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
mechanism. They take a variable and an AccessSpec as
arguments where an AccessSpec is either
), or a list of
such. The `+' prefix may be dropped for convenience. The meaning
of the `+'/`-' prefix is documented below:
put_atts/2are undone on backtracking.
A module that contains an attribute declaration has an opportunity to extend the default unification algorithm by defining the following predicate:
verify_attributes/3. Value is a non-variable term, 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.
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 non-variable term,
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
verify_attributes/3 may determine Var's current
attributes by calling
) with an
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 (
call_residue/2) 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:
call_residue/2. 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:
call_residue/2in 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,
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.
project_attributes/2 is a mechanism for controlling how the
residual constraints should be displayed at top-level.
Similarly during the execution of
), when Goal has
project_attributes/2 is called. After that, all
attributed variables created during the execution of Goal
are located. For each such variable,
produces a term representing the constraint encoded by the
attribute, and Residue is unified with the list of all
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
), 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
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), [ ord_intersection/3, ord_intersect/2, list_to_ord_set/2 ]). :- 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
Var, which is not allowed inside the scope of
verify_attribute/3. Deferring unifications into the third
verify_attribute/3 effectively serializes th
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,[1,5,6,7]), 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]), X=Y. Y = X, domain(X,[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]), 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