linking the jurisdiction and the system

So far we modeled the traffic light system as follows:

LeftGreenArrow ?
RightGreenArrow ?
xor mountLocation

Given our choices of the various jurisdictions:

xor Jurisdiction
UK ?
mux NorthAmerica

we can use constraints to restrict parts of the system.

In Clafer, constraints are formulas of type Boolean and they can be arbitrary first-order logic formulas containing Boolean operators (and: &&, or: ||, not: !, implication: =>, equivalence: <=>), set operators (equality =, union: ++ or ,, subtraction: --, intersection: &) and quantifiers (not exists: no, exactly one: one, exists: some, for all: all) extended with a few relational logic operators (relational join: ., domain restriction: <:, range restriction: :>). The constraint language also supports integers and integer formulas (operators: + - * / ^ and comparisons: > >= < <= =) and string literals ("some text"). Finally there is a set cardinality operator # to compute the size of the set and a ternary operator if then else. For details, see the grammar.

Similarly to OCL, constraints are always declared in the context of some clafer, meaning that the constraint must hold for every instance of that clafer.
Unlike in OCL but similarly to Alloy, constraints always work on sets and relations, never on scalars—a scalar is a singleton set.

In our model, we’d like to say that certain jurisdictions require the presence of certain clafers in the instance. For example, in Europe, the green arrow lamps are used and the lights are mounted in front of intersections. We add the constraints as follows:

The constraints are expressed using square brackets [ ]. Each clafer is interpreted as a set and the default quantifier is some, which means exists. The first constraint, illustrates an implication if there's an instance of Europe then there must be an instance of leftGreenArrow and an instance of rightGreenArrow. The quantifier some can be omitted, as shown in the next two constraints.

The second constraint, illustrates full qualification using the relational join oprerator .: Jurisdiction.Europe is a set of instances of the clafer Jurisdiction joined with the relation Europe (a clafer semantically really is a relation but the join produces a set as in Alloy be ignoring the column on which the join is performed). The Clafer compiler automatically adds the necessary qualification as long as a given clafer can be referenced unambiguously. This is why, in the first and the third constraint, the explicit qualification was dropped.

More information: Tutorial: Constraints

Let’s see what instances we will get now, assuming that we want to restrict the system to UK only. We therefore add another constraint to require the presence of an instance of UK as our jurisdiction.

[ UK ]

After generating the instances, you can edit the model directly in the configurator.

  • Enlarge the view Input Clafer Model and Options using window size buttons window size buttons.
  • Change the constraint [UK] to [Canada].

After each change, the model must be recompiled.

  • Close the instance generator by pressing the button Quit.
  • Press the button Compile right above the text editor.
  • Generate the instances again by pressing Run.

The fact that we see only one instance for UK is good—it means the system is fully configured. However, for Canada, we get four instances which means that the system is only partially specified—we still need to make decisions about the green arrows (e.g., [ leftGreenArrow ] and [ no rightGreenArrow ]). An easy way to make and save decisions is to select or eliminate clafers in the matrix view and copy the corresponding constraints from the view Constraints.

Let’s look at some more differences across the jurisdictions: next nested constraints.

  1. minimal traffic lights
  2. adding variability
  3. grouping choices
  4. complex grouping and nesting