Create a foreign-key-like constraints that checks something more generic than equality

Question

There are some situations where I would like to set up some constraints in a table that depend on values in another table.

For example, I can define two tables as:

CREATE TABLE foo (
    foo_id serial PRIMARY KEY,
    max_bar integer
);
CREATE TABLE bar (
    foo_id integer REFERENCES foo(foo_id),
    bar_id integer CHECK (bar_id >= 0),
    PRIMARY KEY (foo_id, bar_id)
);

I would like to go a little further to ensure that all bar.bar_id values are lower that the “corresponding” foo.max_bar.

Is there a way I can set up such a constraint?

To go a little further, I’ve found that an EXCLUDE constraint using a GiST index is a great way to set up UNIQUE-like (but more generic) constraints. For example I can define the following tables:

CREATE TABLE foo (
    foo_id integer NOT NULL,
    foo_validity tstzrange NOT NULL,
    EXCLUDE USING gist (foo_id WITH =, foo_validity WITH &&)
);
CREATE TABLE bar (
    foo_id integer NOT NULL,
    bar_validity tstzrange NOT NULL,
    EXCLUDE USING gist (foo_id WITH =, bar_validity WITH &&)
);

Then I would like each row in bar to reference a row in foo with foo.foo_id = bar.foo_id AND foo.foo_validity @> bar.bar_validity. It looks to me like it should be feasible with gist indices, but I can’t find a syntax to declare such a constraint…