SQLite

  if( pE2->op==TK_NOTNULL && pE1->op!=TK_ISNULL && pE1->op!=TK_IS ){
    Expr *pX = sqlite3ExprSkipCollate(pE1->pLeft);
    testcase( pX!=pE1->pLeft );
    if( sqlite3ExprCompare(pParse, pX, pE2->pLeft, iTab)==0 ) return 1;
  }
  return 0;
}

/*
** This is the Expr node callback for sqlite3ExprImpliesNotNullRow().
** If the expression node requires that the table at pWalker->iCur
** have a non-NULL column, then set pWalker->eCode to 1 and abort.
*/
static int impliesNotNullRow(Walker *pWalker, Expr *pExpr){
  if( ExprHasProperty(pExpr, EP_FromJoin) ) return WRC_Prune;
  switch( pExpr->op ){
    case TK_ISNULL:
    case TK_IS:
    case TK_OR:
    case TK_FUNCTION:
    case TK_AGG_FUNCTION:
      return WRC_Prune;
    case TK_COLUMN:
    case TK_AGG_COLUMN:
      if( pWalker->u.iCur==pExpr->iTable ){
        pWalker->eCode = 1;
        return WRC_Abort;
      }
      return WRC_Prune;
    default:
      return WRC_Continue;
  }
}

/*
** Return true (non-zero) if expression p can only be true if at least
** one column of table iTab is non-null.  In other words, return true
** if expression p will always be NULL or false if every column of iTab
** is NULL.
**
** Terms of p that are marked with EP_FromJoin (and hence that come from
** the ON or USING clauses of LEFT JOINS) are excluded from the analysis.
**
** This routine is used to check if a LEFT JOIN can be converted into
** an ordinary JOIN.  The p argument is the WHERE clause.  If the WHERE
** clause requires that some column of the right table of the LEFT JOIN
** be non-NULL, then the LEFT JOIN can be safely converted into an
** ordinary join.
*/
int sqlite3ExprImpliesNonNullRow(Expr *p, int iTab){
  Walker w;
  w.xExprCallback = impliesNotNullRow;
  w.xSelectCallback = 0;
  w.xSelectCallback2 = 0;
  w.eCode = 0;
  w.u.iCur = iTab;
  sqlite3WalkExpr(&w, p);
  return w.eCode;
}

/*
** An instance of the following structure is used by the tree walker
** to determine if an expression can be evaluated by reference to the
** index only, without having to do a search for the corresponding
** table entry.  The IdxCover.pIdx field is the index.  IdxCover.iCur
** is the cursor for the table.

        setJoinExpr(p->x.pList->a[i].pExpr, iTable);
      }
    }
    setJoinExpr(p->pLeft, iTable);
    p = p->pRight;
  } 
}

/* Undo the work of setJoinExpr().  In the expression tree p, convert every
** term that is marked with EP_FromJoin and iRightJoinTable==iTable into
** an ordinary term that omits the EP_FromJoin mark.
**
** This happens when a LEFT JOIN is simplified into an ordinary JOIN.
*/
static void unsetJoinExpr(Expr *p, int iTable){
  while( p ){
    if( ExprHasProperty(p, EP_FromJoin) && p->iRightJoinTable==iTable ){
      ExprClearProperty(p, EP_FromJoin);
    }
    if( p->op==TK_FUNCTION && p->x.pList ){
      int i;
      for(i=0; i<p->x.pList->nExpr; i++){
        unsetJoinExpr(p->x.pList->a[i].pExpr, iTable);
      }
    }
    unsetJoinExpr(p->pLeft, iTable);
    p = p->pRight;
  } 
}

/*
** This routine processes the join information for a SELECT statement.
** ON and USING clauses are converted into extra terms of the WHERE clause.
** NATURAL joins also create extra WHERE clause terms.
**
** The terms of a FROM clause are contained in the Select.pSrc structure.

  ** does not already exist */
  v = sqlite3GetVdbe(pParse);
  if( v==0 ) goto select_end;
  if( pDest->eDest==SRT_Output ){
    generateColumnNames(pParse, p);
  }

  /* Try to various optimizations (flattening subqueries, and strength
  ** reduction of join operators) in the FROM clause up into the main query
  */
#if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW)
  for(i=0; !p->pPrior && i<pTabList->nSrc; i++){
    struct SrcList_item *pItem = &pTabList->a[i];
    Select *pSub = pItem->pSelect;
    Table *pTab = pItem->pTab;

    /* Convert LEFT JOIN into JOIN if there are terms of the right table
    ** of the LEFT JOIN used in the WHERE clause.
    */
    if( (pItem->fg.jointype & JT_LEFT)!=0
     && sqlite3ExprImpliesNonNullRow(p->pWhere, pItem->iCursor)
     && OptimizationEnabled(db, SQLITE_SimplifyJoin)
    ){
      SELECTTRACE(0x100,pParse,p,
                ("LEFT-JOIN simplifies to JOIN on term %d\n",i));
      pItem->fg.jointype &= ~JT_LEFT;
      unsetJoinExpr(p->pWhere, pItem->iCursor);
    }

    /* No futher action if this term of the FROM clause is no a subquery */
    if( pSub==0 ) continue;

    /* Catch mismatch in the declared columns of a view and the number of
    ** columns in the SELECT on the RHS */
    if( pTab->nCol!=pSub->pEList->nExpr ){
      sqlite3ErrorMsg(pParse, "expected %d columns for '%s' but got %d",
                      pTab->nCol, pTab->zName, pSub->pEList->nExpr);

#define SQLITE_Transitive     0x0080   /* Transitive constraints */
#define SQLITE_OmitNoopJoin   0x0100   /* Omit unused tables in joins */
#define SQLITE_CountOfView    0x0200   /* The count-of-view optimization */
#define SQLITE_CursorHints    0x0400   /* Add OP_CursorHint opcodes */
#define SQLITE_Stat34         0x0800   /* Use STAT3 or STAT4 data */
   /* TH3 expects the Stat34  ^^^^^^ value to be 0x0800.  Don't change it */
#define SQLITE_PushDown       0x1000   /* The push-down optimization */
#define SQLITE_SimplifyJoin   0x2000   /* Convert LEFT JOIN to JOIN */
#define SQLITE_AllOpts        0xffff   /* All optimizations */

/*
** Macros for testing whether or not optimizations are enabled or disabled.
*/
#define OptimizationDisabled(db, mask)  (((db)->dbOptFlags&(mask))!=0)
#define OptimizationEnabled(db, mask)   (((db)->dbOptFlags&(mask))==0)

void sqlite3Vacuum(Parse*,Token*);
int sqlite3RunVacuum(char**, sqlite3*, int);
char *sqlite3NameFromToken(sqlite3*, Token*);
int sqlite3ExprCompare(Parse*,Expr*, Expr*, int);
int sqlite3ExprCompareSkip(Expr*, Expr*, int);
int sqlite3ExprListCompare(ExprList*, ExprList*, int);
int sqlite3ExprImpliesExpr(Parse*,Expr*, Expr*, int);
int sqlite3ExprImpliesNonNullRow(Expr*,int);
void sqlite3ExprAnalyzeAggregates(NameContext*, Expr*);
void sqlite3ExprAnalyzeAggList(NameContext*,ExprList*);
int sqlite3ExprCoveredByIndex(Expr*, int iCur, Index *pIdx);
int sqlite3FunctionUsesThisSrc(Expr*, SrcList*);
Vdbe *sqlite3GetVdbe(Parse*);
#ifndef SQLITE_UNTESTABLE
void sqlite3PrngSaveState(void);

do_execsql_test e_select-3.1.5 { SELECT k FROM x1 WHERE x IS NULL } {4 5}
do_execsql_test e_select-3.1.6 { SELECT k FROM x1 WHERE z - 78.43 } {2 4 6}

do_execsql_test e_select-3.2.1a {
  SELECT k FROM x1 LEFT JOIN x2 USING(k)
} {1 2 3 4 5 6}
do_execsql_test e_select-3.2.1b {
  SELECT k FROM x1 LEFT JOIN x2 USING(k) WHERE x2.k ORDER BY +k
} {1 3 5}
do_execsql_test e_select-3.2.2 {
  SELECT k FROM x1 LEFT JOIN x2 USING(k) WHERE x2.k IS NULL
} {2 4 6}

do_execsql_test e_select-3.2.3 {
  SELECT k FROM x1 NATURAL JOIN x2 WHERE x2.k

  CREATE TABLE cc(c);
  INSERT INTO aa VALUES('one');
  INSERT INTO bb VALUES('one');
  INSERT INTO cc VALUES('one');
}

do_catchsql_test 2.1 {
  SELECT * FROM aa LEFT JOIN cc ON (a=b) JOIN bb ON (b=coalesce(c,1));
} {1 {ON clause references tables to its right}}
do_catchsql_test 2.2 {
  SELECT * FROM aa JOIN cc ON (a=b) JOIN bb ON (b=c);
} {0 {one one one}}

#-------------------------------------------------------------------------
# Test that a problem causing where.c to overlook opportunities to