Terms

Most declarations in Dusa contain terms. If you’ve been following the language reference, you’ve already seen numbers (0, -213, 100) and strings strings ("Hello world", "whatever?"), but constructors (a, b, f c, h (f d) a) also play an important role.

When you write a rule like edge a b. in Dusa, edge will be treated as a predicate, but both a and b will get treated as constructors that take no arguments (we’ll usually call these “constants.”)

When you a rule like this:

rel (h (g my_fish) 4 aWalk) is 3.

• rel will get treated as a predicate,
• h and g will get treated as constructors that take other terms as arguments, and
• my_fish and aWalk will get treated as constants.

Syntax highlighting gives a hint here: predicates are highlighted in a blue color, and constructors and constants are highlighted in a purple color.

Variables

Rules in Dusa may contain logic variables, which start with uppercase letters. The following rule says the edge relation is symmetric:

edge X Y :- edge Y X.

If we have the fact edge a b, this rule will allow us to match Y = a and X = b in the premise, and then use the rule to derive the fact edge b a.

Each variable can only be assigned one value. This rule:

self X :- edge X X.

cannot make use of the fact edge a b, because there’s no way to assign X = a and X = b simultaneously. However, if we have the fact edge c c, then we can match X = c and derive the fact self c using this rule.

All the variables in the conclusion of a rule must appear in the premises.

Wildcards

You can use and reuse the wildcard _ in place of a variable you don’t care about. edge _ _ will match the fact edge a b and also the fact edge c c.

If you don’t care about a variable’s value, you can precede the variable name with a wildcard: edge _Left _Right treats the variables _Left and _Right like wildcards. A wildcard with a given name can only appear once in a rule. The only purpose for naming a wildcard is documentation and readability.