Consider 7 as Sunday

parser.go

@@ -135,12 +135,19 @@ func (p Parser) Parse(spec string) (Schedule, error) {
 		hour       = field(fields[2], hours)
 		dayofmonth = field(fields[3], dom)
 		month      = field(fields[4], months)
-		dayofweek  = field(fields[5], dow)
+		dayofweek  = field(fields[5], extendedDOW)
 	)
 	if err != nil {
 		return nil, err
 	}
 
+	if 1<<7&dayofweek > 0 {
+		// For compatibility with https://linux.die.net/man/5/crontab
+		// we consider 1 in the 7th bit as Sunday and move it to the first bit
+		dayofweek |= 1
+		dayofweek ^= 1 << 7
+	}
+
 	return &SpecSchedule{
 		Second:   second,
 		Minute:   minute,

parser_test.go

@@ -149,6 +149,9 @@ func TestParseSchedule(t *testing.T) {
 		{secondParser, "CRON_TZ=UTC  0 5 * * * *", every5min(time.UTC)},
 		{standardParser, "CRON_TZ=UTC  5 * * * *", every5min(time.UTC)},
 		{secondParser, "CRON_TZ=Asia/Tokyo 0 5 * * * *", every5min(tokyo)},
+		{standardParser, "CRON_TZ=Asia/Tokyo 0 0 * * 0", everySunday(tokyo)},
+		{standardParser, "CRON_TZ=Asia/Tokyo 0 0 * * 7", everySunday(tokyo)},
+		{standardParser, "CRON_TZ=Asia/Tokyo 0 0 * * Sun", everySunday(tokyo)},
 		{secondParser, "@every 5m", ConstantDelaySchedule{5 * time.Minute}},
 		{secondParser, "@midnight", midnight(time.Local)},
 		{secondParser, "TZ=UTC  @midnight", midnight(time.UTC)},
@@ -370,6 +373,10 @@ func midnight(loc *time.Location) *SpecSchedule {
 	return &SpecSchedule{1, 1, 1, all(dom), all(months), all(dow), loc}
 }
 
+func everySunday(loc *time.Location) *SpecSchedule {
+	return &SpecSchedule{1, 1, 1, all(dom), all(months), 1 << uint(time.Sunday), loc}
+}
+
 func annual(loc *time.Location) *SpecSchedule {
 	return &SpecSchedule{
 		Second:   1 << seconds.min,

spec.go

@@ -46,6 +46,9 @@ var (
 		"fri": 5,
 		"sat": 6,
 	}}
+
+	// extendedDOW is only needed to parse "7" as Sunday
+	extendedDOW = bounds{dow.min, 7, dow.names}
 )
 
 const (