10.3 Attributed Variables—library(atts)

This package implements attributed variables. It provides a means of associating with variables arbitrary attributes, i.e. named properties that can be used as storage locations as well as to extend the default unification algorithm when such variables are unified with other terms or with each other. This facility was primarily designed as a clean interface between Prolog and constraint solvers, but has a number of other uses as well. The basic idea is due to Christian Holzbaur and he was actively involved in the final design. For background material, see the dissertation [Holzbaur 90].

The package provides a means to declare and access named attributes of variables. The attributes are compound terms whose arguments are the actual attribute values. The attribute names are private to the module in which they are defined. They are defined with a declaration

:- attribute AttributeSpec, …, AttributeSpec.

where each AttributeSpec has the form (Name/Arity). There must be at most one such declaration in a module Module.

Having declared some attribute names, these attributes can now be added, updated and deleted from unbound variables. For each declared attribute name, any variable can have at most one such attribute (initially it has none).

The declaration causes the following two access predicates to become defined by means of the goal_expansion/5 mechanism. They take a variable and an AccessSpec as arguments where an AccessSpec is either +(Attribute), -(Attribute), or a list of such. The ‘+’ prefix may be dropped for convenience. Attribute must be nonvariable at compile time. The meaning of the ‘+’/‘-’ prefix is documented below:

Module:get_atts(-Var, ?AccessSpec)

Gets the attributes of Var according to AccessSpec. If AccessSpec is unbound, it will be bound to a list of all present attributes of Var, which must be a variable. The elements of AccessSpec have the following meaning:


The corresponding actual attribute must be present and is unified with Attribute.


The corresponding actual attribute must be absent. The arguments of Attribute are ignored, only the name and arity are relevant.

Module:put_atts(-Var, +AccessSpec)

Sets the attributes of Var, which must be a variable, according to AccessSpec. The effects of put_atts/2 are undone on backtracking.


The corresponding actual attribute is set to Attribute. If the actual attribute was already present, it is simply replaced.


The corresponding actual attribute is removed. If the actual attribute was already absent, nothing happens.

A module that contains an attribute declaration has an opportunity to extend the default unification algorithm by defining the following predicate:

Module:verify_attributes(-Var, +Value, -Goals)   hook

This predicate is called whenever a variable Var that might have attributes in Module is about to be bound to Value (it might have none). The unification resumes after the call to verify_attributes/3. Value is a nonvariable, or another attributed variable. Var might have no attributes present in Module; the unification extension mechanism is not sophisticated enough to filter out exactly the variables that are relevant for Module.

verify_attributes/3 is called before Var has actually been bound to Value. If it fails, the unification is deemed to have failed. It may succeed nondeterminately, in which case the unification might backtrack to give another answer. It is expected to return, in Goals, a list of goals to be called after Var has been bound to Value. Finally, after calling Goals, any goals blocked on Var are called.

verify_attributes/3 may invoke arbitrary Prolog goals, but Var should not be bound by it. Binding Var will result in undefined behavior.

If Value is a nonvariable, verify_attributes/3 will typically inspect the attributes of Var and check that they are compatible with Value and fail otherwise. If Value is another attributed variable, verify_attributes/3 will typically copy the attributes of Var over to Value, or merge them with Value’s, in preparation for Var to be bound to Value. In either case, verify_attributes/3 may determine Var’s current attributes by calling get_atts(Var,List) with an unbound List.

In the case when a single unification binds multiple attributed variables, first all such bindings are undone, then the following actions are carried out for each relevant variable:

  1. For each relevant module M, M:verify_attributes/3 is called, collecting a list of returned Goals.
  2. The variable binding is redone.
  3. Any Goals are called.
  4. Any blocked goals are called.

An important use for attributed variables is in implementing coroutining facilities as an alternative or complement to the built-in coroutining mechanisms. In this context it might be useful to be able to interpret some of the attributes of a variable as a goal that is blocked on that variable. Certain built-in predicates (frozen/2, copy_term/3) and the Prolog top-level need to access blocked goals, and so need a means of getting the goal interpretation of attributed variables by calling:

Module:attribute_goal(-Var, -Goal)   hook

This predicate is called in each module that contains an attribute declaration, when an interpretation of the attributes as a goal is needed, in particular in frozen/2, copy_term/3 and the Prolog top-level. It should unify Goal with the interpretation, or merely fail if no such interpretation is available.

An important use for attributed variables is to provide an interface to constraint solvers. An important function for a constraint solver in the constraint logic programming paradigm is to be able to perform projection of the residual constraints onto the variables that occurred in the top-level query. A module that contains an attribute declaration has an opportunity to perform such projection of its residual constraints by defining the following predicate:

Module:project_attributes(+QueryVars, +AttrVars)   hook

This predicate is called by the Prolog top level in each module that contains an attribute declaration. QueryVars is the list of variables occurring in the query, or in terms bound to such variables, and AttrVars is a list of possibly attributed variables created during the execution of the query. The two lists of variables may or may not be disjoint.

If the attributes on AttrVars can be interpreted as constraints, this predicate will typically “project” those constraints onto the relevant QueryVars. Ideally, the residual constraints will be expressed entirely in terms of the QueryVars, treating all other variables as existentially quantified. Operationally, project_attributes/2 must remove all attributes from AttrVars, and add transformed attributes representing the projected constraints to some of the QueryVars.

Projection has the following effect on the Prolog top-level. When the top-level query has succeeded, project_attributes/2 is called first. The top-level then prints the answer substition and residual constraints. While doing so, it searches for attributed variables created during the execution of the query. For each such variable, it calls attribute_goal/2 to get a printable representation of the constraint encoded by the attribute. Thus, project_attributes/2 is a mechanism for controlling how the residual constraints should be displayed at top-level.

The exact definition of project_attributes/2 is constraint system dependent, but see Answer Constraints and see CLPQR Projection for details about projection in CLPFD and CLP(Q,R) respectively.

In the following example we sketch the implementation of a finite domain “solver”. Note that an industrial strength solver would have to provide a wider range of functionality and that it quite likely would utilize a more efficient representation for the domains proper. The module exports a single predicate domain(-Var,?Domain), which associates Domain (a list of terms) with Var. A variable can be queried for its domain by leaving Domain unbound.

We do not present here a definition for project_attributes/2. Projecting finite domain constraints happens to be difficult.

% domain.pl
:- module(domain, [domain/2]).

:- use_module(library(atts)).
:- use_module(library(ordsets), [

:- attribute dom/1.

verify_attributes(Var, Other, Goals) :-
        get_atts(Var, dom(Da)), !,          % are we involved?
        (   var(Other) ->                   % must be attributed then
            (   get_atts(Other, dom(Db)) -> %   has a domain?
                ord_intersection(Da, Db, Dc),
                Dc = [El|Els],              % at least one element
                (   Els = [] ->             % exactly one element
                    Goals = [Other=El]      % implied binding
                ;   Goals = [],
                    put_atts(Other, dom(Dc))% rescue intersection
            ;   Goals = [],
                put_atts(Other, dom(Da))    % rescue the domain
        ;   Goals = [],
            ord_intersect([Other], Da)      % value in domain?
verify_attributes(_, _, []).                % unification triggered
                                            % because of attributes
                                            % in other modules

attribute_goal(Var, domain(Var,Dom)) :-     % interpretation as goal
        get_atts(Var, dom(Dom)).

domain(X, Dom) :-
        var(Dom), !,
        get_atts(X, dom(Dom)).
domain(X, List) :-
        list_to_ord_set(List, Set),
        Set = [El|Els],                     % at least one element
        (   Els = [] ->                     % exactly one element
            X = El                          % implied binding
        ;   put_atts(Fresh, dom(Set)),
            X = Fresh                       % may call
                                            % verify_attributes/3

Note that the “implied binding” Other=El was deferred until after the completion of verify_attribute/3. Otherwise, there might be a danger of recursively invoke verify_attribute/3, which might bind Var, which is not allowed inside the scope of verify_attribute/3. Deferring unifications into the third argument of verify_attribute/3 effectively serializes th calls to verify_attribute/3.

Assuming that the code resides in the file domain.pl, we can load it via:

| ?- use_module(domain).

Let’s test it:

| ?- domain(X,[5,6,7,1]), domain(Y,[3,4,5,6]), domain(Z,[1,6,7,8]).


| ?- domain(X,[5,6,7,1]), domain(Y,[3,4,5,6]), domain(Z,[1,6,7,8]), 

Y = X,

| ?- domain(X,[5,6,7,1]), domain(Y,[3,4,5,6]), domain(Z,[1,6,7,8]),
     X=Y, Y=Z.

X = 6,
Y = 6,
Z = 6

To demonstrate the use of the Goals argument of verify_attributes/3, we give an implementation of freeze/2. We have to name it myfreeze/2 in order to avoid a name clash with the built-in predicate of the same name.

% myfreeze.pl
:- module(myfreeze, [myfreeze/2]).

:- use_module(library(atts)).

:- attribute frozen/1.

verify_attributes(Var, Other, Goals) :-
        get_atts(Var, frozen(Fa)), !,       % are we involved?
        (   var(Other) ->                   % must be attributed then
            (   get_atts(Other, frozen(Fb)) % has a pending goal?
            ->  put_atts(Other, frozen((Fa,Fb))) % rescue conjunction
            ;   put_atts(Other, frozen(Fa)) % rescue the pending goal
            Goals = []
        ;   Goals = [Fa]
verify_attributes(_, _, []).

attribute_goal(Var, Goal) :-                % interpretation as goal
        get_atts(Var, frozen(Goal)).

myfreeze(X, Goal) :-
        put_atts(Fresh, frozen(Goal)),
        Fresh = X.

Assuming that this code lives in file myfreeze.pl, we would use it via:

| ?- use_module(myfreeze).
| ?- myfreeze(X,print(bound(x,X))), X=2.

bound(x,2)                      % side-effect
X = 2                           % bindings

The two solvers even work together:

| ?- myfreeze(X,print(bound(x,X))), domain(X,[1,2,3]),
     domain(Y,[2,10]), X=Y.

bound(x,2)                      % side-effect
X = 2,                          % bindings
Y = 2

The two example solvers interact via bindings to shared attributed variables only. More complicated interactions are likely to be found in more sophisticated solvers. The corresponding verify_attributes/3 predicates would typically refer to the attributes from other known solvers/modules via the module prefix in Module:get_atts/2.

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