149 lines
5.7 KiB
Text
149 lines
5.7 KiB
Text
module AutomatonV2 where
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{-| This library is a way to package up dynamic behavior. It makes it easier to
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dynamically create dynamic components. See the [original release
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notes](/blog/announce/version-0.5.0.elm) on this library to get a feel for how
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it can be used.
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-}
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import open Basics
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import Signal (lift,foldp,Signal)
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import open List
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import Maybe (Just, Nothing)
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data Automaton input output = Pure (input -> output)
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| Stateful state (input -> state -> (output,state))
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-- The basics
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-- AFRP name: arr
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pure: (i -> o) -> Automaton i o
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pure = Pure
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-- AFRP name: >>>
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andThen: Automaton i inter -> Automaton inter o -> Automaton i o
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andThen first second =
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case first of
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Pure f -> case second of -- f is the function from first
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Pure s -> Pure (s . f) -- s is the function from second
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Stateful b s -> Stateful b (\i -> s (f i)) -- b is the base state from second
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Stateful fb f -> case second of -- fb is the base state from first
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Pure s -> Stateful fb (\i st -> -- sb is the base state from second
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let (inter, st') = f i st -- i is the input
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in (s inter, st')) -- st is the input state
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Stateful sb s -> Stateful (fb, sb) (\i (fst, sst) -> -- inter is the intermediate value
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let (inter, fst') = f i fst -- st' is the new state
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(o, sst') = s inter sst -- fst and sst are the state of first and second
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in (o, (fst', sst'))) -- ect...
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-- AFRP name: first
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extendDown: Automaton i o -> Automaton (i,extra) (o,extra)
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extendDown auto = case auto of
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Pure fun -> Pure (\(i,extra) -> (fun i, extra))
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Stateful base fun -> Stateful base (\(i,extra) s -> (fun i s, extra))
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-- AFRP name: loop
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loop: s -> Automaton (i,s) (o,s) -> Automaton i o
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loop base auto = case auto of
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Pure fun -> Stateful base (curry fun)
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Stateful base2 fun -> -- fun: (i, s) -> s2 -> ((o, s), s2)
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let newFun = (\i (s,s2) ->
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let ((o, s'), s2') = fun (i, s) s2
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in (o, (s', s2'))) -- newFun: i -> (s, s2) -> (o, (s, s2))
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in Stateful (base, base2) newFun
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-- Run an automaton on a given signal
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run: Automaton i o -> o -> Signal i -> Signal o
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run auto baseOut input = case auto of
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Pure fun -> lift fun input
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Stateful base fun -> lift fst
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(foldp (\i (o, s) -> fun i s)
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(baseOut, base) input)
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-- Other frequently used functions/operators
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-- Create an automaton with state. Requires an initial state and a step
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-- function to step the state forward. For example, an automaton that counted
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-- how many steps it has taken would look like this:
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--
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-- count = Automaton a Int
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-- count = state 0 (\\_ c -> c+1)
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--
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-- It is a stateful automaton. The initial state is zero, and the step function
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-- increments the state on every step.
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state : s -> (i -> s -> s) -> Automaton i s
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state base fun = loop base (pure (\(i,s) ->
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let s' = fun i s
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in (s',s')))
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-- Create an automaton with hidden state. Requires an initial state and a
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-- step function to step the state forward and produce an output.
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hiddenState : s -> (i -> s -> (s,o)) -> Automaton i o
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hiddenState base fun = loop base (pure (\(i,s) ->
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let (o,s') = fun i s
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in (s',o)))
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-- AFRP name: second
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extendUp: Automaton i o -> Automaton (extra,i) (extra,o)
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extendUp auto =
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let swap (a, b) = (b, a)
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in pure swap `andThen` extendDown auto `andThen` pure swap
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-- (parallel composition)
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pair: Automaton i1 o1 -> Automaton i2 o2 -> Automaton (i1,i2) (o1,o2)
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pair f g = extendDown f `andThen` extendUp g
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branch : Automaton i o1 -> Automaton i o2 -> Automaton i (o1,o2)
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branch f g =
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let double = pure (\i -> (i,i))
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in double `andThen` pair f g
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combi: Automaton i o -> Automaton i [o] -> Automaton i [o]
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combi a1 a2 = (a1 `branch` a2) `andThen` pure (uncurry (::))
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-- Combine a list of automatons into a single automaton that produces a list.
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combine : [Automaton i o] -> Automaton i [o]
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combine autos =
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let l = length autos
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in if l == 0
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then pure (\_ -> [])
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else foldr combi (last autos `andThen` pure (\a -> [a])) (take (l-1) autos)
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-- Examples of automata
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-- Count the number of steps taken.
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count : Automaton a Int
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count = state 0 (\_ c -> c + 1)
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type Queue t = ([t],[t])
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empty = ([],[])
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enqueue x (en,de) = (x::en, de)
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dequeue q = case q of
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([],[]) -> Nothing
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(en,[]) -> dequeue ([], reverse en)
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(en,hd::tl) -> Just (hd, (en,tl))
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-- Computes the running average of the last `n` inputs.
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average : Int -> Automaton Float Float
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average k =
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let step n (ns,len,sum) =
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if len == k then stepFull n (ns,len,sum)
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else ((enqueue n ns, len+1, sum+n), (sum+n) / (toFloat len+1))
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stepFull n (ns,len,sum) =
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case dequeue ns of
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Nothing -> ((ns,len,sum), 0)
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Just (m,ns') -> let sum' = sum + n - m
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in ((enqueue n ns', len, sum'), sum' / toFloat len)
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in hiddenState (empty,0,0) step
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{-- TODO(evancz): See the following papers for ideas on how to make this
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library faster and better:
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- Functional Reactive Programming, Continued -- took some inspirations from this paper (Apanatshka)
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- Causal commutative arrows and their optimization
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Speeding things up is a really low priority. Language features and
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libraries with nice APIs and are way more important!
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--}
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