A new implementation for the sqlite3ExprImpliesExpr() theorem prover …

…that

does a better job of answering TRUE to "(NOT A) OR B" when B is a NOT NULL
expression.

src/expr.c

@@ -4908,6 +4908,76 @@ int sqlite3ExprCompareSkip(Expr *pA, Expr *pB, int iTab){
              iTab);
 }
 
+/*
+** Return non-zero if Expr p can only be true if pNN is not NULL.
+*/
+static int exprImpliesNotNull(
+  Parse *pParse,      /* Parsing context */
+  Expr *p,            /* The expression to be checked */
+  Expr *pNN,          /* The expression that is NOT NULL */
+  int iTab,           /* Table being evaluated */
+  int seenNot         /* True if p is an operand of NOT */
+){
+  assert( p );
+  assert( pNN );
+  if( sqlite3ExprCompare(pParse, p, pNN, iTab)==0 ) return 1;
+  switch( p->op ){
+    case TK_IN: {
+      if( seenNot && ExprHasProperty(p, EP_xIsSelect) ) return 0;
+      assert( ExprHasProperty(p,EP_xIsSelect)
+           || (p->x.pList!=0 && p->x.pList->nExpr>0) );
+      return exprImpliesNotNull(pParse, p->pLeft, pNN, iTab, seenNot);
+    }
+    case TK_BETWEEN: {
+      ExprList *pList = p->x.pList;
+      assert( pList!=0 );
+      assert( pList->nExpr==2 );
+      if( seenNot ) return 0;
+      if( exprImpliesNotNull(pParse, pList->a[0].pExpr, pNN, iTab, seenNot)
+       || exprImpliesNotNull(pParse, pList->a[1].pExpr, pNN, iTab, seenNot)
+      ){
+        return 1;
+      }
+      return exprImpliesNotNull(pParse, p->pLeft, pNN, iTab, seenNot);
+    }
+    case TK_EQ:
+    case TK_NE:
+    case TK_LT:
+    case TK_LE:
+    case TK_GT:
+    case TK_GE:
+    case TK_PLUS:
+    case TK_MINUS:
+    case TK_STAR:
+    case TK_REM:
+    case TK_BITAND:
+    case TK_BITOR:
+    case TK_SLASH:
+    case TK_LSHIFT:
+    case TK_RSHIFT: 
+    case TK_CONCAT: {
+      if( exprImpliesNotNull(pParse, p->pRight, pNN, iTab, seenNot) ) return 1;
+      /* Fall thru into the next case */
+    }
+    case TK_SPAN:
+    case TK_COLLATE:
+    case TK_BITNOT:
+    case TK_UPLUS:
+    case TK_UMINUS: {
+      return exprImpliesNotNull(pParse, p->pLeft, pNN, iTab, seenNot);
+    }
+    case TK_TRUTH: {
+      if( seenNot ) return 0;
+      if( p->op2!=TK_IS ) return 0;
+      return exprImpliesNotNull(pParse, p->pLeft, pNN, iTab, seenNot);
+    }
+    case TK_NOT: {
+      return exprImpliesNotNull(pParse, p->pLeft, pNN, iTab, 1);
+    }
+  }
+  return 0;
+}
+
 /*
 ** Return true if we can prove the pE2 will always be true if pE1 is
 ** true.  Return false if we cannot complete the proof or if pE2 might
@@ -4944,15 +5014,9 @@ int sqlite3ExprImpliesExpr(Parse *pParse, Expr *pE1, Expr *pE2, int iTab){
     return 1;
   }
   if( pE2->op==TK_NOTNULL
-   && pE1->op!=TK_ISNULL
-   && pE1->op!=TK_IS
-   && pE1->op!=TK_ISNOT
-   && pE1->op!=TK_OR
-   && pE1->op!=TK_CASE
+   && exprImpliesNotNull(pParse, pE1, pE2->pLeft, iTab, 0)
   ){
-    Expr *pX = sqlite3ExprSkipCollate(pE1->pLeft);
-    testcase( pX!=pE1->pLeft );
-    if( sqlite3ExprCompare(pParse, pX, pE2->pLeft, iTab)==0 ) return 1;
+    return 1;
   }
   return 0;
 }