Constraint Library Reference

This page documents available constraints in the EUROPA constraint library.

Constraints in NDDL

The tables that follow overviews built-in constraints and functions, available in NDDL or through the programmatic API. Note that:

• Many constraints can have a variable number of parameters; we use letters (a,b,etc) to indicate required parameters, and '...' to indicate that subsequent parameters are optional.
• In the Variable Types column, we describe restrictions on the variable types as follows:
• Numeric: Type is int, float, bool, or some user-defined numeric type. For bool, the usual C/C++ convention is used; 0 <-> false, non-zero -> true, and true -> 1.
• Numeric Intervals: Same as Numeric except that eumerated types (enumerated numeric types are possible) are disallowed.
• Comparable: Comparable variables must all be numeric, or must all be the same type.
• We use lb and ub to refer to the lower and upper bounds, respectively, of a variable's domain.
• Maintainance of constraints means that for any value in the domain of any variable, there exists values in the domains of all other variables such that the desired property holds. For example, a == b means that for any x in the domain of a, there is a y in the domain of b such that x == y (ie. it restricts the domains of a and b to be the intersection of those domains).

Calculation Constraints

These constraints enforce that one variable (usually a) is constrained by a calculation done on the remaining variables.

Constraint	Syntax	Description	Variable Types
distanceSquares	distanceSquares(a,b,c)	c = sqrt(a + b) if a and b are singleton	Numeric intervals
calcDistance	calcDistance(a,b,c,d,e)	a is the Euclidean distance between points (b,c) and (d,e)	Numeric intervals
sin	sin(a,b)	a = sin(b)	Numeric intervals
allDiff	allDiff(a,b,...)	Restrict all domains so the intersection of any pair of domains is empty	Comparable
EqualMaximum	EqualMax(a,b,...)	a = max(b,...)	Numeric
EqualMinimum	EqualMin(a,b,...)	a = min(b,...)	Numeric
CountZeros	CountZeros(a,b,...)	a is the count of the rest that can be zero	Numeric
CountNonZeros	CountNonZeros(a,b,...)	a is the count of the rest that can be non-zero	Numeric
diffSquare	diffSquare(a,b,c)	c = (a - b)^2^ if a and b are singleton	Numeric intervals
card	card(a,b,...)	a must be greater than or equal the count of the other variables that are true	Numeric

Set Constraints

These constraints are likely to be used for set comparisons etc. Note, however, that many of the other constraints listed on this page could be used for sets (ie Comparable variables) just as these constraints could be applied to numeric domains as well.

Constraint	Syntax	Description	Variable Types
subsetOf	subsetOf(a,b)	a is a subset of b	Comparable
memberImply	memberImply(a,b,c,d)	If a is subset of b, then require that c is subset of d	a and b comparable, c and d comparable
Lock	Lock(a,b)	Restrict a's domain to be contained in b's domain	Comparable

Object Hierarchy Constraints

NOTE: Unlike most constraints on this page, which are imposed on variables, these constraints are imposed on objects and tokens.

These constraints are used to assert which object one or more tokens is contained by. Most often, the commonAncestor constraint is used to subgoal across timelines which must share a contained object in common.

Constraint	Syntax	Description	Variable Types
commonAncestor	commonAncestor(a,b,c)	a and b must be contained by the same object in c (or by c itself)	a, b, and c are all objects
hasAncestor	hasAncestor(a,b)	a must be contained by some object in b	a and b are objects

Here's a snippet of code showing the use of the commonAncestor constraint:

Instrument::TakeSample{
    contained_by(Navigator.At at);
    at.location == rock;
    Rover rovers;
    commonAncestor(at.object, this.object, rovers);
}

This ensures that the Navigator object used for the At token and the Instrument object used for the !TakeSample token token are both contained in the same Rover (you wouldn't want one Rover to be in the right place and another to take the sample!).

Miscellaneous Constraints

Constraint	Syntax	Description	Variable Types
UNARY	NA	Restrict a variable's domain: given a variable and a domain, intersect them. Note: this constraint is only available internally and not exposed in NDDL.	Anything
or	or(a,b,...)	At least one of the variables must be true	Numeric
absVal	absVal(a,b)	a.lb >= 0, a.ub = max(abs(b.lb), abs(b.ub)), b.lb >= -a.lb, b.ub <= a.ub	Numeric