Toyohashi University Parallel Lisp Environment
TUPLE

    (TUPLE) A parallel Lisp based on KCL.

   ["Memory Management and Garbage Collection of an Extended
   Common Lisp System for Massively Parallel SIMD Architecture",
   Taiichi Yuasa, in Memory Management, IWMM92, Springer 1992,
   490-507].

   (1994-11-08)

tuple

    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 type 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 (where bottom represents non-termination) 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
   types) - 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.

   (2012-03-25)