events-01

Reviewed-by: Gregor Kleen <gkleen@yggdrasil.li>

1 files changed, 142 insertions, 0 deletions

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+---
+title: "On the Design of a Turing-Complete Appointment Book"
+published: 2016-05-27
+tags: events
+repo: https://git.yggdrasil.li/gkleen/pub/events
+base: https://git.yggdrasil.li/gkleen/pub/events/tree/events/src/Events/Types.hs?id=e04e707b1fb63b7857878e2d77c560abe3efd51b
+---
+
+I have a long history of using digital appointment books (calendars)
+and not being satisfied with them (I´m currently being frustrated by
+[Google Calendar][] after a long history of using [Remind][]).
+Thus, of course, I had to implement my own, because, as always, all
+existing software does not fullfill my exceedingly unrealistic
+expectations with respect to customizability and extendability.
+
+For now all I want from my appointment book is the ability to, given
+an interval of time, print a list of events in some machine-parsable
+format (probably [JSON][]).
+
+> {-# LANGUAGE TemplateHaskell #-}
+> {-# LANGUAGE MultiParamTypeClasses #-}
+> {-# LANGUAGE FlexibleInstances #-}
+> {-# LANGUAGE UndecidableInstances #-}
+> 
+> module Events.Types
+>        ( TimeRange(..), rangeStart, rangeDuration
+>        , Event(..), payload, occursWithin
+>        , EvalCtx(..), ctxVars, ctxEvents
+>        , ObjCtx(..), objOccurs, objPayload
+>        , Eval, evaluate
+>        , module Data.Aeson
+>        , module Data.Time.Clock
+>        , module Data.Default.Class
+>        ) where
+> 
+> import Control.Lens.TH
+> 
+> import Data.Aeson (Object)
+> 
+> import Data.Time.Clock
+> 
+> import Control.Monad.State.Lazy
+> import ListT (ListT)
+> import qualified ListT
+> 
+> import Data.Default.Class
+> 
+> import Data.Monoid
+> import Control.Monad.Fix
+> import Control.Lens
+> import Data.Maybe
+
+We can quite easily encode an interval of time as a lower bound and a
+duration:
+
+> data TimeRange = TimeRange
+>                  { _rangeStart :: UTCTime
+>                  , _rangeDuration :: NominalDiffTime
+>                  }
+> makeLenses ''TimeRange
+
+For our purposes it´s sufficient to consider an event to be some data
+we´ll display when needed and some way to determine whether the given
+`TimeRange`{.haskell} intersects it:
+
+> data Event = Event
+>              { _payload :: Object
+>              , _occursWithin :: TimeRange -> Bool
+>              }
+> makeLenses ''Event
+
+We are going to want to parse a specification of some kind into a form we can run.
+Below we see one such form.
+
+`ListT`{.haskell} allows for nondeterministic computation – it allows us to split
+our wordline and continue depth-first much like `[]`{.haskell}.
+
+Within every wordline we modify a distinct snapshot of `ObjCtx`{.haskell} we took
+while branching.
+
+We also share one `EvalCtx`{.haskell} across all worldlines.
+
+> type Eval m a = StateT ObjCtx (ListT (StateT EvalCtx m)) a
+
+`ListT`{.haskell} does not ship with extensive support for the
+[transformers package][transformers]:
+
+> instance MonadState s m => MonadState s (ListT m) where
+>   get = lift get
+>   put = lift . put
+
+The context shared among all worldlines mainly contains all objects that
+eventually get computed – haskells lazyness ensures that we terminate as
+long as we don´t have objects depend on themselves in a sufficiently
+degenerate way.
+
+> data EvalCtx = EvalCtx
+>                { _ctxEvents :: [Object]
+>                } deriving (Show)
+> makeLenses ''EvalCtx
+> 
+> instance Default EvalCtx where
+>   def = EvalCtx
+>         { _ctxEvents = mempty
+>         }
+
+Every wordline constructs exactly one object while having access to a set
+of declarations that can occur anywhere on the wordline.
+
+> data ObjCtx = ObjCtx
+>               { _objOccurs :: Bool
+>               , _objPayload :: Maybe Object
+>               , _objVars :: Object
+>               }
+> makeLenses ''ObjCtx
+> 
+> instance Default ObjCtx where
+>   def = ObjCtx
+>         { _objOccurs = False
+>         , _objPayload = Nothing
+>         , _objVars = mempty
+>         }
+
+Constructing an `Object`{.haskell} from an `ObjCtx`{.haskell} is straightforward:
+
+> objCtx :: ObjCtx -> Maybe Object
+> objCtx (ObjCtx False _) = Nothing
+> objCtx (ObjCtx True  o) = o
+
+`mfix`{.haskell} allows all values contained within our various `StateT`{.haskell}
+layers to depend on one another:
+
+> evaluate :: MonadFix m => Eval m () -> m [Object]
+> evaluate x = catMaybes <$> mfix x'
+>   where
+>     x' = evalStateT (ListT.toList (objCtx <$> execStateT x def)) . flip (set ctxEvents) def . catMaybes
+
+[Google Calendar]: <https://calendar.google.com>
+[Remind]: <https://www.roaringpenguin.com/products/remind>
+[JSON]: <https://en.wikipedia.org/wiki/JSON>
+[monad transformers]: <https://en.wikibooks.org/wiki/Haskell/Monad_transformers>
+[transformers]: <https://hackage.haskell.org/package/transformers>