Choices

Functional facts are a key part of how Dusa works: if a solution in Dusa contains a fact like color 3 8 is "red" then we know it can’t contain a fact like color 3 8 is "black", because an attribute like color 3 8 is only allowed to “map” to at most one value.

Dusa allows programmers to write programs with multiple solutions by saying that it’s possible to choose multiple attributes for a single value. Choices can be open or closed.

Closed choices

A closed choice lists an attribute, the keyword is and one or more values: if there is more than one value, the values are surrounded by curly braces and separated by commas.

In any solution, the attribute must have one of the listed values.

color 1 4 is { "black", "red" }.
color 2 1 is { "black", "red" }.
color 3 8 is { "black", "red" }.

Explore this example on dusa.rocks

These three closed rules mean that the program has 2 to the power of 3 solutions.

Whenever we write a simple fact about a functional proposition in a program, like color 4 7 is "red", that’s actually describing a closed rule with just one choice: we could equivalently write color 4 7 is { "red" }.

Closed choices describe intersections

This program has two solutions: one just containing a is "blue" and one just containing a is "orange":

a is { "blue", "orange", "red" }.
a is { "blue", "orange", "green" }.

The rules of forward chaining logic programming say that every rule that can fire must fire, and this program has two rules that can fire. If we imagine considering the first choice first, there are three potential solutions: the first just contains a is "blue", the second just contains a is "orange", and the third just contains a is "red".

• In the first potential solution, where a is "blue", there’s only one valid option for the second choice: choosing blue. Choosing orange or green will just invalidate the potential solution.
• Analogously, in the second potential solution where a is "orange", there’s only one valid way to make the second choice.
• In the third potential solution, where a is "red", there’s no way to make a consistent choice, so this potential solution must be invalidated.

Open choices

An open choice lists an attribute the keyword is?, and one or more values: if there is more than one value, the values are surrounded by curly braces and separated by commas.

In any solution, the attribute must have some value, and that attribute can be any of the listed values… but it doesn’t have to be! Open choices are very chill.

Open rules describe unions

The following programs all have exactly 3 solutions: a is 1, a is 2, and a is 3.

Program 1

a is? { 1, 2, 3 }.

Program 2

a is? 1.
a is? 2.
a is? 3.

Program 3

a is? { 1, 2 }.
a is? { 2, 3 }.

Because open choices don’t preclude other consistent assignments, the possible assignments are the union of the different assignments proposed by different open rules.