Library for finite domain constraint solving.
The general structure of a specification of an FD problem is as follows:
domain_constraint & fd_constraint & labeling
where:
domain_constraint
specifies the possible range of the FD variables (see constraint domain)
fd_constraint
specifies the constraint to be satisfied by a valid solution
(see constraints #+, #-, allDifferent, etc below)
labeling
is a labeling function to search for a concrete solution.
Note: This library is based on the corresponding library of Sicstus-Prolog
but does not implement the complete functionality of the Sicstus-Prolog library.
However, using the PAKCS interface for external functions, it is relatively
easy to provide the complete functionality.
Datatypes:
LabelingOption
Constructors:
All
| Assumptions
| Bisect
| Down
| Enum
| FirstFail
| FirstFailConstrained
| LeftMost
| Max
| Maximize
| Min
| Minimize
| Step
| Up
Functions:
*#
| +#
| -#
| /=#
| <#
| <=#
| =#
| >#
| >=#
| allDifferent
| all_different
| count
| domain
| indomain
| labeling
| scalarProduct
| sum
|
Summary of exported functions:
|
domain :: [Int] -> Int -> Int -> Success 
|
|
Constraint to specify the domain of all finite domain variables.
|
|
(+#) :: Int -> Int -> Int
|
|
Addition of FD variables.
|
|
(-#) :: Int -> Int -> Int
|
|
Subtraction of FD variables.
|
|
(*#) :: Int -> Int -> Int
|
|
Multiplication of FD variables.
|
|
(=#) :: Int -> Int -> Success
|
|
Equality of FD variables.
|
|
(/=#) :: Int -> Int -> Success
|
|
Disequality of FD variables.
|
|
(<#) :: Int -> Int -> Success
|
|
"Less than" constraint on FD variables.
|
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(<=#) :: Int -> Int -> Success
|
|
"Less than or equal" constraint on FD variables.
|
|
(>#) :: Int -> Int -> Success
|
|
"Greater than" constraint on FD variables.
|
|
(>=#) :: Int -> Int -> Success
|
|
"Greater than or equal" constraint on FD variables.
|
|
sum :: [Int] -> (Int -> Int -> Success) -> Int -> Success
|
|
Relates the sum of FD variables with some integer of FD variable.
|
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scalarProduct :: [Int] -> [Int] -> (Int -> Int -> Success) -> Int -> Success
|
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(scalarProduct cs vs relop v) is satisfied if ((cs*vs) relop v) is satisfied.
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count :: Int -> [Int] -> (Int -> Int -> Success) -> Int -> Success
|
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(count v vs relop c) is satisfied if (n relop c), where n is the number of
elements in the list of FD variables vs that are equal to v, is satisfied.
|
|
allDifferent :: [Int] -> Success
|
|
"All different" constraint on FD variables.
|
|
|
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indomain :: Int -> Success
|
|
Instantiate a single FD variable to its values in the specified domain.
|
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labeling :: [LabelingOption] -> [Int] -> Success
|
|
Instantiate FD variables to their values in the specified domain.
|
|
Prelude
This datatype contains all options to control the instantiated of FD variables
with the enumeration constraint labeling.
Constructors:
-
LeftMost
:: LabelingOption
-
LeftMost - The leftmost variable is selected for instantiation (default)
-
FirstFail
:: LabelingOption
-
FirstFail - The leftmost variable with the smallest domain is selected
(also known as first-fail principle)
-
FirstFailConstrained
:: LabelingOption
-
FirstFailConstrained - The leftmost variable with the smallest domain
and the most constraints on it is selected.
-
Min
:: LabelingOption
-
Min - The leftmost variable with the smalled lower bound is selected.
-
Max
:: LabelingOption
-
Max - The leftmost variable with the greatest upper bound is selected.
-
Step
:: LabelingOption
-
Step - Make a binary choice between x=#b and
x/=#b for the selected variable
x where b is the lower or
upper bound of x (default).
-
Enum
:: LabelingOption
-
Enum - Make a multiple choice for the selected variable for all the values
in its domain.
-
Bisect
:: LabelingOption
-
Bisect - Make a binary choice between x<=#m and
x>#m for the selected variable
x where m is the midpoint
of the domain x
(also known as domain splitting).
-
Up
:: LabelingOption
-
Up - The domain is explored for instantiation in ascending order (default).
-
Down
:: LabelingOption
-
Down - The domain is explored for instantiation in descending order.
-
All
:: LabelingOption
-
All - Enumerate all solutions by backtracking (default).
-
Minimize
:: Int -> LabelingOption
-
Minimize v - Find a solution that minimizes the domain variable v
(using a branch-and-bound algorithm).
-
Maximize
:: Int -> LabelingOption
-
Maximize v - Find a solution that maximizes the domain variable v
(using a branch-and-bound algorithm).
-
Assumptions
:: Int -> LabelingOption
-
Assumptions x - The variable x is unified with the number of choices
made by the selected enumeration strategy when a solution
is found.
domain :: [Int] -> Int -> Int -> Success
Constraint to specify the domain of all finite domain variables.
Example call: (domain xs min max)
-
Parameters:
-
xs
- list of finite domain variables
-
min
- minimum value for all variables in xs
-
max
- maximum value for all variables in xs
(+#) :: Int -> Int -> Int
Addition of FD variables.
-
Further infos:
-
-
defined as left-associative infix operator with precedence 6
(-#) :: Int -> Int -> Int
Subtraction of FD variables.
-
Further infos:
-
-
defined as left-associative infix operator with precedence 6
(*#) :: Int -> Int -> Int
Multiplication of FD variables.
-
Further infos:
-
-
defined as left-associative infix operator with precedence 7
(=#) :: Int -> Int -> Success
Equality of FD variables.
-
Further infos:
-
-
defined as non-associative infix operator with precedence 4
(/=#) :: Int -> Int -> Success
Disequality of FD variables.
-
Further infos:
-
-
defined as non-associative infix operator with precedence 4
(<#) :: Int -> Int -> Success
"Less than" constraint on FD variables.
-
Further infos:
-
-
defined as non-associative infix operator with precedence 4
(<=#) :: Int -> Int -> Success
"Less than or equal" constraint on FD variables.
-
Further infos:
-
-
defined as non-associative infix operator with precedence 4
(>#) :: Int -> Int -> Success
"Greater than" constraint on FD variables.
-
Further infos:
-
-
defined as non-associative infix operator with precedence 4
(>=#) :: Int -> Int -> Success
"Greater than or equal" constraint on FD variables.
-
Further infos:
-
-
defined as non-associative infix operator with precedence 4
sum :: [Int] -> (Int -> Int -> Success) -> Int -> Success
Relates the sum of FD variables with some integer of FD variable.
scalarProduct :: [Int] -> [Int] -> (Int -> Int -> Success) -> Int -> Success
(scalarProduct cs vs relop v) is satisfied if ((cs*vs) relop v) is satisfied.
The first argument must be a list of integers. The other arguments are as
in sum.
count :: Int -> [Int] -> (Int -> Int -> Success) -> Int -> Success
(count v vs relop c) is satisfied if (n relop c), where n is the number of
elements in the list of FD variables vs that are equal to v, is satisfied.
The first argument must be an integer. The other arguments are as
in sum.
allDifferent :: [Int] -> Success
"All different" constraint on FD variables.
Example call: (allDifferent xs)
-
Parameters:
-
xs
- list of FD variables
-
Returns:
-
satisfied if the FD variables in the argument list xs
have pairwise different values.
all_different :: [Int] -> Success
For backward compatibility. Use allDifferent.
indomain :: Int -> Success
Instantiate a single FD variable to its values in the specified domain.
labeling :: [LabelingOption] -> [Int] -> Success
Instantiate FD variables to their values in the specified domain.
Example call: (labeling options xs)
-
Parameters:
-
options
- list of option to control the instantiation of FD variables
-
xs
- list of FD variables that are non-deterministically
instantiated to their possible values.
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(Version 0.4.1 of June 7, 2007) at Aug 28 15:27:24 2008