Using INTERSECT with tables from a WITH clause

Question

What is wrong with this query:

WITH volcan AS (SELECT DISTINCT v.numturista
                FROM viaje v, sitio s
                WHERE v.numsitio = s.numsitio
                AND s.tipo = 'Volcan'),
    desierto AS (SELECT DISTINCT v.numturista
                 FROM viaje v, sitio s
                 WHERE v.numsitio = s.numsitio
                 AND s.tipo = 'Desierto')
SELECT DISTINCT pais
FROM turista
WHERE numturista IN (volcan INTERSECT desierto);

Isn't it supposed to be equivalent to the following (since WITH creates named SELECT queries):

SELECT DISTINCT pais
FROM turista
WHERE numturista IN (
(SELECT DISTINCT v.numturista
                FROM viaje v, sitio s
                WHERE v.numsitio = s.numsitio
                AND s.tipo = 'Volcan')
INTERSECT
(SELECT DISTINCT v.numturista
                 FROM viaje v, sitio s
                 WHERE v.numsitio = s.numsitio
                 AND s.tipo = 'Desierto')
);

It says:

syntax error near INTERSECT.

Postgres version: psql (PostgreSQL) 9.1.9

UPDATE: Test tables

CREATE TABLE turista (
    numturista INTEGER,
    nomturista VARCHAR(100),
    pais VARCHAR(100),
    PRIMARY KEY(numturista)
);

CREATE TABLE sitio (
    numsitio INTEGER,
    nomsitio VARCHAR(100),
    tipo VARCHAR(100),
    continente VARCHAR(100),
    PRIMARY KEY(numsitio)
);

CREATE TABLE viaje (
    numviaje VARCHAR(7),
    numturista INTEGER,
    numsitio INTEGER, 
    fechasalida DATE,
    fechallegada DATE,
    ciudadsalida VARCHAR(100),
    PRIMARY KEY(numviaje, numturista, numsitio),
    FOREIGN KEY(numsitio) REFERENCES sitio,
    FOREIGN KEY(numturista) REFERENCES turista
);

INSERT INTO turista VALUES
 (300, 'Carlos', 'Costa Rica')
,(301, 'Pierre', 'Francia')
,(302, 'John', 'Jamaica')
,(303, 'Mario', 'Panama')
,(304, 'Ali', 'Tunez')
,(305, 'Ana', 'Guatemala');

INSERT INTO sitio VALUES 
 (125, 'Isla Moorea', 'Mar Litoral', 'Oceania')
,(126, 'Bahia Matsushima', 'Mar Litoral', 'Asia')
,(127, 'Irazu', 'Volcan', 'America')
,(128, 'Ngorongoro', 'Volcan', 'Africa')
,(129, 'Valle de la Muerte', 'Desierto', 'America')
,(130, 'Kilimandjar', 'Volcan', 'Africa');

INSERT INTO viaje VALUES
 ('03-2012', 301, 125, '2013-03-03', '2013-10-03', 'Paris')
,('04-2012', 303, 129, '2013-04-07', '2014-02-07', 'Las Vegas')
,('05-2012', 301, 128, '2013-05-07', '2013-12-07', 'Dar-es-Salam')
,('06-2012', 304, 127, '2013-06-07', '2014-02-07', 'San Jose')
,('07-2012', 302, 128, '2015-04-11', '2014-01-08', 'Mombasa')
,('04-2012', 305, 129, '2013-04-07', '2014-02-07', 'Las Vegas')
,('06-2012', 305, 127, '2013-06-07', '2014-02-07', 'San Jose');

Answer 1

This would be equivalent:

WITH volcan AS (
    SELECT DISTINCT v.numturista
    FROM   viaje v
    JOIN   sitio s USING (numsitio)
    WHERE  s.tipo = 'Volcan'
   )
, desierto AS (
    SELECT DISTINCT v.numturista
    FROM   viaje v
    JOIN   sitio s USING (numsitio)
    WHERE  s.tipo = 'Desierto'
   )
SELECT DISTINCT pais
FROM   turista
WHERE  numturista IN ((TABLE volcan) INTERSECT (TABLE desierto));

But it's probably pretty inefficient ...

TABLE tbl is just a notational shortcut for SELECT * FROM tbl.

Alternative query

Try this:

SELECT pais
FROM   turista t
WHERE  EXISTS (SELECT 1 FROM viaje v JOIN sitio s USING (numsitio)
               WHERE  v.numturista = t.numturista AND s.tipo = 'Volcan')
AND    EXISTS (SELECT 1 FROM viaje v JOIN sitio s USING (numsitio)
               WHERE  v.numturista = t.numturista AND s.tipo = 'Desierto')

Does the same, just simpler and faster. With EXISTS, you don't need any DISTINCT clauses, except if you really have duplicate countries (pais), which I seriously doubt.