10.39.2.1 Exported Predicates

The predicates described here operate on a data structure FznState representing a FlatZinc program and consisting of the following members:

This data structure 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 which is initialized with respect to FznStream.

Exceptions: Exceptions regarding errors in FznStream (see Zinc Errors).

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

Exceptions:

Consider the following FlatZinc program for solving the 4 Queens problem located in library('zinc/examples/queen4.fzn'). (Note that FlatZinc programs are not intended to be written (or read) by humans, but rather to be automatically generated. One method to generate FlatZinc programs is described in MiniZinc.)

                               
% 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 part of the FlatZinc program represented by FznState to find 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.

Exceptions: An instatiation error if the output variables are not instantiated.

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),
          fzn_output(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 part of queen4.fzn, respectively. Finally, the fourth line runs the output part of queen4.fzn which means that 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:

Exceptions: An existence error if Id is not an identifier of FznState.

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.

Exceptions: An existence error if there is no objective in FznState.

A possible usage 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:

     | ?- 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. They both take as optional argument a list Options which can be used to change the default behavior of the execution. This list may contain zero or more of the following:

solutions(NumberOfSolutions)
where NumberOfSolutions must be an integer greater than zero or the atom all. Describes the number of solutions to search for, default is 1.
output(File)
where File must be the name of a writable file. Causes any output written on the current output stream to be directed to File.
statistics(Boolean)
where Boolean must be true or false (default). If true, the following statistics are written on the current output stream (see the built-in statistics/[0,2] and fd_statistics/[0,2] of library(clpfd) for more detailed information on their meaning):
runtime
Total running time (milliseconds), including parsing the FlatZinc program.
solvetime
Running time (milliseconds) for posting the constraints and performing the search.
solutions
The number of solutions found.
constraints
The number of constraints created.
backtracks
The number of times a contradiction was found by a domain being wiped out, or by a global constraint signalling failure.
prunings
The number of times a domain was pruned.

timeout(Time)
where Time must be an integer between (not including) 0 and 2147483647. Stops the computation if it has not finished before Time milliseconds has elapsed
fzn_run_stream(+FznStream)
fzn_run_stream(+FznStream, +Options)
FznStream is a FlatZinc input stream and Options is a list of options as described above. Performs the following steps:
  1. Loads the FlatZinc program (fzn_load_stream/2), initializing a FlatZinc state.
  2. Posts the constraints of the FlatZinc program (fzn_post/1).
  3. Runs the solve part of the FlatZinc program (fzn_solve/1).
  4. 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 ten consecutive equal signs are output on a separate line.

Exceptions:


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 as described above. This predicate is just a wrapper around fzn_run_stream/[1,2] handling stream opening and closing.

Exceptions:

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 containing zero or more of the following (currently, this is the only available option):

Exceptions: Exceptions related to the opening of File for writing.

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), scalar_product([1,-1], [A,B], #\=, 1), A#\=B, scalar_product([1,-1], [A,B], #\=, -1), scalar_product([1,-1], [A,C], #\=, 2), A#\=C, scalar_product([1,-1], [A,C], #\=, -2), scalar_product([1,-1], [A,D], #\=, 3), A#\=D, scalar_product([1,-1], [A,D], #\=, -3), scalar_product([1,-1], [B,C], #\=, 1), B#\=C, scalar_product([1,-1], [B,C], #\=, -1), scalar_product([1,-1], [B,D], #\=, 2), B#\=D, scalar_product([1,-1], [B,D], #\=, -2), scalar_product([1,-1], [C,D], #\=, 1), C#\=D, scalar_product([1,-1], [C,D], #\=, -1).

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