Haskell function :: [Name] -> [[(Name, Bool)]]

Question

Given the following:

type Name = String
envs :: [Name] -> [[(Name , Bool)]]

I have to implement \'envs\' so that given a list of Names, it r

Answer 1

What you want to do is get all combinations of True and False for the number of names, which can be done easily with replicateM specialised to lists:

replicateM (length names) [False, True]

E.g. if length names == 2, then this produces:

[ [False, False]
, [False, True]
, [True, False]
, [True, True]
]

What remains is just to zip each of these with the names themselves:

envs names =
  [ zip names values
  | let n = length names
  , values <- replicateM n [False, True]
  ]

For envs ["P", "Q"] this produces:

[ [("P", False), ("Q", False)]
, [("P", False), ("Q", True)]
, [("P", True), ("Q", False)]
, [("P", True), ("Q", True)]
]

And it works for any number of inputs, even 0, for which your original implementation would fail since you don’t match []. It always returns 2ⁿ assignments:

-- 2^0 == 1
envs [] == [[]]

-- 2^3 == 8
envs ["P", "Q", "R"] ==
  [ [("P", False), ("Q", False), ("R", False)]
  , [("P", False), ("Q", False), ("R", True)]
  , [("P", False), ("Q", True), ("R", False)]
  , [("P", False), ("Q", True), ("R", True)]
  , [("P", True), ("Q", False), ("R", False)]
  , [("P", True), ("Q", False), ("R", True)]
  , [("P", True), ("Q", True), ("R", False)]
  , [("P", True), ("Q", True), ("R", True)]
  ]