upward closure

1 definition found

upward closure - Free On-line Dictionary of Computing (26 May 2007) :

  closure
  downward closed
  upward closure
  
     1. <programming> In a reduction system, a closure is a data
     structure that holds an expression and an environment of
     variable bindings in which that expression is to be evaluated.
     The variables may be local or global.  Closures are used to
     represent unevaluated expressions when implementing
     functional programming languages with lazy evaluation.  In
     a real implementation, both expression and environment are
     represented by pointers.
  
     A suspension is a closure which includes a flag to say
     whether or not it has been evaluated.  The term "thunk" has
     come to be synonymous with "closure" but originated outside
     functional programming.
  
     2. <theory> In domain theory, given a partially ordered set
     , D and a subset, X of D, the upward closure of X in D is
     the union over all x in X of the sets of all d in D such that
     x <= d.  Thus the upward closure of X in D contains the
     elements of X and any greater element of D.  A set is "upward
     closed" if it is the same as its upward closure, i.e. any d
     greater than an element is also an element.  The downward
     closure (or "left closure") is similar but with d <= x.  A
     downward closed set is one for which any d less than an
     element is also an element.
  
     ("<=" is written in LaTeX as \subseteq and the upward
     closure of X in D is written \uparrow_\D X).
  
     (1994-12-16)