Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Functional programming, design and analysis of algorithms / 4 / a / Solution

Separate the empty prefix from the prefixes beginning with the first element:

inits :: [a] -> [[a]]
inits [] = [[]]
inits (x:xs) = [] : map (x:) (inits xs)

Every nonempty list prefix begins with x and continues with a prefix of xs. Thus the recursive order is increasing prefix length, beginning with length zero. Lazy evaluation can also expose every finite prefix of a productive infinite input.