FlatZinc Exported Predicates (SICStus Prolog)

10.55.2.1 Exported Predicates

The predicates described here operate on a data structure FznState representing a FlatZinc program. The details of FznState is reserved (subject to change). It can be constructed from a FlatZinc program by the predicates fzn_load_stream/2 and fzn_load_file/2 described next, or directly from a MiniZinc program (see MiniZinc).

fzn_load_stream(+FznStream, -FznState): FznStream is a FlatZinc input stream. FznState is a FlatZinc state that is initialized with respect to FznStream.
fzn_load_file(+FznFile, -FznState): FznFile is a FlatZinc file (extension defaults to .fzn). FznState is a FlatZinc state that is initialized with respect to FznFile. This predicate is just a wrapper around fzn_load_stream/2 handling stream opening and closing.

Consider the following FlatZinc program for solving the 4 Queens problem located in library('zinc/examples/queen4.fzn').

% queen4.fzn

int: n = 4;
array[1 .. 4] of var 1 .. 4: q::output_array([ 1 .. 4 ]);
constraint int_lin_ne([ 1, -1 ], [ q[1], q[2] ], 1);
constraint int_ne(q[1], q[2]);
constraint int_lin_ne([ 1, -1 ], [ q[1], q[2] ], -1);
constraint int_lin_ne([ 1, -1 ], [ q[1], q[3] ], 2);
constraint int_ne(q[1], q[3]);
constraint int_lin_ne([ 1, -1 ], [ q[1], q[3] ], -2);
constraint int_lin_ne([ 1, -1 ], [ q[1], q[4] ], 3);
constraint int_ne(q[1], q[4]);
constraint int_lin_ne([ 1, -1 ], [ q[1], q[4] ], -3);
constraint int_lin_ne([ 1, -1 ], [ q[2], q[3] ], 1);
constraint int_ne(q[2], q[3]);
constraint int_lin_ne([ 1, -1 ], [ q[2], q[3] ], -1);
constraint int_lin_ne([ 1, -1 ], [ q[2], q[4] ], 2);
constraint int_ne(q[2], q[4]);
constraint int_lin_ne([ 1, -1 ], [ q[2], q[4] ], -2);
constraint int_lin_ne([ 1, -1 ], [ q[3], q[4] ], 1);
constraint int_ne(q[3], q[4]);
constraint int_lin_ne([ 1, -1 ], [ q[3], q[4] ], -1);
solve satisfy;

A FlatZinc state Queen4State representing the program above can be constructed by typing:

| ?- fzn_load_file(library('zinc/examples/queen4'), Queen4State).

The predicates presented next are used to query an already initialized FlatZinc state.

fzn_post(+FznState): Posts the constraints of the FlatZinc program represented by FznState. May fail if the constraints are inconsistent.
fzn_solve(+FznState): Runs the solve and output parts of the FlatZinc program represented by FznState to find and display an (optimal) solution. Fails if the constraints of the FlatZinc program are inconsistent. Generates the next solution upon backtracking.
fzn_output(+FznState): Outputs the values of the variables in FznState that have been annotated with output_var/0 or output_array/1.

Consider again the FlatZinc program queen4.fzn described above and the following goal at the Prolog top level:

| ?- fzn_load_file(library('zinc/examples/queen4'), Queen4State),
     fzn_post(Queen4State),
     fzn_solve(Queen4State).

The first line initializes Queen4State with respect to queen4.fzn. The second and third line posts the constraints of queen4.fzn and runs the solve and output parts of queen4.fzn, respectively. The following is written on the current output stream:

q = array1d(1..4, [2,4,1,3]);
----------

Upon backtracking the solve and output parts of Queen4State are rerun, which means that the following is written on the current output stream:

q = array1d(1..4, [3,1,4,2]);
----------

fzn_identifier(+FznState, +Id, -Value)

FznState is a FlatZinc state initialized with respect to some FlatZinc program and Id is an identifier of the FlatZinc program. Unifies the FlatZinc value of Id with Value according to the following translation scheme:

A bool is translated into a Prolog integer: false is translated into 0 and true is translated into 1.
An int is translated into a Prolog integer.
A float is translated into a Prolog float.
An range or set is translated into a library(clpfd) range expression (see Syntax of Range Expressions).
An array is translated into a Prolog list containing the (translated) elements of the array. Ordering is preserved such that the nth element of the array is the nth element of the list.
A var is translated into a library(clpfd) domain variable (see CLPFD Interface).

fzn_objective(+FznState, -Objective)

FznState is a FlatZinc state initialized with respect to some FlatZinc program. Unifies Objective with a domain variable representing the FlatZinc objective.

A possible use of fzn_identifier/3 is to post additional library(clpfd) constraints or to apply a Prolog labeling predicate on the FlatZinc variables. For example, given the 4 Queens problem in queen4.fzn described above, the following goal labels the variables to find all solutions:

| ?- use_module(library(clfpd)).
| ?- fzn_load_file(library('zinc/examples/queen4'), Queen4State),
     fzn_post(Queen4State),
     fzn_identifier(Queen4State, q, Q),
     findall(_, (labeling([], Q), fzn_output(Queen4State)), _).

Given this goal, the following is written on the current output stream:

q = array1d(1..4, [2,4,1,3]);
----------
q = array1d(1..4, [3,1,4,2]);
----------

To avoid symmetric solutions where the chess board is rotated 180 degrees, the following goal posts an additional symmetry breaking constraint on the first two queens:

| ?- fzn_load_file(library('zinc/examples/queen4'), Queen4State),
     fzn_post(Queen4State),
     fzn_identifier(Queen4State, q, Q),
     Q = [Q1, Q2|_], Q1 #< Q2,
     findall(_, (labeling([], Q), fzn_output(Queen4State)), _).

Given this goal, the following is written on the current output stream:

q = array1d(1..4, [2,4,1,3]);
----------

Note that, now, only the first one of the previous two solutions is displayed.

The following two predicates can be used to run a FlatZinc program in one go.

fzn_run_stream(+FznStream)

fzn_run_stream(+FznStream, +Options)

FznStream is a FlatZinc input stream and Options is a list of options; see Zinc Options. Performs the following steps:

Loads the FlatZinc program (fzn_load_stream/2), initializing a FlatZinc state.
Posts the constraints of the FlatZinc program (fzn_post/1).
Runs the solve part of the FlatZinc program (fzn_solve/1).
Outputs the values of the variables that have been annotated with output_var/0 or output_array/1.

The two final steps are repeated until the number of solutions as specified in Options have been found or until no more solutions can be found. At this point, if the whole search space have been explored, then ten consecutive equal signs are output on a separate line.

fzn_run_file(+FznFile)

fzn_run_file(+FznFile, +Options)

FznFile is a FlatZinc program file (extension defaults to .fzn) and Options is a list of options; see see Zinc Options. This predicate is just a wrapper around fzn_run_stream/[1,2] handling stream opening and closing.

The next predicate can be used to write the constraints of a FlatZinc program to a file, in the format of library(clpfd).

fzn_dump(+FznState, +File)

fzn_dump(+FznState, +Options, +File)

FznState is a FlatZinc state initialized with respect to some FlatZinc program and File is a writable file (extension defaults to .pl). Writes the constraints of FznState to File in the format of library(clpfd).

Options is a list of options; see see Zinc Options.

Consider again the FlatZinc program queen4.fzn described above and the following goal at the Prolog top level:

| ?- fzn_load_file(library('zinc/examples/queen4'), Queen4State),
     fzn_dump(Queen4State, [variables([q=Q])], queen4).

The file queen4.pl then contains the following:

queen4.pl

:- use_module(library(clpfd)).

query([q=[A,B,C,D]]) :-
        domain([A,B,C,D], 1, 4),
        C#\=D,
        B#\=D,
        B#\=C,
        A#\=D,
        A#\=C,
        A#\=B,
        scalar_product([1,-1], [C,D], #\=, 1),
        scalar_product([1,-1], [C,D], #\=, -1),
        scalar_product([1,-1], [B,D], #\=, 2),
        scalar_product([1,-1], [B,D], #\=, -2),
        scalar_product([1,-1], [B,C], #\=, 1),
        scalar_product([1,-1], [B,C], #\=, -1),
        scalar_product([1,-1], [A,D], #\=, 3),
        scalar_product([1,-1], [A,D], #\=, -3),
        scalar_product([1,-1], [A,C], #\=, 2),
        scalar_product([1,-1], [A,C], #\=, -2),
        scalar_product([1,-1], [A,B], #\=, 1),
        scalar_product([1,-1], [A,B], #\=, -1).

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