Bool, Char)]
   • ([False, True], ('0','1')) :: ([Bool], [Char])
   • [tail, init, reverse] :: [[a] -> [a]]

2. Examples of prescribed types

   • bools: [Bool] / [True]
   • nums :: [[Int]] / [[1,2], [3,4]]
   • add :: Int -> Int -> Int -> Int / add w x y z = w + x + y + z
   • copy :: a -> (a,a) / copy x = (x, x)
   • apply :: (a -> b) -> a -> b / apply f x = f x

3. Types of functions:

   • if second xs = head (tail xs) then :type second is [a] -> a
   • if swap (x,y) = (y,x) then :type swap is (a,b) -> (b,a)
   • if pair x y = (x,y) then :type pair is a -> b -> (a,b)
   • if double x = x * 2 then :type double is Num a => a -> a
   • if palindrome xs = reverse xs == xs then :type palindrome is Eq a => [a] -> Bool (nb only equatable a is required, no other restrictions - order is index based)
   • if twice f x = f (f x) then :type twice is a -> a -> a -> a. Correction - according to ghci the type is actually (a->a) -> a -> a. It makes sense intuitively, twice is not curriable in the sense that you can just 3 values of type a and output an a. Todo find a better way to explain this.

4. Function types cannot generally be instances of Eq as function equivalence is logically equivalent to the halting problem