Constraint programming over finite domains

Author(s): José Manuel Gómez Pérez, Manuel Carro.

This package is not anymore maintained. Prefer package clpfd which provides similar features.

This package is a very preliminary implementation of a finite domain solver. Examples can be found in the source and library directories.

SEND + MORE = MONEY:

:- use_package(fd).
:- use_module(library(prolog_sys), [statistics/2]).
:- use_module(library(format)).


smm(SMM) :-
	statistics(runtime,_),
	do_smm(SMM),
	statistics(runtime,[_, Time]),
	format("Used ~d milliseconds~n", Time).

do_smm(X) :-
	X = [S,E,N,D,M,O,R,Y],
	X in 0 .. 9,
	all_different(X),
	M .>. 0,
	S .>. 0,
	1000*S + 100*E + 10*N + D + 1000*M + 100*O + 10*R + E
        .=. 10000*M + 1000*O + 100*N + 10*E + Y,
	labeling(X).

Queens:

:- use_package(fd).
:- use_module(library(prolog_sys), [statistics/2]).
:- use_module(library(format)).
:- use_module(library(aggregates)).
:- use_module(library(lists), [length/2]).


queens(N, Qs) :-
	statistics(runtime,_),
	do_queens(N, Qs),
	statistics(runtime,[_, Time]),
	format("Used ~d milliseconds~n", Time).

do_queens(N, Qs):- 
	constrain_values(N, N, Qs),
	all_different(Qs),!,
	labeling(Qs).

constrain_values(0, _N, []).
constrain_values(N, Range, [X|Xs]):-
        N > 0, 
        X in 1 .. Range,
        N1 is N - 1,
        constrain_values(N1, Range, Xs),
        no_attack(Xs, X, 1).

no_attack([], _Queen, _Nb).
no_attack([Y|Ys], Queen, Nb):-
	Nb1 is Nb + 1,
	no_attack(Ys, Queen, Nb1),
	Queen .<>. Y + Nb,
	Queen .<>. Y - Nb.

Usage and interface

Library usage:
:- use_package(fd). or :- module(...,...,[fd]).
Exports:
- Predicates:
  labeling/1, pitm/2, choose_var/3, choose_free_var/2, choose_var_nd/2, choose_value/2, retrieve_range/2, retrieve_store/2, glb/2, lub/2, bounds/3, retrieve_list_of_values/2.
- Regular Types:
  fd_item/1, fd_range/1, fd_subrange/1, fd_store/1, fd_store_entity/1.
New operators defined:
.=./2 [700,xfx], .<>./2 [700,xfx], .<./2 [700,xfx], .=<./2 [700,xfx], .>./2 [700,xfx], .>=./2 [700,xfx], ../2 [500,yfx], .&./2 [600,xfy], in/2 [700,xfy].
Imports:
- Packages:
  prelude, nonpure, condcomp, assertions, regtypes, isomodes.

Documentation on exports

REGTYPE

fd_item/1:

Usage:fd_item(FD_item)

FD_item is a finite domain entity, i.e. either a finite domains variable or an integer.

REGTYPE

fd_range/1:

Usage:fd_range(FD_range)

FD_range is the range of a finite domain entity.

REGTYPE

fd_subrange/1:

Usage:

A subrange is a pair representing a single interval.

REGTYPE

fd_store/1:

Usage:fd_store(FD_store)

FD_store is a representation of the constraint store of a finite domain entity.

REGTYPE

fd_store_entity/1:

Usage:

Representation of primitive constraints.

PREDICATE

labeling/1:

Usage:labeling(Vars)

Implements the labeling process. Assigns values to the input variables Vars. On exit all variables are instantiated to a consistent value. On backtracking, the predicate returns all possible assignments. No labeling heuristics implemented so far, i.e. variables are instantiated in their order of appearance.

The following properties should hold at call time:
(basic_props:list/2)Vars is a list of fd_items.

PREDICATE

pitm/2:

Usage:pitm(V,MiddlePoint)

Returns in MiddlePoint the intermediate value of the range of V. In case V is a ground integer value the returned value is V itself.

The following properties should hold at call time:
(term_typing:nonvar/1)V is currently a term which is not a free variable.
(term_typing:var/1)MiddlePoint is a free variable.
(user(... /fd_doc):fd_item/1)V is a finite domain entity, i.e. either a finite domains variable or an integer.
(basic_props:int/1)MiddlePoint is an integer.

PREDICATE

choose_var/3:

Usage:choose_var(ListOfVars,Var,RestOfVars)

Returns a finite domain item Var from a list of fd items ListOfVars and the rest of the list RestOfVarsin a deterministic way. Currently it always returns the first item of the list.

The following properties should hold at call time:
(term_typing:nonvar/1)ListOfVars is currently a term which is not a free variable.
(term_typing:var/1)Var is a free variable.
(term_typing:var/1)RestOfVars is a free variable.
(basic_props:list/2)ListOfVars is a list of fd_items.
(user(... /fd_doc):fd_item/1)Var is a finite domain entity, i.e. either a finite domains variable or an integer.
(basic_props:list/2)RestOfVars is a list of fd_items.

PREDICATE

choose_free_var/2:

Usage:choose_free_var(ListOfVars,Var)

Returns a free variable Var from a list of fd items ListOfVars. Currently it always returns the first free variable of the list.

The following properties should hold at call time:
(term_typing:nonvar/1)ListOfVars is currently a term which is not a free variable.
(term_typing:var/1)Var is a free variable.
(basic_props:list/2)ListOfVars is a list of fd_items.
(term_typing:var/1)Var is a free variable.

PREDICATE

choose_var_nd/2:

Usage:choose_var_nd(ListOfVars,Var)

Returns non deterministically an fd item Var from a list of fd items ListOfVars .

The following properties should hold at call time:
(term_typing:nonvar/1)ListOfVars is currently a term which is not a free variable.
(term_typing:var/1)Var is a free variable.
(basic_props:list/2)ListOfVars is a list of fd_items.
(user(... /fd_doc):fd_item/1)Var is a finite domain entity, i.e. either a finite domains variable or an integer.

PREDICATE

choose_value/2:

Usage:choose_value(Var,Value)

Produces an integer value Value from the domain of Var. On backtracking returns all possible values for Var.

The following properties should hold at call time:
(term_typing:nonvar/1)Var is currently a term which is not a free variable.
(term_typing:var/1)Value is a free variable.
(user(... /fd_doc):fd_item/1)Var is a finite domain entity, i.e. either a finite domains variable or an integer.
(basic_props:int/1)Value is an integer.

PREDICATE

retrieve_range/2:

Usage:retrieve_range(Var,Range)

Returns in Range the range of an fd item Var.

The following properties should hold at call time:
(term_typing:nonvar/1)Var is currently a term which is not a free variable.
(term_typing:var/1)Range is a free variable.
(term_typing:var/1)Var is a free variable.
(user(... /fd_doc):fd_range/1)Range is the range of a finite domain entity.

PREDICATE

retrieve_store/2:

Usage:retrieve_store(Var,Store)

Returns in Store a representation of the constraint store of an fd item Var.

The following properties should hold at call time:
(term_typing:nonvar/1)Var is currently a term which is not a free variable.
(term_typing:var/1)Store is a free variable.
(term_typing:var/1)Var is a free variable.
(user(... /fd_doc):fd_store/1)Store is a representation of the constraint store of a finite domain entity.

PREDICATE

glb/2:

Usage:glb(Var,LowerBound)

Returns in LowerBound the lower bound of the range of Var.

The following properties should hold at call time:
(term_typing:nonvar/1)Var is currently a term which is not a free variable.
(term_typing:var/1)LowerBound is a free variable.
(user(... /fd_doc):fd_item/1)Var is a finite domain entity, i.e. either a finite domains variable or an integer.
(basic_props:int/1)LowerBound is an integer.

PREDICATE

lub/2:

Usage:lub(Var,UpperBound)

Returns in UpperBound the upper bound of the range of Var.

The following properties should hold at call time:
(term_typing:nonvar/1)Var is currently a term which is not a free variable.
(term_typing:var/1)UpperBound is a free variable.
(user(... /fd_doc):fd_item/1)Var is a finite domain entity, i.e. either a finite domains variable or an integer.
(basic_props:int/1)UpperBound is an integer.

PREDICATE

bounds/3:

Usage:bounds(Var,LowerBound,UpperBound)

Returns in LowerBound and UpperBound the lower and upper bounds of the range of Var.

The following properties should hold at call time:
(term_typing:nonvar/1)Var is currently a term which is not a free variable.
(term_typing:var/1)LowerBound is a free variable.
(term_typing:var/1)UpperBound is a free variable.
(user(... /fd_doc):fd_item/1)Var is a finite domain entity, i.e. either a finite domains variable or an integer.
(basic_props:int/1)LowerBound is an integer.
(basic_props:int/1)UpperBound is an integer.

PREDICATE

retrieve_list_of_values/2:

Usage:retrieve_list_of_values(Var,ListOfValues)

Returns in ListOfValues an enumeration of al the values in the range of Var

The following properties should hold at call time:
(term_typing:nonvar/1)Var is currently a term which is not a free variable.
(term_typing:var/1)ListOfValues is a free variable.
(user(... /fd_doc):fd_item/1)Var is a finite domain entity, i.e. either a finite domains variable or an integer.
(basic_props:list/2)ListOfValues is a list of ints.

Constraint programming over finite domains

Usage and interface

Documentation on exports

Package Sections

Global Links

Indices