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)
Exceptions: Exceptions regarding errors in FznStream
(see Zinc Errors).
fzn_load_file(
+FznFile,
-FznState)
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.fznint: n = 4; array[1 .. 4] of var 1 .. 4: q; constraint int_lin_ne([ 1, -1 ], [ q[1], q[2] ], -1); 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[3] ], -2); 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[4] ], -3); 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[2], q[3] ], -1); 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[4] ], -2); 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[3], q[4] ], -1); constraint int_lin_ne([ 1, -1 ], [ q[3], q[4] ], 1); constraint int_ne(q[3], q[4]); solve satisfy; output [ "A solution to the ", "4", " Queens problem: ", show(q), "\n"];
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)
fzn_solve(
+FznState)
fzn_output(
+FznState)
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:
A solution to the 4 Queens problem: [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:
A solution to the 4 Queens problem: [3, 1, 4, 2]
fzn_identifier(
+FznState,
+Id,
-Value)
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.
string
is translated into a Prolog list of character codes.
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)
var int
or a var bool
is allowed in 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:
A solution to the 4 Queens problem: [2, 4, 1, 3] A solution to the 4 Queens problem: [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:
A solution to the 4 Queens problem: [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 (currently, this is the only available option):
solutions(
NumberOfSolutions)
all
. Describes the number of solutions to search
for, default is 1.
fzn_run_stream(
+FznStream)
fzn_run_stream(
+FznStream,
+Options)
fzn_load_stream/2
), initializing a
FlatZinc state.
fzn_post/1
).
fzn_solve/1
).
fzn_output/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 one of the following is written on the current output stream:
Exceptions:
all
.
fzn_run_file(
+FznFile)
fzn_run_file(
+FznFile,
+Options)
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)
library(clpfd)
.
Options is a list containing zero or more of the following (currently, this is the only available option):
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]]) :- domain([A,B,C,D], 1, 4), scalar_product([1,-1], [A,B], #\=, -1), scalar_product([1,-1], [A,B], #\=, 1), A#\=B, scalar_product([1,-1], [A,C], #\=, -2), scalar_product([1,-1], [A,C], #\=, 2), A#\=C, scalar_product([1,-1], [A,D], #\=, -3), scalar_product([1,-1], [A,D], #\=, 3), A#\=D, scalar_product([1,-1], [B,C], #\=, -1), scalar_product([1,-1], [B,C], #\=, 1), B#\=C, scalar_product([1,-1], [B,D], #\=, -2), scalar_product([1,-1], [B,D], #\=, 2), B#\=D, scalar_product([1,-1], [C,D], #\=, -1), scalar_product([1,-1], [C,D], #\=, 1), C#\=D.