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Algebraic data types:

Sum type vs. Product type

Refers to how you would calculate a type’s number of possible values.

• “sum” is logical alternation

  A or B
  a | b

• “product” is a combination of alternation

  (A or B) and (C or D)
  a | b, c | d

Sum type

eg. Either, Maybe

• Bool is a set of 2 values.

• Char is a set of 256 values.

data MySumType = Foo Bool | Bar Char

                 2            + 256
                 True | False | 'a' | 'b' | 'c' | ...

MySumType is a set of 2 + 256 possible values.

Product type

eg. tuple, record

data MyProductType = Baz (Bool, Char)

                *    256  ––>
                2   (True,  'a') | (True,  'b') | (True,  'c') | ...
                    (False, 'a') | (False, 'b') | (False, 'c') | ...

MyProductType is a set of 2 * 256 possible values.

data MyProductType2 = Baz (Char, Char)

                *    256  ––>
               256  ('a', 'a') | ('a', 'b') | ('a', 'c') | ...
                    ('b', 'a') | ('b', 'b') | ('b', 'c') | ...
                |   ('c', 'a') | ('c', 'b') | ('c', 'c') | ...
                V   ('d', 'a') | ('d', 'b') | ('d', 'c') | ...
                    ('e', 'a') | ('e', 'b') | ('e', 'c') | ...
                    ('f', 'a') | ('f', 'b') | ('f', 'c') | ...
                    ('g', 'a') | ('g', 'b') | ('g', 'c') | ...
                    ...

MyProductType2 is a set of 256 * 256 possible values.

data Person = Person {
            isCool  :: Bool
            favChar :: Char,
        }

            *    256 ––>                  
            2   Person {isCool = True,  favChar = 'a'} | ...
                Person {isCool = False, favChar = 'a'} | ...

Hopefully you get the idea.