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# insetdomain(?Set, ?CardSel, ?ElemSel, ?Order)

Instantiate Set to a possible value

Set
  a set or set variable
CardSel
  atom or variable
ElemSel
  atom, structure or variable
Order
  atom or variable

## Description

This predicate instantiates a set variable to a possible value, according to its domain. The predicate backtracks over all possible set instantiations. The three option arguments allow to choose between a number of different enumeration orders. Giving a variable as option argument will select the default.

The CardSel argument determines whether the sets are enumerated according to their cardinality. It can take the following values:

any (default)
  the sets are not enumerated in a particular cardinality order
increasing
  the sets are enumerated with increasing cardinality, ie. small sets are tried first
decreasing
  the sets are enumerated with decreasing cardinality, ie. large sets are tried first

The ElemSel argument determines which potential set elements are considered first for inclusion or exclusion. It can take the following values:

small_first (default)
  small set elements (small numbers) are considered first
big_first
  big set elements (big numbers) are considered first
random
  potential set elements are considered in random order
heavy_first(Weights)
  heavy set elements (according to Weight array) are considered first
light_first(Weights)
  light set elements (according to Weight array) are considered first

The Order argument determines whether it is first tried to make the selected potential element a set member, or whether to exclude it first. The argument can take the following values:

in_notin (default)
  try inclusion first, then exclusion
notin_in
  try exclusion first, then inclusion
sbds
  uses sbds_try/2 to include or exclude an element in or from a set (this is for use in conjunction with the SBDS library, and whether inclusion or exclusion is tried first depends on the "fix pred" specified in the prior call to sbds_initialise/4 or sbds_initialise/5)

Note that there are many different enumeration strategies for a set variable, and insetdomain/4 only allows a limited number of them. For an actual application, it might be more appropriate to choose a problem-specific enumeration order. This can be programmed easily. As a guideline, here is the code for insetdomain with the default options:

        insetdomain(Set, _, _, _) :-
        	nonvar(Set).
        insetdomain(Set, any, small_first, in_notin) :-
        	var(Set),
        	potential_members(Set, PotentialElements),
    	PotentialElements = [Element|_],
    	(
    	    Element in Set
    	;
    	    Element notin Set
    	),
    	insetdomain(Set, any, small_first, in_notin).

### Resatisfiable

yes

### Exceptions

(4) instantiation fault
  Set is a variable, but not a set variable

## Examples

    ?-  X::[]..[1,2,3], insetdomain(X,_,_,_), writeln(X), fail.
    [1, 2, 3]
    [1, 2]
    [1, 3]
    [1]
    [2, 3]
    [2]
    [3]
    []

    no (more) solution.
    ?-  X::[]..[1,2,3], insetdomain(X,increasing,_,_), writeln(X), fail.
    []
    [1]
    [2]
    [3]
    [1, 2]
    [1, 3]
    [2, 3]
    [1, 2, 3]

    no (more) solution.
    ?-  X::[]..[1,2,3], insetdomain(X,_,big_first,_), writeln(X), fail.
    [1, 2, 3]
    [2, 3]
    [1, 3]
    [3]
    [1, 2]
    [2]
    [1]
    []

    no (more) solution.
    ?-  X::[]..[1,2,3], insetdomain(X,_,_,notin_in), writeln(X), fail.
    []
    [3]
    [2]
    [2, 3]
    [1]
    [1, 3]
    [1, 2]
    [1, 2, 3]

    no (more) solution.
    ?-  X::[]..[1,2,3],
    	insetdomain(X, increasing, heavy_first([](2,9,4,7)), _),
    	writeln(X), fail.
    []
    [2]
    [3]
    [1]
    [2, 3]
    [1, 2]
    [1, 3]
    [1, 2, 3]

    no (more) solution.

## See Also

conjunto_fd_sets : refine / 1, conjunto : refine / 1, potential_members / 2, ic_sbds : sbds_try / 2, fd_sbds : sbds_try / 2, ic_gap_sbds : sbds_try / 2, ic_sbds : sbds_initialise / 4, fd_sbds : sbds_initialise / 4, ic_sbds : sbds_initialise / 5, fd_sbds : sbds_initialise / 5, ic_gap_sbds : sbds_initialise / 5