What is semi-join in database?

Simple example. Let's select students with grades using left outer join:

SELECT DISTINCT s.id
FROM  students s
      LEFT JOIN grades g ON g.student_id = s.id
WHERE g.student_id IS NOT NULL

Now the same with left semi-join:

SELECT s.id
FROM  students s
WHERE EXISTS (SELECT 1 FROM grades g
              WHERE g.student_id = s.id)

The latter is generally more efficient (depending on concrete DBMS and query optimizer).

As far as I know SQL dialects that support SEMIJOIN/ANTISEMI are U-SQL/Cloudera Impala.

SEMIJOIN:

Semijoins are U-SQL’s way filter a rowset based on the inclusion of its rows in another rowset. Other SQL dialects express this with the SELECT * FROM A WHERE A.key IN (SELECT B.key FROM B) pattern.

More info Semi Join and Anti Join Should Have Their Own Syntax in SQL:

“Semi” means that we don’t really join the right hand side, we only check if a join would yield results for any given tuple.

-- IN
SELECT *
FROM Employee
WHERE DeptName IN (
  SELECT DeptName
  FROM Dept
)

-- EXISTS
SELECT *
FROM Employee
WHERE EXISTS (
  SELECT 1
  FROM Dept
  WHERE Employee.DeptName = Dept.DeptName
)

EDIT:

Another dialect that supports SEMI/ANTISEMI join is KQL:

kind=leftsemi (or kind=rightsemi)

Returns all the records from the left side that have matches from the right. The result table contains columns from the left side only.

let t1 = datatable(key:long, value:string)  
[1, "a",  
2, "b",
3, "c"];
let t2 = datatable(key:long)
[1,3];
t1 | join kind=leftsemi (t2) on key

demo

Output:

key  value
1    a
3    c