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An abstraction for constructing new types

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For instance, in functional programming with Haskell, these are typical type constructor:

  • The list type constructor for constructing list types from an element type
  • Any tuple type constructor for constructing types of products from two component types
  • The maybe type constructor for adding partiality to a type
  • The either type constructor for combining types as cases
These types could or are defined in Haskell in follows: 

data [a] = [] | (a:[a])
data (a, b) = (a, b)
data Maybe a = Nothing | Just a
data Either a b = Left a | Just a

If we were to remove the special notation for lists and tuples, thus using ordinary type and constructor names, then the first two declarations take this form: 

data List a = Nil | Cons a (List a)
data Pair a b = Pair a b

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