diff --git a/expression/constant_test.go b/expression/constant_test.go
index f07047a5f9bbe..e0eba43757412 100644
--- a/expression/constant_test.go
+++ b/expression/constant_test.go
@@ -32,12 +32,16 @@ var _ = Suite(&testExpressionSuite{})
 type testExpressionSuite struct{}
 
 func newColumn(id int) *Column {
+	return newColumnWithType(id, types.NewFieldType(mysql.TypeLonglong))
+}
+
+func newColumnWithType(id int, t *types.FieldType) *Column {
 	return &Column{
 		UniqueID: int64(id),
 		ColName:  model.NewCIStr(fmt.Sprint(id)),
 		TblName:  model.NewCIStr("t"),
 		DBName:   model.NewCIStr("test"),
-		RetType:  types.NewFieldType(mysql.TypeLonglong),
+		RetType:  t,
 	}
 }
 
@@ -48,6 +52,18 @@ func newLonglong(value int64) *Constant {
 	}
 }
 
+func newDate(year, month, day int) *Constant {
+	var tmp types.Datum
+	tmp.SetMysqlTime(types.Time{
+		Time: types.FromDate(year, month, day, 0, 0, 0, 0),
+		Type: mysql.TypeDate,
+	})
+	return &Constant{
+		Value:   tmp,
+		RetType: types.NewFieldType(mysql.TypeDate),
+	}
+}
+
 func newFunction(funcName string, args ...Expression) Expression {
 	typeLong := types.NewFieldType(mysql.TypeLonglong)
 	return NewFunctionInternal(mock.NewContext(), funcName, typeLong, args...)
@@ -180,6 +196,91 @@ func (*testExpressionSuite) TestConstantPropagation(c *C) {
 	}
 }
 
+func (*testExpressionSuite) TestConstraintPropagation(c *C) {
+	defer testleak.AfterTest(c)()
+	col1 := newColumnWithType(1, types.NewFieldType(mysql.TypeDate))
+	tests := []struct {
+		solver     constraintSolver
+		conditions []Expression
+		result     string
+	}{
+		// Don't propagate this any more, because it makes the code more complex but not
+		// useful for partition pruning.
+		// {
+		// 	solver: newConstraintSolver(ruleColumnGTConst),
+		// 	conditions: []Expression{
+		// 		newFunction(ast.GT, newColumn(0), newLonglong(5)),
+		// 		newFunction(ast.GT, newColumn(0), newLonglong(7)),
+		// 	},
+		// 	result: "gt(test.t.0, 7)",
+		// },
+		{
+			solver: newConstraintSolver(ruleColumnOPConst),
+			conditions: []Expression{
+				newFunction(ast.GT, newColumn(0), newLonglong(5)),
+				newFunction(ast.LT, newColumn(0), newLonglong(5)),
+			},
+			result: "0",
+		},
+		{
+			solver: newConstraintSolver(ruleColumnOPConst),
+			conditions: []Expression{
+				newFunction(ast.GT, newColumn(0), newLonglong(7)),
+				newFunction(ast.LT, newColumn(0), newLonglong(5)),
+			},
+			result: "0",
+		},
+		{
+			solver: newConstraintSolver(ruleColumnOPConst),
+			// col1 > '2018-12-11' and to_days(col1) < 5 => false
+			conditions: []Expression{
+				newFunction(ast.GT, col1, newDate(2018, 12, 11)),
+				newFunction(ast.LT, newFunction(ast.ToDays, col1), newLonglong(5)),
+			},
+			result: "0",
+		},
+		{
+			solver: newConstraintSolver(ruleColumnOPConst),
+			conditions: []Expression{
+				newFunction(ast.LT, newColumn(0), newLonglong(5)),
+				newFunction(ast.GT, newColumn(0), newLonglong(5)),
+			},
+			result: "0",
+		},
+		{
+			solver: newConstraintSolver(ruleColumnOPConst),
+			conditions: []Expression{
+				newFunction(ast.LT, newColumn(0), newLonglong(5)),
+				newFunction(ast.GT, newColumn(0), newLonglong(7)),
+			},
+			result: "0",
+		},
+		{
+			solver: newConstraintSolver(ruleColumnOPConst),
+			// 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()
+		conds := make([]Expression, 0, len(tt.conditions))
+		for _, cd := range tt.conditions {
+			conds = append(conds, FoldConstant(cd))
+		}
+		newConds := tt.solver.Solve(ctx, conds)
+		var result []string
+		for _, v := range newConds {
+			result = append(result, v.String())
+		}
+		sort.Strings(result)
+		c.Assert(strings.Join(result, ", "), Equals, tt.result, Commentf("different for expr %s", tt.conditions))
+	}
+}
+
 func (*testExpressionSuite) TestConstantFolding(c *C) {
 	defer testleak.AfterTest(c)()
 	tests := []struct {
diff --git a/expression/constraint_propagation.go b/expression/constraint_propagation.go
index 986576aa3261e..aafbf1660d306 100644
--- a/expression/constraint_propagation.go
+++ b/expression/constraint_propagation.go
@@ -16,6 +16,7 @@ package expression
 import (
 	"bytes"
 
+	"github.com/pingcap/parser/ast"
 	"github.com/pingcap/parser/mysql"
 	"github.com/pingcap/tidb/sessionctx"
 	"github.com/pingcap/tidb/types"
@@ -78,24 +79,35 @@ func newExprSet(conditions []Expression) *exprSet {
 	return &exprs
 }
 
+type constraintSolver []constraintPropagateRule
+
+func newConstraintSolver(rules ...constraintPropagateRule) constraintSolver {
+	return constraintSolver(rules)
+}
+
 type pgSolver2 struct{}
 
-// PropagateConstant propagate constant values of deterministic predicates in a condition.
 func (s pgSolver2) PropagateConstant(ctx sessionctx.Context, conditions []Expression) []Expression {
+	solver := newConstraintSolver(ruleConstantFalse, ruleColumnEQConst)
+	return solver.Solve(ctx, conditions)
+}
+
+// Solve propagate constraint according to the rules in the constraintSolver.
+func (s constraintSolver) Solve(ctx sessionctx.Context, conditions []Expression) []Expression {
 	exprs := newExprSet(conditions)
 	s.fixPoint(ctx, exprs)
 	return exprs.Slice()
 }
 
-// fixPoint is the core of the constant propagation algorithm.
+// fixPoint is the core of the constraint propagation algorithm.
 // It will iterate the expression set over and over again, pick two expressions,
 // apply one to another.
 // If new conditions can be inferred, they will be append into the expression set.
 // Until no more conditions can be inferred from the set, the algorithm finish.
-func (s pgSolver2) fixPoint(ctx sessionctx.Context, exprs *exprSet) {
+func (s constraintSolver) fixPoint(ctx sessionctx.Context, exprs *exprSet) {
 	for {
 		saveLen := len(exprs.data)
-		iterOnce(ctx, exprs)
+		s.iterOnce(ctx, exprs)
 		if saveLen == len(exprs.data) {
 			break
 		}
@@ -104,7 +116,7 @@ func (s pgSolver2) fixPoint(ctx sessionctx.Context, exprs *exprSet) {
 }
 
 // iterOnce picks two expressions from the set, try to propagate new conditions from them.
-func iterOnce(ctx sessionctx.Context, exprs *exprSet) {
+func (s constraintSolver) iterOnce(ctx sessionctx.Context, exprs *exprSet) {
 	for i := 0; i < len(exprs.data); i++ {
 		if exprs.tombstone[i] {
 			continue
@@ -116,24 +128,19 @@ func iterOnce(ctx sessionctx.Context, exprs *exprSet) {
 			if i == j {
 				continue
 			}
-			solve(ctx, i, j, exprs)
+			s.solve(ctx, i, j, exprs)
 		}
 	}
 }
 
 // solve uses exprs[i] exprs[j] to propagate new conditions.
-func solve(ctx sessionctx.Context, i, j int, exprs *exprSet) {
-	for _, rule := range rules {
+func (s constraintSolver) solve(ctx sessionctx.Context, i, j int, exprs *exprSet) {
+	for _, rule := range s {
 		rule(ctx, i, j, exprs)
 	}
 }
 
-type constantPropagateRule func(ctx sessionctx.Context, i, j int, exprs *exprSet)
-
-var rules = []constantPropagateRule{
-	ruleConstantFalse,
-	ruleColumnEQConst,
-}
+type constraintPropagateRule func(ctx sessionctx.Context, i, j int, exprs *exprSet)
 
 // ruleConstantFalse propagates from CNF condition that false plus anything returns false.
 // false, a = 1, b = c ... => false
@@ -164,3 +171,134 @@ func ruleColumnEQConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
 		}
 	}
 }
+
+// ruleColumnOPConst propagates the "column OP const" condition.
+func ruleColumnOPConst(ctx sessionctx.Context, i, j int, exprs *exprSet) {
+	cond := exprs.data[i]
+	f1, ok := cond.(*ScalarFunction)
+	if !ok {
+		return
+	}
+	if f1.FuncName.L != ast.GE && f1.FuncName.L != ast.GT &&
+		f1.FuncName.L != ast.LE && f1.FuncName.L != ast.LT {
+		return
+	}
+	OP1 := f1.FuncName.L
+
+	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
+	}
+
+	// The simple case:
+	// col >= c1, col < c2, c1 >= c2 => false
+	// col >= c1, col <= c2, c1 > c2 => false
+	// col >= c1, col OP c2, c1 ^OP c2, where OP in [< , <=] => false
+	// col OP1 c1 where OP1 in [>= , <], col OP2 c2 where OP1 opsite OP2, c1 ^OP2 c2 => false
+	//
+	// The extended case:
+	// col >= c1, f(col) < c2, f is monotonous, f(c1) >= c2 => false
+	//
+	// Proof:
+	// col > c1, f is monotonous => f(col) > f(c1)
+	// f(col) > f(c1), f(col) < c2, f(c1) >= c2 => false
+	OP2 := f2.FuncName.L
+	if !opsiteOP(OP1, OP2) {
+		return
+	}
+
+	con2, ok := f2.GetArgs()[1].(*Constant)
+	if !ok {
+		return
+	}
+	arg0 := f2.GetArgs()[0]
+	// The simple case.
+	var fc1 Expression
+	col2, ok := arg0.(*Column)
+	if ok {
+		fc1 = con1
+	} else {
+		// The extended case.
+		scalarFunc, ok := arg0.(*ScalarFunction)
+		if !ok {
+			return
+		}
+		_, ok = monotoneIncFuncs[scalarFunc.FuncName.L]
+		if !ok {
+			return
+		}
+		col2, ok = scalarFunc.GetArgs()[0].(*Column)
+		if !ok {
+			return
+		}
+		var err error
+		fc1, err = NewFunction(ctx, scalarFunc.FuncName.L, scalarFunc.RetType, con1)
+		if err != nil {
+			log.Warn(err)
+			return
+		}
+	}
+	if !col1.Equal(ctx, col2) {
+		return
+	}
+	v, isNull, err := compareConstant(ctx, negOP(OP2), fc1, con2)
+	if err != nil {
+		log.Warn(err)
+		return
+	}
+	if !isNull && v > 0 {
+		exprs.SetConstFalse()
+	}
+	return
+}
+
+// opsiteOP the opsite direction of a compare operation, used in ruleColumnOPConst.
+func opsiteOP(op1, op2 string) bool {
+	switch {
+	case op1 == ast.GE || op1 == ast.GT:
+		return op2 == ast.LT || op2 == ast.LE
+	case op1 == ast.LE || op1 == ast.LT:
+		return op2 == ast.GT || op2 == ast.GE
+	}
+	return false
+}
+
+func negOP(cmp string) string {
+	switch cmp {
+	case ast.LT:
+		return ast.GE
+	case ast.LE:
+		return ast.GT
+	case ast.GT:
+		return ast.LE
+	case ast.GE:
+		return ast.LT
+	}
+	return ""
+}
+
+// monotoneIncFuncs are those functions that for any x y, if x > y => f(x) > f(y)
+var monotoneIncFuncs = map[string]struct{}{
+	ast.ToDays: {},
+}
+
+// compareConstant compares two expressions. c1 and c2 should be constant with the same type.
+func compareConstant(ctx sessionctx.Context, fn string, c1, c2 Expression) (int64, bool, error) {
+	cmp, err := NewFunction(ctx, fn, types.NewFieldType(mysql.TypeTiny), c1, c2)
+	if err != nil {
+		return 0, false, err
+	}
+	return cmp.EvalInt(ctx, chunk.Row{})
+}