Class: BoolExpr

A class that represents a boolean expression in the model. The expression may depend on one or more variables and therefore its value may be unknown until a solution is found.

Examples

For example, the following code creates two interval variables x and y and a boolean expression isBefore that is true if x ends before y starts, that is, if the end of x is less than or equal to the start of y (see IntExpr.le):

let model = new CP.Model();
let x = model.intervalVar({ length: 10, name: "x" });
let y = model.intervalVar({ length: 20, name: "y" });
let isBefore = x.end().le(y.start());
let result = await CP.solve(model);

Boolean expressions can be used to create constraints using function Model.constraint. In the example above, we may require that isBefore is true:

model.constraint(isBefore);

Optional boolean expressions

OptalCP is using 3-value logic: a boolean expression can be true, false or absent. Typically the the expression is absent only if one or more underlying variables is absent. The value absent means that the expression doesn't have a meaning because one or more underlying variables are absent (they are not part of the solution).

Difference between constraints and boolean expressions

Boolean expressions can take arbitrary value (true, false, or absent) and can be combined into composed expressions (e.g. using and or or).

Constraints can only be true or absent (in a solution) and cannot be combined into composed expressions.

Some functions create constraints directly, e.g. Model.noOverlap. Then, it is not necessary to to pass them to function Model.constraint. It is also not possible to combine constraints into composed expressions such as or(noOverlap(..), noOverlap(..)).

Let's consider a similar example to the one above but with optional interval variables a and b:

let model = new CP.Model();
let a = model.intervalVar({ length: 10, name: "a", optional: true });
let b = model.intervalVar({ length: 20, name: "b", optional: true });
let isBefore = a.end().le(b.start());
model.constraint(isBefore);
let result = await CP.solve(model);

The function Model.constraint requires that the constraint cannot be false in a solution. It could be absent though. Therefore, in our example, there are four kinds of solutions:

1. Both a and b are present and a ends before b starts.
2. Only a is present and b is absent.
3. Only b is present and a is absent.
4. Both a and b are absent.

In the case 1 the expression isBefore is true. In all the other cases isBefore is absent as at least one of the variables a and b is absent, and then isBefore doesn't have a meaning.

Boolean expressions as integer expressions

Class BoolExpr derives from IntExpr. Therefore boolean expressions can be used as integer expressions. In this case true is equal to 1, false is equal to 0, and absent remains absent.

Extends

• IntExpr

Methods

abs()

abs(): IntExpr

Creates an integer expression which is absolute value of the expression.

Returns

IntExpr

Remarks

If the expression has value absent then the resulting expression has also value absent.

Same as Model.abs.

Inherited from

IntExpr.abs

---

and()

and(arg: boolean | BoolExpr): BoolExpr

Returns logical AND of the expression and arg.

Parameters

Parameter	Type
arg	boolean | BoolExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.and.

---

div()

div(arg: number | IntExpr): IntExpr

Returns integer division of the expression arg. The division rounds towards zero.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

IntExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.div.

Inherited from

IntExpr.div

---

eq()

eq(arg: number | IntExpr): BoolExpr

Creates Boolean expression this = arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Use function Model.constraint to create a constraint from this expression.

Same as Model.eq.

Inherited from

IntExpr.eq

---

ge()

ge(arg: number | IntExpr): BoolExpr

Creates Boolean expression this ≥ arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Use function Model.constraint to create a constraint from this expression.

Same as Model.ge.

Inherited from

IntExpr.ge

---

getName()

getName(): undefined | string

Returns the name assigned to the node.

Returns

undefined | string

Inherited from

IntExpr.getName

---

gt()

gt(arg: number | IntExpr): BoolExpr

Creates Boolean expression this > arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Use function Model.constraint to create a constraint from this expression.

Same as Model.gt.

Inherited from

IntExpr.gt

---

guard()

guard(absentValue: number): IntExpr

Creates an expression that replaces value absent by a constant.

Parameters

Parameter	Type	Default value
absentValue	number	0

Returns

IntExpr

Remarks

The resulting expression is:

• equal to the expression if the expression is present
• and equal to absentValue otherwise (i.e. when the expression is absent).

The default value of absentValue is 0.

The resulting expression is never absent.

Same as Model.guard.

Inherited from

IntExpr.guard

---

identity()

identity(arg: number | IntExpr): void

Constrains the expression to be identical to the argument, including their presence status.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

void

Remarks

Identity is different than equality. For example, if x is absent, then x.eq(0) is absent, but x.identity(0) is false.

Same as Model.identity.

Inherited from

IntExpr.identity

---

implies()

implies(arg: boolean | BoolExpr): BoolExpr

Returns implication between the expression and arg.

Parameters

Parameter	Type
arg	boolean | BoolExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.implies.

---

inRange()

inRange(lb: number, ub: number): BoolExpr

Creates Boolean expression lb ≤ this ≤ ub.

Parameters

Parameter	Type
lb	number
ub	number

Returns

BoolExpr

Remarks

If the expression has value absent then the resulting expression has also value absent.

Use function Model.constraint to create a constraint from this expression.

Same as Model.inRange.

Inherited from

IntExpr.inRange

---

le()

le(arg: number | IntExpr): BoolExpr

Creates Boolean expression this ≤ arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Use function Model.constraint to create a constraint from this expression.

Same as Model.le.

Inherited from

IntExpr.le

---

lt()

lt(arg: number | IntExpr): BoolExpr

Creates Boolean expression this < arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Use function Model.constraint to create a constraint from this expression.

Same as Model.lt.

Inherited from

IntExpr.lt

---

max2()

max2(arg: number | IntExpr): IntExpr

Creates an integer expression which is the maximum of the expression and arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

IntExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.max2. See Model.max for n-ary maximum.

Inherited from

IntExpr.max2

---

maximize()

maximize(): void

Maximize the expression. I.e. search for a solution that achieves the maximal value of the expression.

Returns

void

Remarks

Equivalent of function Model.maximize.

The opposite of minimize.

Inherited from

IntExpr.maximize

---

min2()

min2(arg: number | IntExpr): IntExpr

Creates an integer expression which is the minimum of the expression and arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

IntExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.min2. See Model.min for n-ary minimum.

Inherited from

IntExpr.min2

---

minimize()

minimize(): void

Minimize the expression. I.e. search for a solution that achieves the minimal value of the expression.

Returns

void

Remarks

Equivalent of function Model.minimize.

Example

In the following model, we search for a solution that minimizes the maximum end of the two intervals x and y:

let model = new CP.Model();
let x = model.intervalVar({ length: 10, name: "x" });
let y = model.intervalVar({ length: 20, name: "y" });
model.max2(x.end(), y.end()).minimize();
let result = await CP.solve(model);

Inherited from

IntExpr.minimize

---

minus()

minus(arg: number | IntExpr): IntExpr

Returns subtraction of the expression and arg.@remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.minus.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

IntExpr

Inherited from

IntExpr.minus

---

ne()

ne(arg: number | IntExpr): BoolExpr

Creates Boolean expression this ≠ arg.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Use function Model.constraint to create a constraint from this expression.

Same as Model.ne.

Inherited from

IntExpr.ne

---

neg()

neg(): IntExpr

Returns negation of the expression.

Returns

IntExpr

Remarks

If the expression has value absent then the resulting expression has also value absent.

Same as Model.neg.

Inherited from

IntExpr.neg

---

not()

not(): BoolExpr

Returns negation of the expression.

Returns

BoolExpr

Remarks

If the expression has value absent then the resulting expression has also value absent.

Same as Model.not.

---

or()

or(arg: boolean | BoolExpr): BoolExpr

Returns logical OR of the expression and arg.

Parameters

Parameter	Type
arg	boolean | BoolExpr

Returns

BoolExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.or.

---

plus()

plus(arg: number | IntExpr): IntExpr

Returns addition of the expression and the argument.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

IntExpr

Remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.plus.

Inherited from

IntExpr.plus

---

presence()

presence(): BoolExpr

Returns an expression which is true if the expression is present and false when it is absent.

Returns

BoolExpr

Remarks

The resulting expression is never absent.

Same as Model.presenceOf.

Inherited from

IntExpr.presence

---

setName()

setName(name: string): this

Assigns a name to the node.

Parameters

Parameter	Type	Description
name	string	Named to be assigned.

Returns

this

The node itself so it can be used in chained expression.

Remarks

Assigning a name is optional. However is useful for debugging because variable names appear in the development traces. It is also useful for exporting the model to a file (see problem2json).

Example

let model = new CP.Model();
let x = model.intervalVar({ length: 10 }).setName("x");
// The line above is equivalent to:
//   let x = model.intervalVar({ length: 10, name:"x" });
let endOfX = model.endOf(x).setName("endOfX");
let result = await CP.solve(model);

Inherited from

IntExpr.setName

---

times()

times(arg: number | IntExpr): IntExpr

Returns multiplication of the expression and arg.@remarks

If the expression or arg has value absent then the resulting expression has also value absent.

Same as Model.times.

Parameters

Parameter	Type
arg	number | IntExpr

Returns

IntExpr

Inherited from

IntExpr.times