Description
The monad laws are the following. a . Left identity. return a >>= f is equivalent to f a b . Right identity. m >>= return is equivalent to m c . Associativity. m >>= f >>= g is equivalent to m >>= (\ x -> f x >>= g)
1 . Prove that the Maybe Monad satisfies the monadic laws. [10] 2 . Prove that the List Monad satisfies the monadic laws. [10] 3 . Write a memoized version of the function to compute the nth Fibonacci number. Assume that the first Fibonacci number is 1. Hint: Use an appropriate monad. [10]
4 . Write an interactive function which takes a sequence of non-negative integers as input, one on each line. The end of sequence occurs when the user inputs -1. You should output the sum of the non-negative integers.
a . Do the above exercise using the do notation in Haskell. [10]
b . Do the same exercise, without using the do notation. [10]
1
