Haskell’09 Proceedings of the 2009 ACM SIGPLAN Haskell by Stephanie Weirich Haskell’09 Program Chair

By Stephanie Weirich Haskell’09 Program Chair

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Additional resources for Haskell’09 Proceedings of the 2009 ACM SIGPLAN Haskell Symposium

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This representation adds an expense of its own, which is removed in Sections 10 and 11. When t is a future time, what meanings do we want for ∅ and (⊕)? Two future values can be combined only when both are known, so (⊕) = max . Since ∅ is an identity for (⊕), it follows b must have a least element. that ∅ = minBound , and so T The Applicative semantics for futures follow from these considerations choosing force to be an applicative functor morphism: instancesem Applicative Future where force (pure a) = pure a = (∅, a) = (minBound , a) force (uf <∗> ux ) = force uf <∗> force ux = (tˆf , f ) <∗> (tˆx , x ) = (tˆf ⊕ tˆx , f x ) = (tˆf ‘max ‘ tˆx , f x ) where (tˆf , f ) = force uf (tˆx , x ) = force ux • For each sample time t, the semantics of switcher involves searching through an event for the last occurrence before t.

A third alternative is to try both methods in parallel and just use sinkB :: Sink a → Behavior a → IO b sinkB snk (O rf ) = do snkF ← newTFunSink snk sinkR snkF rf The procedure newTFunSink makes a sink that consumes successive time functions. For each consumed constant function K a, the value a is rendered just once (with snk ). When a non-constant function Fun f is consumed, a thread is started that repeatedly samples f at the current time and renders: forkIO (forever (f <$> getTime > >= snk )) In either case, the constructed sink begins by killing the current rendering thread, if any.

The join operation collapses an event-valued event ee into an event. Each occurrence of ee delivers a new event, all of which get adjusted to insure temporal monotonicity and merged together into a single event. The event ee can have infinitely many occurrences, each of which (being an event) can also have an infinite number of occurrences. Thus joinE has the tricky task of merging (a representation of) a sorted infinite stream of sorted infinite streams into a single sorted infinite stream. Since an event is represented as a Future, the join makes essential use of the Future monad7 : Monad The Monad instance is perhaps most easily understood via its join: joinR :: Reactive (Reactive a) → Reactive a The definition of joinR is similar to (<∗>) above: joinE :: Event (Event a) → Event a joinE (Event u) = Event (u > >= eFuture ◦ g) where g (e ‘Stepper ‘ ee) = e ⊕ joinE ee eFuture (Ev u) = u joinR ((a ‘Stepper ‘ Ev ur ) ‘Stepper ‘ Ev urr ) = a ‘Stepper ‘ Ev u where u = ...

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