Finite-domain variables

A finite domain is a set of ground terms given as a list. The special notation $Begin$..$Step$..$End$ denotes the set of integers $\{B_1,B_2,\ldots,B_k\}$ where $B1=Begin$, $B_i = B_{i-1}+Step$ for $i=2,...,k$, $B_k \le End$ and $B_k+Step>End$. When the increment $Step$ is 1, the notation can be abbreviated as $Begin..End$. For example, the notation $1..2..10$ means the list [1,3,5,7,9], and $1..3$ means the list [1,2,3].

• Vars in D: The variables in Vars take on values from the finite domain D, where Vars can be a single variable or a list of variables. For example, the call X in 1..3 states that the domain of X is [1,2,3], the call X in 1..2..5 states that the domain is [1,3,5], and the call X in [a,b,c] states that the domain is [a,b,c].

• Vars :: D: The same as Vars in D.

• domain(Vars,L,U): The same as Vars in L..U.

• Vars notin D: Vars does not reside in D.

The following primitives are available on integer domain variables. As domain variables are also suspension variables, primitives on suspension variables such as frozen/1 can be applied to domain variables as well.

• fd_var(V): V is a domain variable.

• fd_new_var(V): Create a new domain variable V whose domain is -268435455..268435455.

• fd_max(V,N): The maximum element in the domain of V is N. V must be an integer domain variable or an integer.

• fd_min(V,N): The minimum element in the domain of V is N. V must be an integer domain variable or an integer.

• fd_min_max(V,Min,Max): The minimum and maximum elements in the domain of V are Min and Max, respectively. V must be an integer domain variable or an integer.

• fd_size(V,N): The size of the domain of V is N.

• fd_dom(V,L): L is the list of elements in the domain of V.

• fd_true(V,E): E is an element in the domain of V.

• fd_set_false(V,E): Exclude the element E from the domain of V. If this operation results in a hole in the domain of $V$, then the domain changes from an interval representation into a bit-vector representation however big it is.

• fd_next(V,E,NextE): NextE is the next element following E in V's domain.

• fd_prev(V,E,PrevE): PrevE is the element preceding E in V's domain.

• fd_include(V1,V2): Succeeds if V1's domain includes V2's domain as a set.

• fd_disjoint(V1,V2): Succeeds if V1's domain and V2's domain are disjoint.

• fd_degree(V,N): The number of connected variables with V in the constraint network is N.

• fd_vector_min_max(Min,Max): Specifies the range of bit vectors. Domain variables, when being created, are usually represented internally by using intervals. An interval turns to a bit vector when a hole occurs in it. The default values for Min and Max are -3200 and 3200, respectively.