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1−module AutomatonV2 where
2−{-| This library is a way to package up dynamic behavior. It makes it easier to
3−dynamically create dynamic components. See the [original release
4−notes](/blog/announce/version-0.5.0.elm) on this library to get a feel for how
5−it can be used.
6−-}
7−
8−import open Basics
9−import Signal (lift,foldp,Signal)
10−import open List
11−import Maybe (Just, Nothing)
12−
13−data Automaton input output = Pure (input -> output)
14− | Stateful state (input -> state -> (output,state))
15−
16−-- The basics
17−
18−-- AFRP name: arr
19−pure: (i -> o) -> Automaton i o
20−pure = Pure
21−
22−-- AFRP name: >>>
23−andThen: Automaton i inter -> Automaton inter o -> Automaton i o
24−andThen first second =
25− case first of
26− Pure f -> case second of -- f is the function from first
27− Pure s -> Pure (s . f) -- s is the function from second
28− Stateful b s -> Stateful b (\i -> s (f i)) -- b is the base state from second
29− Stateful fb f -> case second of -- fb is the base state from first
30− Pure s -> Stateful fb (\i st -> -- sb is the base state from second
31− let (inter, st') = f i st -- i is the input
32− in (s inter, st')) -- st is the input state
33− Stateful sb s -> Stateful (fb, sb) (\i (fst, sst) -> -- inter is the intermediate value
34− let (inter, fst') = f i fst -- st' is the new state
35− (o, sst') = s inter sst -- fst and sst are the state of first and second
36− in (o, (fst', sst'))) -- ect...
37−
38−-- AFRP name: first
39−extendDown: Automaton i o -> Automaton (i,extra) (o,extra)
40−extendDown auto = case auto of
41− Pure fun -> Pure (\(i,extra) -> (fun i, extra))
42− Stateful base fun -> Stateful base (\(i,extra) s -> (fun i s, extra))
43−
44−-- AFRP name: loop
45−loop: s -> Automaton (i,s) (o,s) -> Automaton i o
46−loop base auto = case auto of
47− Pure fun -> Stateful base (curry fun)
48− Stateful base2 fun -> -- fun: (i, s) -> s2 -> ((o, s), s2)
49− let newFun = (\i (s,s2) ->
50− let ((o, s'), s2') = fun (i, s) s2
51− in (o, (s', s2'))) -- newFun: i -> (s, s2) -> (o, (s, s2))
52− in Stateful (base, base2) newFun
53−
54−-- Run an automaton on a given signal
55−run: Automaton i o -> o -> Signal i -> Signal o
56−run auto baseOut input = case auto of
57− Pure fun -> lift fun input
58− Stateful base fun -> lift fst
59− (foldp (\i (o, s) -> fun i s)
60− (baseOut, base) input)
61−
62−
63−-- Other frequently used functions/operators
64−
65−-- Create an automaton with state. Requires an initial state and a step
66−-- function to step the state forward. For example, an automaton that counted
67−-- how many steps it has taken would look like this:
68−--
69−-- count = Automaton a Int
70−-- count = state 0 (\\_ c -> c+1)
71−--
72−-- It is a stateful automaton. The initial state is zero, and the step function
73−-- increments the state on every step.
74−state : s -> (i -> s -> s) -> Automaton i s
75−state base fun = loop base (pure (\(i,s) ->
76− let s' = fun i s
77− in (s',s')))
78−
79−-- Create an automaton with hidden state. Requires an initial state and a
80−-- step function to step the state forward and produce an output.
81−hiddenState : s -> (i -> s -> (s,o)) -> Automaton i o
82−hiddenState base fun = loop base (pure (\(i,s) ->
83− let (o,s') = fun i s
84− in (s',o)))
85−
86−-- AFRP name: second
87−extendUp: Automaton i o -> Automaton (extra,i) (extra,o)
88−extendUp auto =
89− let swap (a, b) = (b, a)
90− in pure swap `andThen` extendDown auto `andThen` pure swap
91−
92−-- (parallel composition)
93−pair: Automaton i1 o1 -> Automaton i2 o2 -> Automaton (i1,i2) (o1,o2)
94−pair f g = extendDown f `andThen` extendUp g
95−
96−branch : Automaton i o1 -> Automaton i o2 -> Automaton i (o1,o2)
97−branch f g =
98− let double = pure (\i -> (i,i))
99− in double `andThen` pair f g
100−
101−combi: Automaton i o -> Automaton i [o] -> Automaton i [o]
102−combi a1 a2 = (a1 `branch` a2) `andThen` pure (uncurry (::))
103−
104−-- Combine a list of automatons into a single automaton that produces a list.
105−combine : [Automaton i o] -> Automaton i [o]
106−combine autos =
107− let l = length autos
108− in if l == 0
109− then pure (\_ -> [])
110− else foldr combi (last autos `andThen` pure (\a -> [a])) (take (l-1) autos)
111−
112−
113−-- Examples of automata
114−
115−-- Count the number of steps taken.
116−count : Automaton a Int
117−count = state 0 (\_ c -> c + 1)
118−
119−type Queue t = ([t],[t])
120−empty = ([],[])
121−enqueue x (en,de) = (x::en, de)
122−dequeue q = case q of
123− ([],[]) -> Nothing
124− (en,[]) -> dequeue ([], reverse en)
125− (en,hd::tl) -> Just (hd, (en,tl))
126−
127−-- Computes the running average of the last `n` inputs.
128−average : Int -> Automaton Float Float
129−average k =
130− let step n (ns,len,sum) =
131− if len == k then stepFull n (ns,len,sum)
132− else ((enqueue n ns, len+1, sum+n), (sum+n) / (toFloat len+1))
133− stepFull n (ns,len,sum) =
134− case dequeue ns of
135− Nothing -> ((ns,len,sum), 0)
136− Just (m,ns') -> let sum' = sum + n - m
137− in ((enqueue n ns', len, sum'), sum' / toFloat len)
138− in hiddenState (empty,0,0) step
139−
140−
141−{-- TODO(evancz): See the following papers for ideas on how to make this
142−library faster and better:
143−
144−- Functional Reactive Programming, Continued -- took some inspirations from this paper (Apanatshka)
145−- Causal commutative arrows and their optimization
146−
147−Speeding things up is a really low priority. Language features and
148−libraries with nice APIs and are way more important!
149−--}