Finite-domain variables

A finite domain is a list of different ground terms in the form: [e₁,e₂,...,e_n]. The special notation L..U denotes a set of integers between L and U, inclusive.

A Prolog variable Var becomes a finite-domain variable after its domain is declared by:

      Var :: D

  or

      Var in D

where D is a finite-domain. For example, the call

      X :: 1..3

says that X is an integer between 1 and 3 and the call

      X :: [a,b,c]

says that X can be a, b, or c.

Let Vars be a list of variables that share the same domain D. The domain of the variables can be declared as follows:

      Vars :: D

If the domain is the set of integers between L and U, then the domain can also be declared as

      domain(Var,L,U)

for one variable Var and as

      domain(Vars,L,U)

for a list of variables Vars.

The following primitives restrict the domains of variables.

• domain(Var,L,U): The domain of the variable Var is the set of integers between L and U. L and U must be integers. If Var is an integer, the call is equivalent to

        Var>=L,Var=<U
  

  If Var is neither a variable nor an integer, this call raises the illegal_argument exception.  

• domain([V1,...,Vn],L,U): Equivalent to:

         domain(V1,L,U),...,domain(Vn,L,U)
  

• Var :: D: The domain of the variable Var is D, where D is either an integer interval L..U or a list of ground terms. If D is a list that contains non-integer terms, then the call is equivalent to member(Var,D).  

• [V1,...,Vn] :: D: Equivalent to:

         V1 :: D,...,Vn :: D
  

• Var notin D: Var does not reside in D.
• [V1,...,Vn] notin D: Equivalent to:

         V1 noin D,...,Vn noin 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_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.