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FD set predicates |

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- Documentation
- Reference manual
- The SWI-Prolog library
- library(clpfd): CLP(FD): Constraint Logic Programming over Finite Domains
- CLP(FD) predicate index
- Arithmetic constraints
- Membership constraints
- Enumeration predicates
- Global constraints
- Reification predicates
- Reflection predicates
- FD set predicates
- in_set/2
- fd_set/2
- is_fdset/1
- empty_fdset/1
- fdset_parts/4
- empty_interval/2
- fdset_interval/3
- fdset_singleton/2
- fdset_min/2
- fdset_max/2
- fdset_size/2
- list_to_fdset/2
- fdset_to_list/2
- range_to_fdset/2
- fdset_to_range/2
- fdset_add_element/3
- fdset_del_element/3
- fdset_disjoint/2
- fdset_intersect/2
- fdset_intersection/3
- fdset_member/2
- fdset_eq/2
- fdset_subset/2
- fdset_subtract/3
- fdset_union/3
- fdset_union/2
- fdset_complement/2

- FD miscellaneous predicates

- CLP(FD) predicate index

- library(clpfd): CLP(FD): Constraint Logic Programming over Finite Domains

- The SWI-Prolog library
- Packages

- Reference manual

These predicates allow operating directly on the internal
representation of CLP(FD) domains. In this context, such an internal
domain representation is called an **FD set**.

Note that the exact term representation of FD sets is unspecified and
will vary across CLP(FD) implementations or even different versions of
the same implementation. FD set terms should be manipulated **only**
using the predicates in this section. The behavior of other operations
on FD set terms is undefined. In particular, you should **not**
construct or deconstruct FD sets by unification, and you **cannot**
reliably compare FD sets using unification or generic term
equality/comparison predicates.

`?Var`**in_set**`+Set``Var`is an element of the FD set`Set`.- [det]
**fd_set**(`?Var, -Set`) `Set`is the FD set representation of the current domain of`Var`.- [semidet]
**is_fdset**(`@Set`) `Set`is currently bound to a valid FD set.- [det]
**empty_fdset**(`-Set`) `Set`is the empty FD set.- [semidet]
**fdset_parts**(`?Set, ?Min, ?Max, ?Rest`) `Set`is a non-empty FD set representing the domain`Min`..`Max``\/`

`Rest`, where`Min`..`Max`is a non-empty interval (see fdset_interval/3) and`Rest`is another FD set (possibly empty).If

`Max`is**sup**, then`Rest`is the empty FD set. Otherwise, if`Rest`is non-empty, all elements of`Rest`are greater than`Max`+1.This predicate should only be called with either

`Set`or all other arguments being ground.- [semidet]
**empty_interval**(`+Min, +Max`) `Min`..`Max`is an empty interval.`Min`and`Max`are integers or one of the atoms**inf**or**sup**.- [semidet]
**fdset_interval**(`?Interval, ?Min, ?Max`) `Interval`is a non-empty FD set consisting of the single interval`Min`..`Max`.`Min`is an integer or the atom**inf**to denote negative infinity.`Max`is an integer or the atom**sup**to denote positive infinity.Either

`Interval`or`Min`and`Max`must be ground.- [semidet]
**fdset_singleton**(`?Set, ?Elt`) `Set`is the FD set containing the single integer`Elt`.Either

`Set`or`Elt`must be ground.- [semidet]
**fdset_min**(`+Set, -Min`) `Min`is the lower bound (infimum) of the non-empty FD set`Set`.`Min`is an integer or the atom**inf**if`Set`has no lower bound.- [semidet]
**fdset_max**(`+Set, -Max`) `Max`is the upper bound (supremum) of the non-empty FD set`Set`.`Max`is an integer or the atom**sup**if`Set`has no upper bound.- [det]
**fdset_size**(`+Set, -Size`) `Size`is the number of elements of the FD set`Set`, or the atom**sup**if`Set`is infinite.- [det]
**list_to_fdset**(`+List, -Set`) `Set`is an FD set containing all elements of`List`, which must be a list of integers.- [det]
**fdset_to_list**(`+Set, -List`) `List`is a list containing all elements of the finite FD set`Set`, in ascending order.- [det]
**range_to_fdset**(`+Domain, -Set`) `Set`is an FD set equivalent to the domain`Domain`.`Domain`uses the same syntax as accepted by (in)/2.- [det]
**fdset_to_range**(`+Set, -Domain`) `Domain`is a domain equivalent to the FD set`Set`.`Domain`is returned in the same format as by fd_dom/2.- [det]
**fdset_add_element**(`+Set1, +Elt, -Set2`) `Set2`is the same FD set as`Set1`, but with the integer`Elt`added. If`Elt`is already in`Set1`, the set is returned unchanged.- [det]
**fdset_del_element**(`+Set1, +Elt, -Set2`) `Set2`is the same FD set as`Set1`, but with the integer`Elt`removed. If`Elt`is not in`Set1`, the set returned unchanged.- [semidet]
**fdset_disjoint**(`+Set1, +Set2`) - The FD sets
`Set1`and`Set2`have no elements in common. - [semidet]
**fdset_intersect**(`+Set1, +Set2`) - The FD sets
`Set1`and`Set2`have at least one element in common. - [det]
**fdset_intersection**(`+Set1, +Set2, -Intersection`) `Intersection`is an FD set (possibly empty) of all elements that the FD sets`Set1`and`Set2`have in common.- [nondet]
**fdset_member**(`?Elt, +Set`) - The integer
`Elt`is a member of the FD set`Set`. If`Elt`is unbound,`Set`must be finite and all elements are enumerated on backtracking. - [semidet]
**fdset_eq**(`+Set1, +Set2`) - True if the FD sets
`Set1`and`Set2`are equal, i. e. contain exactly the same elements. This is not necessarily the same as unification or a term equality check, because some FD sets have multiple possible term representations. - [semidet]
**fdset_subset**(`+Set1, +Set2`) - The FD set
`Set1`is a (non-strict) subset of`Set2`, i. e. every element of`Set1`is also in`Set2`. - [det]
**fdset_subtract**(`+Set1, +Set2, -Difference`) - The FD set
`Difference`is`Set1`with all elements of`Set2`removed, i. e. the set difference of`Set1`and`Set2`. - [det]
**fdset_union**(`+Set1, +Set2, -Union`) - The FD set
`Union`is the union of FD sets`Set1`and`Set2`. - [det]
**fdset_union**(`+Sets, -Union`) - The FD set
`Union`is the n-ary union of all FD sets in the list`Sets`. If`Sets`is empty,`Union`is the empty FD set. - [det]
**fdset_complement**(`+Set, -Complement`) - The FD set
`Complement`is the complement of the FD set`Set`. Equivalent to`fdset_subtract(inf..sup, Set, Complement)`

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