or
randi vertongen imported from SE
sql-server sql-server-2017
**Purpose**

When trying to create a test example of a self referencing function, one version fails while another one succeeds.

The only difference being an added `SELECT` to the function body resulting in a different execution plan for both.


----------


**The function that works** 

    CREATE FUNCTION dbo.test5(@i int)
    RETURNS INT
    AS 
    BEGIN
    RETURN(
    SELECT TOP 1
    CASE 
    WHEN @i = 1 THEN 1
    WHEN @i = 2 THEN 2
    WHEN @i = 3 THEN  dbo.test5(1) + dbo.test5(2)
    END
    )
    END;

**Calling the function**

    SELECT dbo.test5(3);
    

**Returns**

    (No column name)
    3


----------


**The function that does not work**

    CREATE FUNCTION dbo.test6(@i int)
    RETURNS INT
    AS 
    BEGIN
    RETURN(
    SELECT TOP 1
    CASE 
    WHEN @i = 1 THEN 1
    WHEN @i = 2 THEN 2
    WHEN @i = 3 THEN (SELECT dbo.test6(1) + dbo.test6(2))
    END
    )END;
    

**Calling the function**

    SELECT dbo.test6(3);

or 

    SELECT dbo.test6(2);

**Results in the error**

> Maximum stored procedure, function, trigger, or view nesting level
> exceeded (limit 32).

**Guessing the cause**

There is an additional compute scalar on the estimated plan of the failed function, calling 

    <ColumnReference Column="Expr1002" />
    <ScalarOperator ScalarString="CASE WHEN [@i]=(1) THEN (1) ELSE CASE WHEN [@i]=(2) THEN (2) ELSE CASE WHEN [@i]=(3) THEN [Expr1000] ELSE NULL END END END">

**And expr1000 being**

    <ColumnReference Column="Expr1000" />
    <ScalarOperator ScalarString="[dbo].[test6]((1))+[dbo].[test6]((2))">

*Which could explain the recursive references exceeding 32.*

**The actual question**

The added `SELECT` makes the function call itself over and over, resulting in an endless loop, but why is adding a `SELECT` giving this result?


----------

**Additional info**

[Estimated execution plans][1]

[DB<>Fiddle][2]

    Build version:
    14.0.3045.24

*Tested on compatibility_levels 100 and 140*


  [1]: https://www.brentozar.com/pastetheplan/?id=rJVbfl36E
  [2]: https://dbfiddle.uk/?rdbms=sqlserver_2017&fiddle=99511f8276f8e74b225deaf3fb8fd344
Top Answer
Paul White
This is a bug in *project normalization*, exposed by using a subquery inside a case expression with a non-deterministic function.

To explain, we need to note two things up front:

1. SQL Server cannot execute subqueries directly, so they are always unrolled or converted to an *apply*.
2. The semantics of `CASE` are such that a `THEN` expression should only be evaluated if the `WHEN` clause returns true.

The (trivial) subquery introduced in the problematic case therefore results in an apply operator (nested loops join). To meet the second requirement, SQL Server initially places the expression `dbo.test6(1) + dbo.test6(2)` on the inner side of the apply: 

[![highlighted compute scalar][1]][1]

```
[Expr1000] = Scalar Operator([dbo].[test6]((1))+[dbo].[test6]((2)))
```

...with the `CASE` semantics honoured by a *pass-through* predicate on the join:

```
[@i]=(1) OR [@i]=(2) OR IsFalseOrNull [@i]=(3)
```

The inner side of the loop is only evaluated if the *pass-through* condition evaluates to *false* (meaning `@i = 3`). This is all correct so far. The *Compute Scalar* following the nested loops join also honours the `CASE` semantics correctly:

```
[Expr1001] = Scalar Operator(CASE WHEN [@i]=(1) THEN (1) ELSE CASE WHEN [@i]=(2) THEN (2) ELSE CASE WHEN [@i]=(3) THEN [Expr1000] ELSE NULL END END END)
```

The problem is that the *project normalization* stage of query compilation sees that `Expr1000` is uncorrelated and determines that it would be safe (*narrator: it isn't*) to move it outside the loop:

[![moved project][2]][2]

```
[Expr1000] = Scalar Operator([dbo].[test6]((1))+[dbo].[test6]((2)))
```

This breaks* the semantics implemented by the *pass-through* predicate, so the function is evaluated when it should not be, and an infinite loop results.

You should report this bug. A workaround is to prevent the expression being moved outside the apply by making it correlated (i.e. including `@i` in the expression) but this is a hack of course. There is a way to disable project normalization, but I have been asked before not to share it publicly, so I won't.

This problem does not arise in SQL Server 2019 when the [scalar function is inlined][3], because the inlining logic operates directly on the parsed tree (well before project normalization). The simple logic in the question can be simplified by the inlining logic to the non-recursive:

```
[Expr1019] = (Scalar Operator((1)))
[Expr1045] = Scalar Operator(CONVERT_IMPLICIT(int,CONVERT_IMPLICIT(int,[Expr1019],0)+(2),0))
```

...which returns 3.


Another way to illustrate the core issue is:

```
-- Not schema bound to make it non-det
CREATE OR ALTER FUNCTION dbo.Error() 
RETURNS integer 
-- WITH INLINE = OFF -- SQL Server 2019 only
AS
BEGIN
    RETURN 1/0;
END;
GO
DECLARE @i integer = 1;

SELECT
    CASE 
        WHEN @i = 1 THEN 1
        WHEN @i = 2 THEN 2
        WHEN @i = 3 THEN (SELECT dbo.Error()) -- 'subquery'
        ELSE NULL
    END;
```

Reproduces on the latest builds of all versions from 2008 R2 to 2019 CTP 3.0.

A further example (without a scalar function) provided by [Martin Smith][4]:

```
SELECT IIF(@@TRANCOUNT >= 0, 1, (SELECT CRYPT_GEN_RANDOM(4)/ 0))
```

This has all the key elements needed:

* `CASE` (implemented internally as `ScaOp_IIF`)
* A non-deterministic function (`CRYPT_GEN_RANDOM`)
* A subquery on the branch that should not be executed (`(SELECT ...)`)

---

\*Strictly, the above transformation could still be correct if evaluation of `Expr1000` was deferred correctly, since it is referenced only by the safe construction:

```
[Expr1002] = Scalar Operator(CASE WHEN [@i]=(1) THEN (1) ELSE CASE WHEN [@i]=(2) THEN (2) ELSE CASE WHEN [@i]=(3) THEN [Expr1000] ELSE NULL END END END)
```

...but this requires an internal *ForceOrder* flag (not query hint), which is not set either. In any case, the implementation of the logic applied by *project normalization* is incorrect or incomplete.

**[Bug report][5]** on the Azure Feedback site for SQL Server.

  [1]: https://i.stack.imgur.com/i0QaY.png
  [2]: https://i.stack.imgur.com/l8olq.png
  [3]: https://docs.microsoft.com/en-us/sql/relational-databases/user-defined-functions/scalar-udf-inlining
  [4]: https://dba.stackexchange.com/users/3690/martin-smith
  [5]: https://feedback.azure.com/forums/908035-sql-server/suggestions/37774186-self-referencing-scalar-function-nesting-level-exc
Self referencing scalar function nesting level exceeded when adding a select

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