In
functional languages, a data object containing two or more components. Also known as a product
type or pair, triple, quad, etc. Tuples of different sizes have different
types, in contrast to lists where the
type is independent of the length. The components of a tuple may be of different
types whereas all elements of a list have the same
type. Examples of tuples in
Haskell notation are (1,2), ("Tuple",True), (w,(x,y),z). The degenerate tuple with zero components, written (), is known as the unit
type since it has only one possible value which is also written (). The implementation of tuples in a language may be either "
lifted" or not. If tuples are lifted then (bottom,bottom) /= bottom and the evaluation of a tuple may fail to terminate. E.g. in Haskell: f (x,y) = 1 --> f bottom = bottom f (bottom,bottom) = 1 With lifted tuples, a tuple pattern is refutable. Thus in Haskell,
pattern matching on tuples is the same as pattern matching on
types with multiple constructors ({algebraic data
type}s) - the expression being matched is evaluated as far as the top level constructor, even though, in the case of tuples, there is only one possible constructor for a given
type. If tuples are unlifted then (bottom, bottom) = bottom and evaluation of a tuple will never fail to terminate though any of the components may. E.g. in
Miranda: f (x,y) = 1 --> f bottom = 1 f (bottom,bottom) = 1 Thus in Miranda, any object whose
type is compatible with a tuple pattern is assumed to match at the top level without evaluation - it is an
irrefutable pattern. This also applies to user defined data
types with only one constructor. In Haskell, patterns can be made irrefutable by adding a "~" as in f ~(x,y) = 1. If tuple constructor functions were
strict in all their arguments then (bottom,x) = (x,bottom) = bottom for any x so matching a refutable pattern would fail to terminate if any component was bottom.
In addition suitable contents:
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