I don’t know if this is relevant but for manipulating time intervals, I have found the intervals package very useful.

Message: 5 Date: Wed, 2 Nov 2016 21:26:32 +0100 From: Olaf Klinke To: list@mroth.net Cc: haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] Suggestion for Data Structure regarding Timetabling and Time Intervals Message-ID: <63753058-716B-4D2B-8D8F-4B0F77732C2A@aatal-apotheke.de> Content-Type: text/plain; charset=us-ascii

Dear Michael,

if you can be sure your intervals will never overlap, why not use a binary search tree, such as Data.Set from containers? You could make a data structure distinguishing major and minor intervals such as:

type Time = -- your favourite totally ordered time type data Major = Major { fromTime :: Time, untilTime :: Time} deriving (Eq) data Minor = Minor { after :: Time before :: Time} deriving (Eq) type TimeInterval = Either Minor Major

instance Ord (Either Minor Major) where Left a <= Left b = before a <= after b Right a <= Right b = untilTime a <= fromTime b Left a <= Right b = before a <= fromTime b Right a <= Left b = untilTime a <= after b

If I understood your intentions correctly, inserting a minor interval between a :: Major and b :: Major where a < b would mean to insert

Minor {after = untilTime a, before = fromTime b}

It might also be handy to define a new type (isomorphic to the product (a,b))

Anno a b = Anno a b

whose Ord instance uses the Ord instance of b only, so that

Anno "Some annotation" (Major t0 t1)

is an interval bearing some annotation that can be ordered just like the Major type.

If your intervals _do_ overlap, then two intervals can be in six different configurations (instead of LT, GT and EQ), and several tree structures exist that support some operations more or less efficiently. Bioinformatics and geometry has developed good data structures and algorithms to deal with efficient overlap searches.

Olaf

Dominic Steinitz dominic@steinitz.org http://idontgetoutmuch.wordpress.com