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Composition

Expr := Expr "." Expr

The meaning of R.S is x..., y... : exists(t: R(x..., t) and S(t, y...)). Note that the arguments must have at least arity 1.

For specific cases this meaning can be presented more simply. In particular, since a variable is a singleton relation, x.R is R[x], and R.x is y... : R(y..., x).

The composition operator is sometimes called the dot join operator.

Examples:

  • If parent is a binary relation, then parent.parent is equivalent to x, y: ∃(t: parent(x, t) and parent(t, y)).
  • If players is a binary relation and t is a unary relation, then t.players is equivalent to p: players(t, p).
  • If, additionally, age is a binary relation, then t.players.age is equivalent to v: ∃(p: players(t, p) and age(p, v)).
  • If brand_name is a binary relation, then brand_name."Tesla" is equivalent to b: brand_name(b, "Tesla").

The precedence of the composition operator . is high, so an expression such as R . Q(x) is equivalent to (R . Q)(x). If that is not what you want, you should put the relational application in parentheses: R . (Q(x)).

The same caveat applies to partial relational applications: R . Q[x] is equivalent to (R . Q)[x].

Next: Restriction

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