### 9.8 Symbolic constraints

- `fd_all_different/1`
- `fd_element/3`
- `fd_element_var/3`
- `fd_atmost/3`, `fd_atleast/3`, `fd_exactly/3`
- `fd_relation/2`, `fd_relationc/2`

#### 9.8.1 `fd_all_different/1`

Templates

  `fd_all_different(+fd_variable_list)`

Description

`fd_all_different(List)` constrains all variables in `List` to take distinct values. This is equivalent to posting an inequality constraint for each pair of variables. This constraint is triggered when a variable becomes ground, removing its value from the domain of the other variables.

Errors

`List` is a partial list |  | `instantiation_error`
`List` is neither a partial list nor a list |  | `type_error(list, List)`
an element `E` of the `List` list is neither a variable nor an integer nor an FD variable |  | `type_error(fd_variable, E)`

Portability

GNU Prolog predicate.

#### 9.8.2 `fd_element/3`

Templates

  `fd_element(?fd_variable, +integer_list, ?fd_variable)`

Description

`fd_element(I, List, X)` constraints `X` to be equal to the `I` th integer (from 1) of `List`.

Errors

`I` is neither a variable nor an FD variable nor an integer |  | `type_error(fd_variable, I)`
`X` is neither a variable nor an FD variable nor an integer |  | `type_error(fd_variable, X)`
`List` is a partial list or a list with an element `E` which is a variable |  | `instantiation_error`
`List` is neither a partial list nor a list |  | `type_error(list, List)`
an element `E` of the `List` list is neither a variable nor an integer |  | `type_error(integer, E)`

Portability

GNU Prolog predicate.

#### 9.8.3 `fd_element_var/3`

Templates

  `fd_element_var(?fd_variable, +fd_variable_list, ?fd_variable)`

Description

`fd_element_var(I, List, X)` constraints `X` to be equal to the `I` th variable (from 1) of `List`. This constraint is similar to `fd_element/3` (section 9.8.2) but `List` can also contain FD variables (rather than just integers).

Errors

`I` is neither a variable nor an FD variable nor an integer |  | `type_error(fd_variable, I)`
`X` is neither a variable nor an FD variable nor an integer |  | `type_error(fd_variable, X)`
`List` is a partial list |  | `instantiation_error`
`List` is neither a partial list nor a list |  | `type_error(list, List)`
an element `E` of the `List` list is neither a variable nor an integer nor an FD variable |  | `type_error(fd_variable, E)`

Portability

GNU Prolog predicate.

#### 9.8.4 `fd_atmost/3`, `fd_atleast/3`, `fd_exactly/3`

Templates

  `fd_atmost(+integer, +fd_variable_list, +integer)
  fd_atleast(+integer, +fd_variable_list, +integer)
  fd_exactly(+integer, +fd_variable_list, +integer)`

Description

`fd_atmost(N, List, V)` posts the constraint that at most `N` variables of `List` are equal to the value `V`.

`fd_atleast(N, List, V)` posts the constraint that at least `N` variables of `List` are equal to the value `V`.

`fd_exactly(N, List, V)` posts the constraint that at exactly `N` variables of `List` are equal to the value `V`.

These constraints are special cases of `fd_cardinality/2` (section 9.7.3) but their implementation is more efficient.

Errors

`N` is a variable |  | `instantiation_error`
`N` is neither a variable nor an integer |  | `type_error(integer, N)`
`V` is a variable |  | `instantiation_error`
`V` is neither a variable nor an integer |  | `type_error(integer, V)`
`List` is a partial list |  | `instantiation_error`
`List` is neither a partial list nor a list |  | `type_error(list, List)`
an element `E` of the `List` list is neither a variable nor an FD variable nor an integer |  | `type_error(fd_variable, E)`

Portability

GNU Prolog predicates.

#### 9.8.5 `fd_relation/2`, `fd_relationc/2`

Templates

  `fd_relation(+integer_list_list, ?fd_variable_list)
  fd_relationc(+integer_list_list, ?fd_variable_list)`

Description

`fd_relation(Relation, Vars)` constraints the tuple of variables `Vars` to be equal to one tuple of the list `Relation`. A tuple is represented by a list.

Example: definition of the boolean AND relation so that X AND Y ⇔ Z:

      and(X,Y,Z):-
              fd_relation([[0,0,0],[0,1,0],[1,0,0],[1,1,1]], [X,Y,Z]).

`fd_relationc(Columns, Vars)` is similar to `fd_relation/2` except that the relation is not given as the list of tuples but as the list of the columns of the relation. A column is represented by a list.

Example:

      and(X,Y,Z):-
              fd_relationc([[0,0,1,1],[0,1,0,1],[0,0,0,1]], [X,Y,Z]).

Errors

`Relation` is a partial list or a list with a sub-term `E` which is a variable |  | `instantiation_error`
`Relation` is neither a partial list nor a list |  | `type_error(list, Relation)`
an element `E` of the `Relation` list is neither a variable nor an integer |  | `type_error(integer, E)`
`Vars` is a partial list |  | `instantiation_error`
`Vars` is neither a partial list nor a list |  | `type_error(list, Vars)`
an element `E` of the `Vars` list is neither a variable nor an integer nor an FD variable |  | `type_error(fd_variable, E)`

Portability

GNU Prolog predicates.

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