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A data type for tuples

Illustration

We illustrate here the Haskell approach to tuple types.

We can form tuples of different length: pairs, triples, quadruples, ....:

Prelude> (1,"2")
(1,"2")
Prelude> (1,"2",True)
(1,"2",True)
Prelude> (1,"2",True,42.0)
(1,"2",True,42.0)

These tuples are of different tuple types:

Prelude> (1,"2") :: (Int,String)
(1,"2")
Prelude> (1,"2",True) :: (Int,String,Bool)
(1,"2",True)
Prelude> (1,"2",True,42.0) :: (Int,String,Bool,Float)
(1,"2",True,42.0)

We can think of these tuple types as being defined as polymorphic types like this:

type (a,b) = (a,b)
type (a,b,c) = (a,b,c)
type (a,b,c,d) = (a,b,c,d)

Specific tuple types can also be expressed by other means than a designated type constructor for such types. For instance, the illustrative tuple types given above could also be declared like this:

data TupleType1 = TupleType1 Int String
data TupleType2 = TupleType2 Int String Bool
data TupleType3 = TupleType3 Int String Bool Float

(We reuse type names as constructor symbols here, which is possible in Haskell, as these are separate namespaces.) The advantage of the type type constructors (of different arities) is that they capture universally (polymorphically) the notion of ordered tuples, that is, for arbitrary operand types.

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