This module provides a monad for computing with Allen's interval algebra. The monad keeps track of the interval graph that is being built up during the computation. The interval graph is represented as a map from interval identifiers to intervals.

Intervals

Intervals can be created using the interval function:

calc :: Allen ()
calc = do 
  sleeps <- interval
  snores <- interval
  wakeup <- interval
  ...

Retrieving interval data

Most functions perform operations on intervals solely with the use of their IDs. However, sometimes it is useful to retrieve the actual interval data. To get the actual interval data, use the fromID function:

calc :: Allen () 
calc = do 
  sleeps         <- interval 
  sleepsInterval <- fromID sleeps
  ...

Note that in the above example, updating the interval sleeps will not update the interval sleepsInterval.

Combining calculations

Sometimes, it is useful to define a set of intervals in one place and use then repeatedly in other places. Here is an example that reuses the intervals a and b:

network :: Allen (IntervalID, IntervalID)
network = do 
  a <- interval 
  b <- interval 

  assume a During b 

  return (a, b)

calc1 :: Allen () 
calc1 = do 
  (a, b) <- network 
  c      <- interval

  assume a Precedes c
  ...

calc2 :: Allen ()
calc2 = do 
  (a, b) <- network 
  c      <- interval

  assume a Contains c
  ...

Relations

Intervals can have relations with one another. For example, in the above example a valid relation would be that one sleeps during snores. Adding relations is done using one of the assume functions:

calc :: Allen () 
calc = do 
   sleeps <- interval
   snores <- interval
   wakeup <- interval

   assume snores During sleeps
   assume wakeup PrecededBy sleeps

Sometimes, intervals have more than one possible relation with one another. For example, snores is During sleeps, but it could also be StartedBy sleeps, or it could Equals sleeps. In such cases, the assumeSet function can be used:

calc :: Allen () 
calc = do 
   sleeps <- interval
   snores <- interval
   wakeup <- interval

   assumeSet snores [During, StartedBy, Equals] sleeps

There are thirteen different relations intervals can have with each other. They are identified with the Relation type.