The Global Constraint Programming Interface

This section describes a programming interface by means of which new constraints can be written. The interface consists of a set of predicates provided by this library module. Constraints defined in this way can take arbitrary arguments and may use any constraint solving algorithm, provided it makes sense. Reification cannot be expressed in this interface; instead, reification may be achieved by explicitly passing a 0/1-variable to the constraint in question.

Global constraints have state which may be updated each time the constraint is resumed. The state information may be used e.g. in incremental constraint solving.

The following two predicates are the principal entrypoints for defining and posting new global constraints:

clpfd:dispatch_global(+Constraint, +State0, -State, -Actions) [Hook]

Tells the solver how to solve constraints of the form Constraint. Defined as a dynamic, multifile predicate.

When defining a new constraint, a clause of this predicate must be added. Its body defines a constraint solving method and should always succeed deterministically. When a global constraint is called or resumed, the solver will call this predicate to deal with the constraint. NOTE: the constraint is identified by its principal functor; there is no provision for having two constraints with the same name in different modules. It is good practice to include a cut in every clause of clpfd:dispatch_global/4.

State0 and State are the old and new state respectively.

The constraint solving method must not invoke the constraint solver recursively e.g. by binding variables or posting new constraints; instead, Actions should be unified with a list of requests to the solver. Each request should be of the following form:

exit

The constraint has become entailed, and ceases to exist.

fail

The constraint has become disentailed, causing the solver to backtrack.

X = V

The solver binds X to V.

X in R

The solver constrains X to be a member of the ConstantRange R (see Syntax of Indexicals).

X in_set S

The solver constrains X to be a member of the FD set S (see FD Set Operations).

call(Goal)

The solver calls the goal or constraint Goal, which should be module prefixed unless it is a built-in predicate or an exported predicate of the clpfd module.

Goal is executed as any Prolog goal, but in a context where some constraints may already be enqueued for execution, in which case those constraints will run after the completion of the call request.

fd_global(:Constraint, +State, +Susp)

fd_global(:Constraint, +State, +Susp, +Options)

where Constraint is a constraint goal, State is its initial state, and Susp is a term encoding how the constraint should wake up in response to domain changes. This predicate posts the constraint.

Susp is a list of F(Var) terms where Var is a variable to suspend on and F is a functor encoding when to wake up:

dom(X)

wake up when the domain of X has changed

min(X)

wake up when the lower bound of X has changed

max(X)

wake up when the upper bound of X has changed

minmax(X)

wake up when the lower or upper of X has changed

val(X)

wake up when X has become ground

Options is a list of zero or more of the following:

source(Term)

By default, the symbolic form computed by fd_copy_term/3, and shown in the answer constraint if clpfd:full_answer holds, equals Constraint, module name expanded. With this option, the symbolic form will instead be Term. In particular, if Term equals true, the constraint will not appear in the Body argument of fd_copy_term/3. This can be useful if you are posting some redundant (implied) constraint.

idempotent(Boolean)

If true (the default), the constraint solving method is assumed to be idempotent. That is, in the scope of clpfd:dispatch_global/4, the solver will not check for the resumption conditions for the given constraint, while performing its Actions. If false, an action may well cause the solver to resume the constraint that produced the action.

If a variable occurs more than once in a global constraint that is being posted, or due to a variable-variable unification, the solver will no longer trust the constraint solving method to be idempotent.

For an example of usage, see A Global Constraint Example.