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relationalai.experimental.solvers.implies()

implies(left: SolverExpression, right: SolverExpression) -> SolverExpression

Returns a solver expression representing a logical implication: if left is true, then right must also be true. Both left and right must be binary-valued solver expressions, such as binary variables or logical comparisons. Must be called in a Model.rule() or solvers.operators() context.

Parameters

Name	Type	Description
`left`	`SolverExpression`	The condition that riggers the implication. Must evaluate to a binary value (`True`/`False` or `1`/`0`), such as a binary variable or a logical comparison.
`right`	`SolverExpression`	The outcome enforced when `left` is true. Must also evaluate to a binary value.

Returns

A SolverExpression object.

Example

Use implies() with the SolverModel.constraint() method to encode a dependency between two conditions:

import relationalai as rai
from relationalai.experimental import solvers


# Create a RAI model.
model = rai.Model("WeeklyShiftAssignment")

# Declare entity types and properties.

# Entity types.
Employee = model.Type("Employee")
Shift = model.Type("Shift")
Day = model.Type("Day")
Available = model.Type("Available")
Scenario = model.Type("Scenario")  # All possible employee–shift–day combinations.
Assignment = model.Type("Assignment")  # A Scenario that is assigned.

# Properties.
Employee.name.declare()
Shift.name.declare()
Shift.capacity.declare()
Available.employee.declare()
Available.day.declare()
Scenario.employee.declare()
Scenario.shift.declare()
Scenario.day.declare()

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# Define sample data.

# Employees.
with model.rule(dynamic=True):
    for name in ["Alice", "Bob", "Carol", "Dave", "Eve"]:
        Employee.add(name=name)

# Shifts.
with model.rule():
    Shift.add(name="Morning").set(capacity=2)
    Shift.add(name="Evening").set(capacity=3)

# Days of the week.
with model.rule(dynamic=True):
    for name in ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]:
        Day.add(name=name)

# Employee-day availability.
with model.rule(dynamic=True):
    # Alice works weekdays only
    for name in ["Mon", "Tue", "Wed", "Thu", "Fri"]:
        Available.add(employee=Employee(name="Alice"), day=Day(name=name))
    # Bob works all days
    Available.add(employee=Employee(name="Bob"), day=Day())
    # Carol works weekends only
    for name in ["Sat", "Sun"]:
        Available.add(employee=Employee(name="Carol"), day=Day(name=name))
    # Dave works Mon/Wed/Fri
    for name in ["Mon", "Wed", "Fri"]:
        Available.add(employee=Employee(name="Dave"), day=Day(name=name))
    # Eve works Tue/Thu/Sat
    for name in ["Tue", "Thu", "Sat"]:
        Available.add(employee=Employee(name="Eve"), day=Day(name=name))

# All possible employee–shift–day combinations
with model.rule():
    Scenario.add(employee=Employee(), shift=Shift(), day=Day())

# Create a SolverModel instance from the model.
solver_model = solvers.SolverModel(model)

# Define solver variables.

# Scenario assignment: binary variable for each employee–shift–day combination.
with model.rule():
    scenario = Scenario()
    solver_model.variable(
        scenario,
        type="zero_one",
        name_args=["assigned", scenario.employee.name, scenario.day.name, scenario.shift.name],
    )

# Define solver constraints.

# If an employee is assigned the morning shift, they are not assigned the evening shift on the same day.
with solvers.operators():
    works_morning = Scenario(shift=Shift(name="Morning"))
    works_evening = Scenario(
        shift=Shift(name="Evening"),
        employee=works_morning.employee,
        day=works_morning.day
    )
    solver_model.constraint(
        solvers.implies(works_morning, solvers.not_(works_evening))
    )

See Also