Describe the unexpected behaviour
When we use lagInFrame/leadInFrame window function, the returned value of rows that to be out of the frame is 0 or an empty string(depends on the type of the original column). However, like most other DBMSs' implementation, the returned value is null instead of 0 or empty string. Semantically, 0 or empty string can be computed while null cannot. Consequently, 0 or "" leads to incorrect behavior in subsequent procedures if this kind of returned values are accepted, 0 and empty strings really means something semantically in many cases.

I looked into the document, don't quite understand the term "respect the frame", not sure if it means 0 and empty string must be the default value it should use, when the target row to calculate is out of frame.

How to reproduce

• Which ClickHouse server version to use
  Any version since window function lagInFrame/leadInFrame are introduced.
  For example, in the query below:

SELECT
    number,
    lagInFrame(number, 1) OVER w AS prevOne,
    lagInFrame(number, 2) OVER w AS prevTwo
FROM numbers(10)
WINDOW w AS (ORDER BY number ASC)

Query id: 1027831f-0764-4a08-bc6a-70fd2752a4dc

┌─number─┬─prevOne─┬─prevTwo─┐
│      0 │       0 │       0 │
│      1 │       0 │       0 │
│      2 │       1 │       0 │
│      3 │       2 │       1 │
│      4 │       3 │       2 │
│      5 │       4 │       3 │
│      6 │       5 │       4 │
│      7 │       6 │       5 │
│      8 │       7 │       6 │
│      9 │       8 │       7 │
└────────┴─────────┴─────────┘

In the row 1, I'm expecting prevOne and prevTwo to be NULL, and in row 2, expecting prevTwo to be NULL, but obviously they are 0 instead.

Expected behavior
For rows that the function runs on target row is out of frame, expected returned value must be null as query below:

SELECT
    number,
    lagInFrame(number, 1) OVER w AS prevOne,
    lagInFrame(number, 2) OVER w AS prevTwo
FROM numbers(10)
WINDOW w AS (ORDER BY number ASC)

Query id: ad65c077-90ef-4821-9376-c9567be203ff

┌─number─┬─prevOne─┬─prevTwo─┐
│      0 │    ᴺᵁᴸᴸ │    ᴺᵁᴸᴸ │
│      1 │       0 │    ᴺᵁᴸᴸ │
│      2 │       1 │       0 │
│      3 │       2 │       1 │
│      4 │       3 │       2 │
│      5 │       4 │       3 │
│      6 │       5 │       4 │
│      7 │       6 │       5 │
│      8 │       7 │       6 │
│      9 │       8 │       7 │
└────────┴─────────┴─────────┘

A simple fix of this I can think of is making the return type of the function to be ColumnNullable():

DataTypePtr getReturnType() const override
    { return std::make_shared<DataTypeNullable>(argument_types[0]); }