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Time, patterns and a little more

In this tutorial we’re going to explore the use of pattern synonyms in Haskell, later we’ll give a brief overview to the Stack Builders’ contribution to the `time` Haskell library and finally we’ll review how to use the utilities that were introduced in the contribution.

As Stack Builders one of the core values of our company is contributing to open source (OSS). We believe that we have the power to change people’s lives (or at least make it easier) by pushing the boundaries of the software industry and we’re happy to announce that we were able to contribute to one of Haskell's core libraries, time.

All started with the idea: “What if we bring some utilities that Ruby on Rails (RoR) has to Haskell?”. For instance, “How can one get the range of days that a month has?” or “How can one get a quarter’s boundaries?” were some of the questions that came to our mind. In the following example the RoR code needed to get all days in a month will be shown and then Haskell version to do so:

today =
=> Wed, 01 Nov 2021..Fri, 30 Nov 2021
allMonth :: Day -> [Day]
allMonth day =
    let (y, m , _) = toGregorian day
    in [fromGregorian y m 1 .. fromGregorian y m 31]

and then in ghci this function can be invoked:

> today <- utctDay <$> getCurrentTime
> allMonth today
[2021-11-01 .. 2021-11-30]

As you can see, the Haskell code has to be implemented to then be called, there is not a helper function that performs the same behavior as in RoR. Why the last day of the month is always set to be 31st, if some months have less than 31 days? Could be crossing your mind right now. That’s because fromGregorian clips the values to be correct for each month, but now, what is fromGregorian? Well that’s exactly what this contribution aims, adding some alternative helper functions with clearer names when using the time library.

As Uncle bob mentioned:

"Indeed, the ratio of time spent reading versus writing is well over 10 to 1. We are constantly reading old code as part of the effort to write new code. ...Therefore, making it easy to read makes it easier to write.”

So this was the motivation, to make something similar to the utilities that RoR has and to ease Haskell developers' lives.

So first of all, an issue on GitHub was opened. Quick parenthesis here, when you want to work on OSS it's recommended to start by opening an issue in the repo and discuss/brainstorm your ideas with the maintainers, sometimes there are some good reasons why the feature you’re proposing have not been yet implemented and if you open a PR directly it could rejected, so save yourself a disappointment and open an issue first. Back to the issue, the time's library maintainer proposed to implement these helper functions using pattern synonyms, so let's start with a quick introduction to some basics about this Haskell feature that, actually, it has been around for some years now.

A little about pattern synonyms

First of a little caveat, this guide is not meant to explain pattern synonyms in depth, instead it’s meant to be a practical introduction to this concept.

The GHC documentation describes pattern synonyms like:

“Pattern synonyms enable giving names to parametrized pattern schemes. They can also be thought of as abstract constructors that don’t have a bearing on data representation.”

And probably this does not make sense yet, so let's introduce pattern synonyms with a real world example. Let's borrow a pattern that exists in the time library. The MonthOfYear pattern allows to define months of the year not by a number but by its name.

The MonthOfYear data type is defined like this:

type MonthOfYear = Int

As you can see, MonthOfYear is only an alias for Int. Now, it's possible to define months like Ints, where January will correspond to 1 and so on. But fortunately, since GHC 7.8 it's feasible to use pattern synonyms and, instead of using raw Ints is possible to write this down in a pattern style and have a more idiomatic way of defining months:

pattern January :: MonthOfYear
pattern January = 1

pattern February :: MonthOfYear
pattern February = 2

pattern March :: MonthOfYear
pattern March = 3

-- | The twelve 'MonthOfYear' patterns form a @COMPLETE@ set.
pattern December :: MonthOf
pattern December = 12

{-# COMPLETE January, February, March, April, May, June, July, August, September, October, November, December #-}Year

If you’re curious about why the {-# COMPLETE #-} pragma is being used, see the COMPLETE pragma documentation for more information.

Just to make sure that November and 11 are equivalent, let's test it in a repl:

> November == 11

To exemplify, this pattern will be used in a function that receives a Day and yields if the corresponding date is a holiday:

dayToHoliday :: Day -> String
dayToHoliday (YearMonthDay _ January  _)  = "Happy new year!"
dayToHoliday (YearMonthDay _ November 1)  = "Let's eat colada morada"
dayToHoliday (YearMonthDay _ December 25) = "HO HO HO Merry Christmas"
dayToHoliday _                            = "Probably just a regular day"

Another pattern synonym is introduced here. The YearMonthDay pattern builds a Day in terms of the Year, MonthOfYear (do you remember this one?) and DayOfMOnth, where all three are basically Ints. Here is its definition:

pattern YearMonthDay :: Year -> MonthOfYear -> DayOfMonth -> Day
pattern YearMonthDay y m d <-
   (toGregorian -> (y, m, d))
       YearMonthDay y m d = fromGregorian y m d

Back to the dayToHoliday function, let's check that is working:

> dayToHoliday (YearMonthDay 2021 11 01)
"Let's eat colada morada"

> dayToHoliday (YearMonthDay 2021 12 25)
"HO HO HO Merry Christmas"

(Now you're probably wondering what “colada morada” is? Haha no worries, it’s an Ecuatorian meal that is purple corn based with spices and fruits, pretty amazing to be honest.)

Back to Haskell, probably it’s pretty clear what the dateToHoliday function does, the first clause matches all days of January, second one matches the All Saints holiday, the third one matches for Christmas and the last one it’s the fallback for all other days. Using the MonthOfYear and YearMontDay patterns makes the code more readable. Having something like:

dateToHoliday 12 25  = "HO HO HO Merry Christmas"

Is not as straightforward and readable as the function that was presented in the previous code sample.

It has not being mentioned yet, but the patterns that were built previously, are called bidirectional patterns, why? Because one can use them as expressions as well, so something like this is totally valid:

ghci> dateToHoliday (YearMonthDay 2021 January 12)
"Happy new year!"

ghci> dateToHoliday (YearMonthDay 2021 November 1)
"Let's eat colada morada"

So now it's possible to use 11, November in the MonthOfYear context interchangeably across the code.

Stack Builders contribution to Haskell’s time library

Well all of this preamble was needed to present the contribution itself. Pattern synonyms is what was used when working on time’s new features. You can check the complete pull request(PR). It's important to clarify something, the PR has some different code than the one that is going to be reviewed here, since the maintainer decided to do some renaming and changed the original PR’s code, you can check the changes here. Also, some extra features were added, and now it's possible to get the days that belong to a period (periodAllDays) and a period's length (periodLength).

The new type class DayPeriod was declared as the first step:

class Ord p => DayPeriod p where
   periodFirstDay :: p -> Day
   periodLastDay :: p -> Day
   dayPeriod :: Day -> p

As you can see the DayPeriod type class defines three methods: periodFirstDay that will return the first day of a period, periodLastDay will return the last day and dayPeriod will return the period the Day pass as an argument is in.

One more thing to highlight is that these functions should satisfy some laws (where p is period and d is day):

  • For all p. periodFirstDay p <= periodLastDay p
  • For all p. dayPeriod (periodFirstDay p) == p
  • For all p. dayPeriod (periodLastDay p) == p
  • For all d. periodFirstDay (dayPeriod d) <= d
  • For all d. periodLastDay (dayPeriod d) >= d

Other particular laws for the periodLength function are:

  • For Day. for all p. periodLength p == 1
  • For Months. for all p. periodLength p >= 28
  • For Quarters. for all p. periodLength p >= 90
  • For Years. for all p. periodLength p >= 365

Another particular law for the periodAllDays function is:

  • For all p. (periodAllDay p) ∈ p

The last two sets of laws will be specially usefull later when talking about property testing, so keep these in mind.

After the DayPeriod type class was defined all that is missing is to create the instances of the type class for the different data types: Year, Quarter, Month and Day itself, so here is the code:

instance DayPeriod Year where
   periodFirstDay y = YearMonthDay y January 1
   periodLastDay y = YearMonthDay y December 31
   dayPeriod (YearMonthDay y _ _) = y

The YearMonthDay pattern is being used again to define that January 1st and December 31st are the the first and last days of a year, respectively. Also it's possible to know the year that a day is in with the dayPeriod function.

Now, let’s check the Quarter instance:

instance DayPeriod Quarter where
   periodFirstDay (YearQuarter y q) =
       case q of
           Q1 -> periodFirstDay $ YearMonth y January
           Q2 -> periodFirstDay $ YearMonth y April
           Q3 -> periodFirstDay $ YearMonth y July
           Q4 -> periodFirstDay $ YearMonth y October
   periodLastDay (YearQuarter y q) =
       case q of
           Q1 -> periodLastDay $ YearMonth y March
           Q2 -> periodLastDay $ YearMonth y June
           Q3 -> periodLastDay $ YearMonth y September
           Q4 -> periodLastDay $ YearMonth y Dec

This instance is defined in terms of the periodFirstDay and periodLastDay of a Month and it uses (once again) a pattern named YearMonth.

Let’s move over to the Month instance of DayPeriod:

instance DayPeriod Month where
   periodFirstDay (YearMonth y m) = YearMonthDay y m 1
   periodLastDay (YearMonth y m) = YearMonthDay y m 31 -- clips to correct day
   dayPeriod (YearMonthDay y my _) = YearMonth y my

Apparently patterns are everywhere, and why not? They are pretty useful.

And last but not least, let's review the Day instance of DayPeriod:

instance DayPeriod Day where
   periodFirstDay = id
   periodLastDay = id
   dayPeriod = id

As you could imagine, the first and last day of a day is the day itself and the period is also the same day.

Examples of some new time features

So let's see what these new features that were introduced in the contribution offers. This section will present some concrete code samples of how these new features can help you in your daily software development routine. After making the proper imports it's possible to have something like this.

  • Let's compare the first function that was presented, how to get a month's all days. Now in ghci it's possible to directly call the periodAllDays function with a Month and that will be enough:
ghci> periodAlldays (YearMonth 2021 November)
[2021-11-01 .. 2021-11-30]
  • To get starting and ending days of all quarters of a given year:
type QuarterFirstDay = Day
type QuarterLastDay  = Day

allQuartersBoundaries :: Year -> [(QuarterFirstDay, QuarterLastDay)]
allQuartersBoundaries y =
     map (\q -> (periodFirstDay $ getQuarter q, periodLastDay $ getQuarter q)) [Q1 .. Q4]
             getQuarter q = YearQuarter y q
  • Get quarters' length of a given year. Why the year is needed? Because in a leap year the length of the second quarter will be different:
type QuarterLength = Int

getAllQuarterLength :: Year -> [QuarterLength]
getAllQuarterLength y = map (\q -> periodLength $ YearQuarter y q) [Q1,Q2,Q3,Q4]
  • Get all days of a specific quarter:
allDaysQuarter :: Year -> QuarterOfYear -> [Days]
allDaysQuarter y q = periodAllDays $ YearQuarter y q
  • Get starting and ending days of every month of a given year:
type MonthFirstDay = Day
type MonthLastDay  = Day

getAllMonthsBoundaries :: Year -> [(MonthFirstDay, MonthLastDay)]
getAllMonthsBoundaries y =
     map (\m -> (periodFirstDay $ YearMonth y m, periodLastDay $ YearMonth y m))  [January .. December]
  • Get length of months in a given year:
type MonthLength = Int

allMonthsLenght :: Year -> [MonthLength]
allMonthsLenght y = map (\m -> periodLength $ YearMonth y m) [January .. December]

Second Contribution

Once the first contribution was merged and that the maintainer performed all the refactoring, a follow up PR was opened, the purpose was to add some testing. As it was mentioned previously the maintainer added a couple of extra functions, these are: dayPeriod, periodAllDays and periodLength but they were not tested. The tests implemented in this contribution made use of patterns synonyms (yes, once again) and property testing, so in this section this code will review . Here is the PR that was proposed:

In this context, patterns were pretty useful too. A lot of value was added almost free. Let's review a piece of code:

newtype WDay = MkWDay Day
    deriving (Eq, Show)

instance Arbitrary WDay where
    arbitrary = do
        (MkWYear y) <- arbitrary
        (MkWMonthOfYear m) <- arbitrary
        (MkWDayOfMonth d) <- arbitrary
        pure $ MkWDay $ YearMonthDay y m d

This first part is not related to patterns, instead the Arbitray instance of WDay is being declared, this instance is basically a Day wrapper that allows to generate random days in order to perform property testing. When using property testing you can stop thinking of generating the data that will feed the tests manually, and you can focus on testing that the code is behaving the way it's supposed to. The Arbitrary instaces for: Day, DayOfMonth, Month, MonthOfYear, Quarter, QuarterOfYear and Year were declared too. Probably a better example of this instances is the MonthOfYear instance (sounds familiar? Yes, it's the pattern that was shown as an example in the previous section), so what is going on here is all clear:

newtype WMonthOfYear = MkWMonthOfYear MonthOfYear
    deriving (Eq, Show)
instance Arbitrary WMonthOfYear where
    arbitrary = fmap MkWMonthOfYear $ choose (-5, 17)

Why does it have -5 and 17 boundaries? Well, this function should be able to clip those values to the correct ones, so this clipping is being tested too.

Let's move forward to explore the use of patterns in the context of tests:

testMonth :: [TestTree]
testMonth =
    [ testProperty "periodFirstDay" $ \(MkWMonth my@(YearMonth y m)) ->
        periodFirstDay my == YearMonthDay y m 1
      , testGroup
         [ testCase "leap year" $
            periodLastDay (YearMonth 2024 February) @?= YearMonthDay 2024 February 29
        , testCase "regular year" $
            periodLastDay (YearMonth 2023 February) @?= YearMonthDay 2023 February 28
    , testProperty "dayPeriod" $ \(MkWMonth my@(YearMonth y m), MkWDayOfMonth d) ->
        dayPeriod (YearMonthDay y m d) == my
    , testProperty "periodAllDays" $ \(MkWMonth my@(YearMonth y1 m1)) ->
        all (== (y1, m1)) $ map (\(YearMonthDay y2 m2 _) -> (y2, m2)) $ periodAllDays my
    , testGroup
        [ testProperty "property tests" $ \(MkWMonth my) ->
            periodLength my >= 28
        , testCase "leap year" $
            periodLength (YearMonth 2024 February) @?= 29
        , testCase "regular year" $
            periodLength (YearMonth 2023 February) @?= 28

All of these test are written and will be explained in the Month's context. So in the first line this test is being declared to be of the type testProperty (or property test) and then it yields the function that is being tested (periodFirstDay), then it creates a MkWMonth that is the arbitrary version of Month and is the one that will generate the randomness for property testing and finally it compares that the first day of a month is the same when the periodFirstDay function is used than when using the YearMonthDay pattern.

The periodLastDay tests are a little peculiar, property testing was not used in this case since it was needed to test some particular cases. Here the tests are checking that February's last day is calculated properly for both leap and regular years. As you can see in some cases unit tests can be useful too, so don't stick too much to property testing.

Well, probably the two previous examples are very straightforward, but let's see what the periodAllDays tests are doing. When implementing property tests is a little harder to think of what to test, you have to search a common property (that's why they are called property test) that let you describe the expected behavior. So what it's being checked in this test is that all elements (Days) that the periodAllDays function produces, when the DayPeriod is a Month, belong to the same year and month.

Finally the periodLength was tested and in this case the test suite is a combination of unit tests and property tests. Test are checking that the period's length of all months is at least 28 days and that February's length is correctly calculated in a leap and in a regular year.

Do you remember the laws that were mentioned in the previous section, well those were translated to property tests. Isn't it awesome? When working and creating property tests you need to think out of the box and find the property (law) that every test subject should satisfy, but once that is found is pretty clear what you should check for.

In this test code snippet the best of patterns is put in action. They're being used to generate a random month: MkWMonth my@(YearMonth y1 m1), and to deconstruct a Day into Year, MonthOfYear and DayOfMonth: (YearMonthDay y2 m2 _) -> (y2, m2).


It was a journey, but hopefully you got something from this tutorial. If there are things that need to be highlighted, they would be the following:

  • When working on OSS always start by opening an issue and brainstorm your ideas with the library's mainterners.

  • Pattern synonyms is a Haskell's feature that will make the code base more reable, and as shown in this tutorial could be useful in many scenarios. The YearMonthDay pattern is probably one of the more versatile ones, so if you're working with the time library have this in mind.

  • Time library now has some cool helper functions that are pretty simple to use and hopefully pretty useful too. Keep in mind the periodFirstDay, periodLastDay, periodAllDays and periodLength functions.


As you can see weeks were not mentioned in this tutorial. That's becasue weeks are not canonical, some years have 52 weeks and others have 53 and depending on what part of the world you're in, the week could start in different days (Saturday, Sunday, Monday). A dicussion with the maintainer is going on right now but haven't gotten an answer yet. But if you want to get all Days of a week and specify its starting day, this issue could be useful.

Published on: Dec. 15, 2021

Written by:

Felix Miño

Felix Miño

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