diff --git a/expression/constant_test.go b/expression/constant_test.go
index b788363c97972..acd1240b4aaad 100644
--- a/expression/constant_test.go
+++ b/expression/constant_test.go
@@ -258,6 +258,15 @@ func (*testExpressionSuite) TestConstraintPropagation(c *C) {
 			},
 			result: "0",
 		},
+		{
+			solver: newConstraintSolver(ruleColumnLTConst),
+			// col1 < '2018-12-11' and to_days(col1) > 737999 => false
+			conditions: []Expression{
+				newFunction(ast.LT, col1, newDate(2018, 12, 11)),
+				newFunction(ast.GT, newFunction(ast.ToDays, col1), newLonglong(737999)),
+			},
+			result: "0",
+		},
 	}
 	for _, tt := range tests {
 		ctx := mock.NewContext()
diff --git a/expression/constraint_propagation.go b/expression/constraint_propagation.go
index f30ba13590150..317d403d5b21a 100644
--- a/expression/constraint_propagation.go
+++ b/expression/constraint_propagation.go
@@ -174,11 +174,21 @@ func ruleColumnEQConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
 	}
 }
 
-// ruleColumnGTConst propagates the "column > const" condition.
+// ruleColumnLTConst propagates the "column > const" condition.
 func ruleColumnGTConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
+	ruleColumnXXConst(ctx, i, j, exprs, ast.GT, ast.LT, ast.GE)
+}
+
+// ruleColumnLTConst propagates the "column < const" condition.
+func ruleColumnLTConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
+	ruleColumnXXConst(ctx, i, j, exprs, ast.LT, ast.GT, ast.LE)
+}
+
+// ruleColumnXXConst propagates the "column OP const" condition, where op may be '>' and '<'
+func ruleColumnXXConst(ctx sessionctx.Context, i, j int, exprs *exprSet, GT string, LT string, GE string) {
 	cond := exprs.data[i]
 	f1, ok := cond.(*ScalarFunction)
-	if !ok || f1.FuncName.L != ast.GT {
+	if !ok || f1.FuncName.L != GT {
 		return
 	}
 	var col1 *Column
@@ -199,7 +209,7 @@ func ruleColumnGTConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
 	}
 
 	// col > c1, col > c2, c1 > c2 => col > c1
-	if f2.FuncName.L == ast.GT {
+	if f2.FuncName.L == GT {
 		col2, ok := f2.GetArgs()[0].(*Column)
 		if !ok || !col1.Equal(ctx, col2) {
 			return
@@ -212,7 +222,7 @@ func ruleColumnGTConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
 			return
 		}
 
-		v, isNull, err := compareConstant(ctx, ast.GT, con1, con2)
+		v, isNull, err := compareConstant(ctx, GT, con1, con2)
 		if err != nil {
 			log.Warn(err)
 			return
@@ -232,7 +242,7 @@ func ruleColumnGTConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
 	// Prove:
 	// col > c1, f is monotonous => f(col) > f(c1)
 	// f(col) > f(c1), f(col) < c2, f(c1) >= c2 => false
-	if f2.FuncName.L == ast.LT {
+	if f2.FuncName.L == LT {
 		con2, ok := f2.GetArgs()[1].(*Constant)
 		if !ok {
 			return
@@ -267,7 +277,7 @@ func ruleColumnGTConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
 		if !col1.Equal(ctx, col2) {
 			return
 		}
-		v, isNull, err := compareConstant(ctx, ast.GE, fc1, con2)
+		v, isNull, err := compareConstant(ctx, GE, fc1, con2)
 		if err != nil {
 			log.Warn(err)
 			return
@@ -292,79 +302,3 @@ func compareConstant(ctx sessionctx.Context, fn string, c1, c2 Expression) (int6
 	}
 	return cmp.EvalInt(ctx, chunk.Row{})
 }
-
-// ruleColumnLTConst propagates the "column < const" condition.
-func ruleColumnLTConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
-	cond := exprs.data[i]
-	f1, ok := cond.(*ScalarFunction)
-	if !ok || f1.FuncName.L != ast.LT {
-		return
-	}
-	var col1 *Column
-	var con1 *Constant
-	col1, ok = f1.GetArgs()[0].(*Column)
-	if !ok {
-		return
-	}
-	con1, ok = f1.GetArgs()[1].(*Constant)
-	if !ok {
-		return
-	}
-
-	expr := exprs.data[j]
-	f2, ok := expr.(*ScalarFunction)
-	if !ok {
-		return
-	}
-	// col < c1, col < c2, c1 < c2 => col < c1
-	if f2.FuncName.L == ast.LT {
-		col2, ok := f2.GetArgs()[0].(*Column)
-		if !ok || !col1.Equal(ctx, col2) {
-			return
-		}
-		con2, ok := f2.GetArgs()[1].(*Constant)
-		if !ok {
-			return
-		}
-		if !con1.RetType.Equal(con2.RetType) {
-			return
-		}
-
-		v, isNull, err := compareConstant(ctx, ast.LT, con1, con2)
-		if err != nil {
-			log.Warn(err)
-			return
-		}
-		if !isNull && v > 0 {
-			exprs.tombstone[j] = true
-		}
-		return
-	}
-
-	// col < c1, col > c2, c1 <= c2 => false
-	if f2.FuncName.L == ast.GT {
-		col2, ok := f2.GetArgs()[0].(*Column)
-		if !ok || !col1.Equal(ctx, col2) {
-			return
-		}
-		con2, ok := f2.GetArgs()[1].(*Constant)
-		if !ok {
-			return
-		}
-
-		if !con1.RetType.Equal(con2.RetType) {
-			return
-		}
-
-		v, isNull, err := compareConstant(ctx, ast.LE, con1, con2)
-		if err != nil {
-			log.Warn(err)
-			return
-		}
-		if !isNull && v > 0 {
-			exprs.SetConstFalse()
-		}
-		return
-	}
-	return
-}
diff --git a/go.mod b/go.mod
index c1ed756e0b4b8..08135b2bc61e1 100644
--- a/go.mod
+++ b/go.mod
@@ -47,7 +47,7 @@ require (
 	github.com/pingcap/errors v0.11.0
 	github.com/pingcap/goleveldb v0.0.0-20171020122428-b9ff6c35079e
 	github.com/pingcap/kvproto v0.0.0-20181105061835-1b5d69cd1d26
-	github.com/pingcap/parser v0.0.0-20181210061630-27e9d3e251d4
+	github.com/pingcap/parser v0.0.0-20181211024540-4e6d047fcaae
 	github.com/pingcap/pd v2.1.0-rc.4+incompatible
 	github.com/pingcap/tidb-tools v0.0.0-20181112132202-4860a0d5de03
 	github.com/pingcap/tipb v0.0.0-20181012112600-11e33c750323
diff --git a/go.sum b/go.sum
index 6a8c51c3ac0a9..be57fc9899053 100644
--- a/go.sum
+++ b/go.sum
@@ -107,8 +107,8 @@ github.com/pingcap/goleveldb v0.0.0-20171020122428-b9ff6c35079e h1:P73/4dPCL96rG
 github.com/pingcap/goleveldb v0.0.0-20171020122428-b9ff6c35079e/go.mod h1:O17XtbryoCJhkKGbT62+L2OlrniwqiGLSqrmdHCMzZw=
 github.com/pingcap/kvproto v0.0.0-20181105061835-1b5d69cd1d26 h1:JK4VLNYbSn36QSbCnqALi2ySXdH0DfcMssT/zmLf4Ls=
 github.com/pingcap/kvproto v0.0.0-20181105061835-1b5d69cd1d26/go.mod h1:0gwbe1F2iBIjuQ9AH0DbQhL+Dpr5GofU8fgYyXk+ykk=
-github.com/pingcap/parser v0.0.0-20181210061630-27e9d3e251d4 h1:2rCHDk4h8VZw0fiC2CFJffOlXU3iMuz1kOt5wTMCemY=
-github.com/pingcap/parser v0.0.0-20181210061630-27e9d3e251d4/go.mod h1:1FNvfp9+J0wvc4kl8eGNh7Rqrxveg15jJoWo/a0uHwA=
+github.com/pingcap/parser v0.0.0-20181211024540-4e6d047fcaae h1:RD98+89F/yakFLnztEL4Pi9f+RkOAm2vgRJcB1p6tTw=
+github.com/pingcap/parser v0.0.0-20181211024540-4e6d047fcaae/go.mod h1:1FNvfp9+J0wvc4kl8eGNh7Rqrxveg15jJoWo/a0uHwA=
 github.com/pingcap/pd v2.1.0-rc.4+incompatible h1:/buwGk04aHO5odk/+O8ZOXGs4qkUjYTJ2UpCJXna8NE=
 github.com/pingcap/pd v2.1.0-rc.4+incompatible/go.mod h1:nD3+EoYes4+aNNODO99ES59V83MZSI+dFbhyr667a0E=
 github.com/pingcap/tidb-tools v0.0.0-20181112132202-4860a0d5de03 h1:xVuo5U+l6XAWHsb+xhkZ8zz3jerIwDfCHAO6kR2Kaog=