The predicates described here operate on a data structure FznState representing a FlatZinc program and consisting of the following members:
var_is_introduced
annotation.
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 that 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 that 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 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
.
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).
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:
bool
is translated into a Prolog integer:
false
is translated into 0
and true
is translated
into 1
.
int
is translated into a Prolog integer.
float
is translated into a Prolog float.
library(clpfd)
FD set term (see FD Set Operations).
var int
is translated into a library(clpfd)
domain
variable (see CLPFD Interface).
var bool
is translated into a library(clpfd)
domain
variable with the domain 0..1
(see CLPFD Interface).
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 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:
| ?- 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:
search(Method) since release 4.3
where Method must be one of the atoms bab
and
restart
. Tells the solver which optimization algorithm to use:
branch-and-bound (the default), or to restart the search each time a new
solution is found. The corresponding spfz
option is
-search Method.
solutions(NumberOfSolutions)
where NumberOfSolutions must be an integer greater than zero or
the atom all
. Describes the number of solutions to search
for; the default is 1. The corresponding spfz
options are
-n N and -a.
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.
The corresponding spfz
option is -o File.
ozn_file(File) since release 4.2.3
where File must be the name of an existing file, containing the
MiniZinc output commands that
solns2out
should use. If not given, then solns2out
will
not be used, and the solutions will be printed unformatted.
statistics(Boolean)
where Boolean must be true
or false
(default).
The corresponding spfz
option is -s.
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 should be an integer greater than zero. Stops the
computation if it has not finished before Time milliseconds has
elapsed. In any event, the best solution found so far is reported.
The corresponding spfz
option is -time Time.
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:
fzn_load_stream/2
), initializing a
FlatZinc state.
fzn_post/1
).
fzn_solve/1
).
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.
Exceptions:
all
.
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:
all
.
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):
variables(ListOfVarDef)
where ListOfVarDef is a list of elements of the form
Id=Var where Id is a FlatZinc identifier and
Var is a Prolog variable. Means that Var is unified with the
value of Id after the FlatZinc program is loaded and that
Id=Var is included in a list of arguments to query/1
that is written to File. Default is
ListOfVarDef=[vars=Vars]
, with the meaning that Vars
is a list containing all variables of the FlatZinc state, in the order
they were introduced.
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]]) :- true, domain([A,B,C,D], 1, 4), scalar_product([1,-1], [A,B], #\=, -1), scalar_product([1,-1], [A,B], #\=, 1), scalar_product([1,-1], [A,C], #\=, -2), scalar_product([1,-1], [A,C], #\=, 2), scalar_product([1,-1], [A,D], #\=, -3), scalar_product([1,-1], [A,D], #\=, 3), scalar_product([1,-1], [B,C], #\=, -1), scalar_product([1,-1], [B,C], #\=, 1), scalar_product([1,-1], [B,D], #\=, -2), scalar_product([1,-1], [B,D], #\=, 2), scalar_product([1,-1], [C,D], #\=, -1), scalar_product([1,-1], [C,D], #\=, 1), A#\=B, A#\=C, A#\=D, B#\=C, B#\=D, C#\=D.