tuple

Toyohashi University Parallel Lisp Environment
TUPLE

   <language> (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 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
   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.