org.clafer.choco.constraint

Class Constraints

java.lang.Object

org.clafer.choco.constraint.Constraints

public class Constraints
extends Object

Custom Choco constraints. Designed for Clafer. Note that these constraints requires that the envelope and kernel to be in sorted order from lowest to highest, which is not explicitly enforced by Choco.

Author:

jimmy

Method Summary

Methods

Modifier and Type	Method and Description
static solver.constraints.Constraint	acyclic(solver.variables.IntVar... edges) A constraint enforcing no cycles.
static solver.constraints.Constraint	and(solver.variables.BoolVar... operands) A constraint enforcing {@code operands[0] ∧ operands[1] ∧ ...
static solver.constraints.Constraint	arrayToSet(solver.variables.IntVar[] ivars, solver.variables.SetVar svar, solver.variables.IntVar svarCard) A constraint enforcing {ivar[0], ivar[1], ..., ivar[n]} = svar.
static solver.constraints.Constraint	arrayToSet(solver.variables.IntVar[] ivars, solver.variables.SetVar svar, solver.variables.IntVar svarCard, Integer globalCardinality) A constraint enforcing {ivar[0], ivar[1], ..., ivar[n]} = svar and for all constant k, |{i | ivar[i] = k}| ≤ globalCardinality.
static solver.constraints.Constraint	difference(solver.variables.SetVar minuend, solver.variables.IntVar minuendCard, solver.variables.SetVar subtrahend, solver.variables.IntVar subtrahendCard, solver.variables.SetVar difference, solver.variables.IntVar differenceCard) A constraint enforcing minuend - subtrahend = difference.
static solver.constraints.Constraint	equal(solver.variables.SetVar set1, solver.variables.IntVar set1Card, solver.variables.SetVar set2, solver.variables.IntVar set2Card) A constraint enforcing set1 = set2.
static solver.constraints.Constraint	filterString(solver.variables.SetVar set, solver.variables.IntVar setCard, int offset, solver.variables.IntVar[] string, solver.variables.IntVar[] result) A constraint enforcing result[i] = if i < array(set).length then string[array(set)[i] - offset] else -1 where array is the sorted array representation of the set.
static solver.constraints.Constraint	ifThenElse(solver.variables.BoolVar antecedent, solver.variables.BoolVar consequent, solver.variables.BoolVar alternative) A constraint enforcing antecedent => consequent && !antecedent => alternative.
static solver.constraints.Constraint	intChannel(solver.variables.SetVar[] sets, solver.variables.IntVar[] ints) A constraint enforcing x ∈ sets[i] <=> ints[x] = i.
static solver.constraints.Constraint	intersection(solver.variables.SetVar[] operands, solver.variables.IntVar[] operandCards, solver.variables.SetVar intersection, solver.variables.IntVar intersectionCard) A constraint enforcing {@code operands[0] ∩ operands[1] ∩ ...
static solver.constraints.Constraint	joinFunction(solver.variables.SetVar take, solver.variables.IntVar takeCard, solver.variables.IntVar[] refs, solver.variables.SetVar to, solver.variables.IntVar toCard) A constraint enforcing take.refs = to where refs is a function.
static solver.constraints.Constraint	joinFunction(solver.variables.SetVar take, solver.variables.IntVar takeCard, solver.variables.IntVar[] refs, solver.variables.SetVar to, solver.variables.IntVar toCard, Integer globalCardinality) A constraint enforcing take.refs = to where refs is a function and for all k in take, |{i | refs[i] = k}| ≤ globalCardinality.
static solver.constraints.Constraint	joinInjectiveRelation(solver.variables.SetVar take, solver.variables.IntVar takeCard, solver.variables.SetVar[] children, solver.variables.IntVar[] childrenCards, solver.variables.SetVar to, solver.variables.IntVar toCard) A constraint enforcing take.children = to where children is an injective relation.
static solver.constraints.Constraint	joinRelation(solver.variables.SetVar take, solver.variables.SetVar[] children, solver.variables.SetVar to) Deprecated.
static solver.constraints.Constraint	lexChainChannel(solver.variables.IntVar[][] strings, solver.variables.IntVar[] ints) A constraint enforcing strings[i] ≤ strings[j] <=> ints[i] ≤ ints[j] and strings[i] = strings[j] <=> ints[i] = ints[j].
static solver.constraints.Constraint	lone(solver.variables.BoolVar... operands) A constraint enforcing {@code operands[0] + operands[1] + ...
static solver.constraints.Constraint	mask(solver.variables.SetVar set, solver.variables.IntVar setCard, solver.variables.SetVar masked, solver.variables.IntVar maskedCard, int from, int to) A constraint enforcing {i + from | i ∈ member} = set ∩ {from, from + 1, ..., to - 1}.
static solver.constraints.Constraint	notEqual(solver.variables.SetVar set, int[] constant) A constraint enforcing set ≠ {constant}.
static solver.constraints.Constraint	notEqual(solver.variables.SetVar set1, solver.variables.IntVar set1Card, solver.variables.SetVar set2, solver.variables.IntVar set2Card) A constraint enforcing set1 ≠ set2.
static solver.constraints.Constraint	notMember(solver.variables.IntVar element, solver.variables.SetVar set) A constraint enforcing element ∉ set.
static solver.constraints.Constraint	one(solver.variables.BoolVar... operands) A constraint enforcing {@code operands[0] + operands[1] + ...
static solver.constraints.Constraint	or(solver.variables.BoolVar... operands) A constraint enforcing {@code operands[0] ∨ operands[1] ∨ ...
static solver.constraints.Constraint	or(solver.constraints.Constraint... constraints) A constraint enforcing {@code constraints[0] ∨ constraints[1] ∨ ...
static solver.constraints.Constraint	reifyEqual(solver.variables.BoolVar reify, solver.variables.IntVar variable, int constant) A constraint enforcing reify <=> (variable = constant).
static solver.constraints.Constraint	reifyEqual(solver.variables.BoolVar reify, solver.variables.IntVar v1, solver.variables.IntVar v2) A constraint enforcing reify <=> (v1 = v2).
static solver.constraints.Constraint	reifyNotEqual(solver.variables.BoolVar reify, solver.variables.IntVar variable, int constant) A constraint enforcing reify <=> (variable ≠ constant).
static solver.constraints.Constraint	reifyNotEqual(solver.variables.BoolVar reify, solver.variables.IntVar v1, solver.variables.IntVar v2) A constraint enforcing reify <=> (v1 ≠ v2).
static solver.constraints.Constraint	selectN(solver.variables.BoolVar[] bools, solver.variables.IntVar n) A constraint enforcing that bools[i] <=> i < n.
static solver.constraints.Constraint	setSum(solver.variables.SetVar set, solver.variables.IntVar setCard, solver.variables.IntVar sum) A constraint enforcing Σ set= sum.
static solver.constraints.Constraint	singleton(solver.variables.IntVar ivar, solver.variables.SetVar svar) A constraint enforcing {ivar} = svar.
static solver.constraints.Constraint	singleton(solver.variables.IntVar ivar, solver.variables.SetVar svar, solver.variables.IntVar svarCard) A constraint enforcing {ivar} = svar and svarCard = 1.
static solver.constraints.Constraint	sortedSets(solver.variables.SetVar[] sets, solver.variables.IntVar[] setCards) A constraint enforcing {@code array(sets[0]) ++ array(sets[1]) ++ ...
static solver.constraints.Constraint	subsetEq(solver.variables.SetVar sub, solver.variables.IntVar subCard, solver.variables.SetVar sup, solver.variables.IntVar supCard) A constraint enforcing sub ⊆ sup.
static solver.constraints.Constraint	union(solver.variables.SetVar[] operands, solver.variables.IntVar[] operandCards, solver.variables.SetVar union, solver.variables.IntVar unionCard, boolean disjoint) A constraint enforcing {@code operands[0] ∪ operands[1] ∪ ...
static solver.constraints.Constraint	unreachable(solver.variables.IntVar[] edges, int from, int to) A constraint enforcing no path from one node to another.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

and

public static solver.constraints.Constraint and(solver.variables.BoolVar... operands)

A constraint enforcing operands[0] ∧ operands[1] ∧ ... ∧ operands[n].

Parameters:

operands - the operands

Returns:

constraint operands[0] ∧ operands[1] ∧ ... ∧ operands[n]

lone

public static solver.constraints.Constraint lone(solver.variables.BoolVar... operands)

A constraint enforcing operands[0] + operands[1] + ... + operands[n] ≤ 1.

Parameters:

operands - the operands

Returns:

constraint operands[0] + operands[1] + ... + operands[n] ≤ 1

one

public static solver.constraints.Constraint one(solver.variables.BoolVar... operands)

A constraint enforcing operands[0] + operands[1] + ... + operands[n] = 1.

Parameters:

operands - the operands

Returns:

constraint operands[0] + operands[1] + ... + operands[n] = 1

or

public static solver.constraints.Constraint or(solver.variables.BoolVar... operands)

A constraint enforcing operands[0] ∨ operands[1] ∨ ... ∨ operands[n].

Parameters:

operands - the operands

Returns:

constraint operands[0] ∨ operands[1] ∨ ... ∨ operands[n]

or

public static solver.constraints.Constraint or(solver.constraints.Constraint... constraints)

A constraint enforcing constraints[0] ∨ constraints[1] ∨ ... ∨ constraints[n]. The reason this constraint is useful is because it does not require introducing new reified variables to the solver thus can be added dynamically while the solver is in progress.

Parameters:

constraints - the constraints

Returns:

constraint constraints[0] ∨ constraints[1] ∨ ... ∨ constraints[n]

ifThenElse

public static solver.constraints.Constraint ifThenElse(solver.variables.BoolVar antecedent,
                                       solver.variables.BoolVar consequent,
                                       solver.variables.BoolVar alternative)

A constraint enforcing antecedent => consequent && !antecedent => alternative.

Parameters:

antecedent - the antecedent

consequent - the consequent

alternative - the alternative

Returns:

constraint antecedent => consequent && !antecedent => alternative

reifyEqual

public static solver.constraints.Constraint reifyEqual(solver.variables.BoolVar reify,
                                       solver.variables.IntVar variable,
                                       int constant)

A constraint enforcing reify <=> (variable = constant).

Parameters:

reify - the reified constraint

variable - the variable

constant - the constant

Returns:

constraint reify <=> (variable = constant)

reifyEqual

public static solver.constraints.Constraint reifyEqual(solver.variables.BoolVar reify,
                                       solver.variables.IntVar v1,
                                       solver.variables.IntVar v2)

A constraint enforcing reify <=> (v1 = v2).

Parameters:

reify - the reified constraint

v1 - the first variable

v2 - the second variable

Returns:

constraint reify <=> (v1 = v2)

reifyNotEqual

public static solver.constraints.Constraint reifyNotEqual(solver.variables.BoolVar reify,
                                          solver.variables.IntVar variable,
                                          int constant)

A constraint enforcing reify <=> (variable ≠ constant).

Parameters:

reify - the reified constraint

variable - the variable

constant - the constant

Returns:

constraint reify <=> (variable ≠ constant)

reifyNotEqual

public static solver.constraints.Constraint reifyNotEqual(solver.variables.BoolVar reify,
                                          solver.variables.IntVar v1,
                                          solver.variables.IntVar v2)

A constraint enforcing reify <=> (v1 ≠ v2).

Parameters:

reify - the reified constraint

v1 - the first variable

v2 - the second variable

Returns:

constraint reify <=> (v1 ≠ v2)

equal

public static solver.constraints.Constraint equal(solver.variables.SetVar set1,
                                  solver.variables.IntVar set1Card,
                                  solver.variables.SetVar set2,
                                  solver.variables.IntVar set2Card)

A constraint enforcing set1 = set2. Does not enforce that set1Card = |set1Card| nor set2Card = |set2Card| because of how the compilation works, it is already enforced elsewhere.

Parameters:

set1 - the left set

set1Card - the cardinality of set1

set2 - the right set

set2Card - the cardinality of set2

Returns:

constraint set1 = set2

notEqual

public static solver.constraints.Constraint notEqual(solver.variables.SetVar set1,
                                     solver.variables.IntVar set1Card,
                                     solver.variables.SetVar set2,
                                     solver.variables.IntVar set2Card)

A constraint enforcing set1 ≠ set2.

Parameters:

set1 - the left set

set1Card - the cardinality of set1

set2 - the right set

set2Card - the cardinality of set2

Returns:

constraint set1 ≠ set2

notEqual

public static solver.constraints.Constraint notEqual(solver.variables.SetVar set,
                                     int[] constant)

A constraint enforcing set ≠ {constant}.

Parameters:

set - the set

constant - the constant

Returns:

constraint set1 ≠ set2

notMember

public static solver.constraints.Constraint notMember(solver.variables.IntVar element,
                                      solver.variables.SetVar set)

A constraint enforcing element ∉ set.

Parameters:

element - the element

set - the set

Returns:

constraint element ∉ set.

subsetEq

public static solver.constraints.Constraint subsetEq(solver.variables.SetVar sub,
                                     solver.variables.IntVar subCard,
                                     solver.variables.SetVar sup,
                                     solver.variables.IntVar supCard)

A constraint enforcing sub ⊆ sup. Does not enforce that subCard = |sub| nor supCard = |sup| because of how the compilation works, it is already enforced elsewhere.

Parameters:

sub - the subset

subCard - the cardinality of sub

sup - the superset

supCard - the cardinality of sup

Returns:

constraint sub ⊆ sup

intChannel

public static solver.constraints.Constraint intChannel(solver.variables.SetVar[] sets,
                                       solver.variables.IntVar[] ints)

A constraint enforcing x ∈ sets[i] <=> ints[x] = i.

Parameters:

sets - the sets

ints - the integers

Returns:

constraint x ∈ sets[i] <=> ints[x] = i

sortedSets

public static solver.constraints.Constraint sortedSets(solver.variables.SetVar[] sets,
                                       solver.variables.IntVar[] setCards)

A constraint enforcing array(sets[0]) ++ array(sets[1]) ++ ... ++ array(sets[n]) ∈ N where array is the sorted array representation of the set, ++ is append, and N = {[0,1,...,i] | i ≥ 0}.

Parameters:

sets - the sets

setCards - the cardinalities of sets

Returns:

constraint array(sets[0]) ++ array(sets[1]) ++ ... ++ array(sets[n]) ∈ N

lexChainChannel

public static solver.constraints.Constraint lexChainChannel(solver.variables.IntVar[][] strings,
                                            solver.variables.IntVar[] ints)

A constraint enforcing strings[i] ≤ strings[j] <=> ints[i] ≤ ints[j] and strings[i] = strings[j] <=> ints[i] = ints[j].

Parameters:

strings - the strings

ints - the integers

Returns:

constraint strings[i] ≤ strings[j] <=> ints[i] ≤ ints[j] and strings[i] = strings[j] <=> ints[i] = ints[j]

selectN

public static solver.constraints.Constraint selectN(solver.variables.BoolVar[] bools,
                                    solver.variables.IntVar n)

A constraint enforcing that bools[i] <=> i < n.

Parameters:

bools - the booleans

n - the number of true booleans

Returns:

constraint bools[i] <=> i < n

acyclic

public static solver.constraints.Constraint acyclic(solver.variables.IntVar... edges)

A constraint enforcing no cycles. edges[i] = j implies that there is a directed edge from node i to node j. edges[i] = edges.length implies that there are no direct edges from node i.

Parameters:

edges - the edges of the graph

Returns:

constraint enforcing no cycles

unreachable

public static solver.constraints.Constraint unreachable(solver.variables.IntVar[] edges,
                                        int from,
                                        int to)

A constraint enforcing no path from one node to another. edges[i] = j implies that there is a directed edge from node i to node j. edges[i] ≥ edges.length implies that there are no direct edges from node i.

Parameters:

edges - the edges of the graph

Returns:

constraint enforcing no path from one node to another

filterString

public static solver.constraints.Constraint filterString(solver.variables.SetVar set,
                                         solver.variables.IntVar setCard,
                                         int offset,
                                         solver.variables.IntVar[] string,
                                         solver.variables.IntVar[] result)

A constraint enforcing result[i] = if i < array(set).length then string[array(set)[i] - offset] else -1 where array is the sorted array representation of the set. Does not enforce that setCard = |setCard| because of how the compilation works, it is already enforced elsewhere.

Parameters:

set - the set

setCard - the cardinality of set

offset - the offset

string - the string

result - the result

Returns:

constraint result[i] = if i < array(set).length then string[array(set)[i] - offset] else -1

setSum

public static solver.constraints.Constraint setSum(solver.variables.SetVar set,
                                   solver.variables.IntVar setCard,
                                   solver.variables.IntVar sum)

A constraint enforcing Σ set= sum. Does not enforce that sumCard = |sum| because of how the compilation works, it is already enforced elsewhere.

More * efficient than the standard operation in the Choco library when the cardinality is bounded to be relatively small.

For example:

   Animal 2
     Age -> integer
   [Animal.Age = 1000]
 

Animal.Age is a set with a very large envelope. However, due to static analysis of the model, it is easy to see that the cardinality must be 2. In general, the cardinality is bounded by the scope of Age, although often times the analysis will find a tighter bound. Once the first integer x is selected for the set, the second integer 1000 - x is already determined due to cardinality = 2. Since the Choco library's setSum constraint is not given the cardinality, it cannot make this deduction.

Parameters:

set - the set of integers

setCard - the cardinality of set

sum - the sum of the set

Returns:

constraint Σ set= sum

singleton

public static solver.constraints.Constraint singleton(solver.variables.IntVar ivar,
                                      solver.variables.SetVar svar)

A constraint enforcing {ivar} = svar.

Parameters:

ivar - the integer

svar - the singleton set

Returns:

constraint {ivar} = svar

singleton

public static solver.constraints.Constraint singleton(solver.variables.IntVar ivar,
                                      solver.variables.SetVar svar,
                                      solver.variables.IntVar svarCard)

A constraint enforcing {ivar} = svar and svarCard = 1. Does not enforce that svarCard = |svarCard| because of how the compilation works, it is already enforced elsewhere.

Parameters:

ivar - the integer

svar - the singleton set

svarCard - the cardinality of svar

Returns:

constraint {ivar} = svar

arrayToSet

public static solver.constraints.Constraint arrayToSet(solver.variables.IntVar[] ivars,
                                       solver.variables.SetVar svar,
                                       solver.variables.IntVar svarCard)

A constraint enforcing {ivar[0], ivar[1], ..., ivar[n]} = svar.

Parameters:

ivars - the array

svar - the set

svarCard - the cardinality of svar

Returns:

constraint {ivar[0], ivar[1], ..., ivar[n]} = svar

arrayToSet

public static solver.constraints.Constraint arrayToSet(solver.variables.IntVar[] ivars,
                                       solver.variables.SetVar svar,
                                       solver.variables.IntVar svarCard,
                                       Integer globalCardinality)

A constraint enforcing {ivar[0], ivar[1], ..., ivar[n]} = svar and for all constant k, |{i | ivar[i] = k}| ≤ globalCardinality. Does not enforce that svarCard = |svar| because of how the compilation works, it is already enforced elsewhere.

Parameters:

ivars - the array

svar - the set

svarCard - the cardinality of svar

globalCardinality - the global cardinality of the array elements

Returns:

constraint {ivar[0], ivar[1], ..., ivar[n]} = svar and for all constant k |{i | ivar[i] = k}| ≤ globalCardinality

joinRelation

@Deprecated
public static solver.constraints.Constraint joinRelation(solver.variables.SetVar take,
                                                    solver.variables.SetVar[] children,
                                                    solver.variables.SetVar to)

Deprecated.

joinInjectiveRelation

public static solver.constraints.Constraint joinInjectiveRelation(solver.variables.SetVar take,
                                                  solver.variables.IntVar takeCard,
                                                  solver.variables.SetVar[] children,
                                                  solver.variables.IntVar[] childrenCards,
                                                  solver.variables.SetVar to,
                                                  solver.variables.IntVar toCard)

A constraint enforcing take.children = to where children is an injective relation. The representation of the relation is explained in PropJoinRelation. Does not enforce that the children relation is injective nor takeCard = |take| nor childrenCards[i] = |children[i]| nor toCard = |to| because of how the compilation works, it is already enforced elsewhere.

Parameters:

take - the left-hand side set

takeCard - the cardinality of take

children - the set representation of a injective binary relation

childrenCards - the cardinalities of children

to - the right-hand side set

toCard - the cardinality of to

Returns:

constraint take.children = to

See Also:

PropJoinFunction

joinFunction

public static solver.constraints.Constraint joinFunction(solver.variables.SetVar take,
                                         solver.variables.IntVar takeCard,
                                         solver.variables.IntVar[] refs,
                                         solver.variables.SetVar to,
                                         solver.variables.IntVar toCard)

A constraint enforcing take.refs = to where refs is a function. The representation of the function is explained in PropJoinFunction. Does not enforce that takeCard = |take| nor toCard = |to| because of how the compilation works, it is already enforced elsewhere.

Parameters:

take - the left-hand side set

takeCard - the cardinality of take

refs - the integer representation of a binary function

to - the right-hand side set

toCard - the cardinality of to

Returns:

constraint take.refs = to

See Also:

PropJoinFunction

joinFunction

public static solver.constraints.Constraint joinFunction(solver.variables.SetVar take,
                                         solver.variables.IntVar takeCard,
                                         solver.variables.IntVar[] refs,
                                         solver.variables.SetVar to,
                                         solver.variables.IntVar toCard,
                                         Integer globalCardinality)

A constraint enforcing take.refs = to where refs is a function and for all k in take, |{i | refs[i] = k}| ≤ globalCardinality. The representation of the function is explained in PropJoinFunction. Does not enforce that takeCard = |take| nor toCard = |to| because of how the compilation works, it is already enforced elsewhere.

Parameters:

take - the left-hand side set

takeCard - the cardinality of take

refs - the integer representation of a binary function

to - the right-hand side set

toCard - the cardinality of to

globalCardinality - the global cardinality of the refs function for the domain of take

Returns:

constraint take.refs = to and for all k in take, |{i | refs[i] = k}| ≤ globalCardinality

See Also:

PropJoinFunction

difference

public static solver.constraints.Constraint difference(solver.variables.SetVar minuend,
                                       solver.variables.IntVar minuendCard,
                                       solver.variables.SetVar subtrahend,
                                       solver.variables.IntVar subtrahendCard,
                                       solver.variables.SetVar difference,
                                       solver.variables.IntVar differenceCard)

A constraint enforcing minuend - subtrahend = difference. Does not enforce that minuendCard = |minuend| nor subtrahendCard = |subtrahend| nor differenceCard = |difference| because of how the compilation works, it is already enforced elsewhere.

Parameters:

minuend - the minuend

minuendCard - the cardinality of minuend

subtrahend - the subtrahend

subtrahendCard - the cardinality of subtrahend

difference - the difference

differenceCard - the cardinality of difference

Returns:

constraint minuend - subtrahend = difference

intersection

public static solver.constraints.Constraint intersection(solver.variables.SetVar[] operands,
                                         solver.variables.IntVar[] operandCards,
                                         solver.variables.SetVar intersection,
                                         solver.variables.IntVar intersectionCard)

A constraint enforcing operands[0] ∩ operands[1] ∩ ... ∩ operands[n] = intersection. Does not enforce that operandCards[i] = |operands[i]| nor intersectionCard = |intersection| because of how the compilation works, it is already enforced elsewhere.

Parameters:

operands - the operands

operandCards - the cardinalities of operands

intersection - the intersection

intersectionCard - the cardinality of intersection

Returns:

constraint operands[0] ∩ operands[1] ∩ ... ∩ operands[n] = intersection

union

public static solver.constraints.Constraint union(solver.variables.SetVar[] operands,
                                  solver.variables.IntVar[] operandCards,
                                  solver.variables.SetVar union,
                                  solver.variables.IntVar unionCard,
                                  boolean disjoint)

A constraint enforcing operands[0] ∪ operands[1] ∪ ... ∪ operands[n] = union. Does not enforce that operandCards[i] = |operands[i]| nor unionCard = |union| because of how the compilation works, it is already enforced elsewhere.

Parameters:

operands - the operands

operandCards - the cardinalities of operands

union - the union

unionCard - the cardinality of union

disjoint - the sets are disjoint

Returns:

constraint operands[0] ∪ operands[1] ∪ ... ∪ operands[n] = union

mask

public static solver.constraints.Constraint mask(solver.variables.SetVar set,
                                 solver.variables.IntVar setCard,
                                 solver.variables.SetVar masked,
                                 solver.variables.IntVar maskedCard,
                                 int from,
                                 int to)

A constraint enforcing {i + from | i ∈ member} = set ∩ {from, from + 1, ..., to - 1}. Does not enforce that setCard = |set| nor maskedCard = |masked| because of how the compilation works, it is already enforced elsewhere.

Parameters:

set - the set

setCard - the cardinality of set

masked - the masked set

maskedCard - the cardinality of masked

from - the inclusive start of the mask

to - the exclusive end of the mask

Returns:

constraint {i + from | i ∈ member} = set ∩ {from, from + 1, ..., to - 1}