FRP learning note

frp_note.txt

reference: Functional Reactive Animation - by Conal Elliott et al

* 2 things:
	- Behavior a
	- Event a

* semantic functions
	- at  :: Behavior a -> Time -> a
	- occ :: Event a -> (Time, a)

* functions related to Behavior
	- time :: Behavior Time
	-> at time t = t

	- lift2 :: (a1 -> a2 -> b) ->
				 Behavior a1 -> Behavior a2 -> Behavior b

	- untilB :: Behavior a -> Event (Behavior a) -> Behavior a
	-> at (b untilB e) t = 
			if t<=te then (at b t) else (at b' t)
			where (te,b') = occ e

* Behavior example
	-  wiggle :: Behavior R
	-> wiggle = sin (pi * time)

	- wiggleRange lo hi = lo + (hi-lo) * (wiggle+1)/2

* functions related to Event
	-  (+=>) :: Event a -> (Time -> a -> b) -> Event b
	-> occ (e +=> f) = (te, f te x)
			where (te,x) = occ e

	- (==>) :: Event a -> (a -> b) -> Event b
	- (*=>) :: Event a -> (Time -> b) -> Event b
	- (-=>) :: Event a -> b -> Event b

	- click :: Time -> Event (Event ())

	example: 	b1 `untilB` (click t0) ==> \e ->
			b2 `untilB` e -=>
			b3



	-  predicate :: Behavior Bool -> Time -> Event ()
	-> occ (predicate b t0) = (inf {t > t0 | (at b t)}, ())

	example: b1 `untilB` (predicate (sin time = 0.5) t0) 
           -=> b2

	- (.|.) :: Event a -> Event a -> Event a     --choice



example: 一個預設值為0, 當按下左鍵會變成-1, 按下右鍵會變成1
	bSign :: Time -> Behavior Int
	bSign t0 =
		0 `untilB` leftClick t0 ==> nonZero (-1) .|.
					 rightClick t0 ==> nonZero 1
		where nonZero r stop =
				r `untilB` stop *=> bSign

另一個寫法（但是不正確）

    RACSignal* leftClickedSignal;
    RACSignal* rightClickedSignal;
    RACSignal* zeroSignal;
    RACSignal* bSignTemp;
    bSignTemp = [RACSignal combineLatest:@[[zeroSignal takeUntil:leftClickedSignal],
                                     [zeroSignal takeUntil:rightClickedSignal]]
                      reduce:^(NSNumber *leftClicked, NSNumber* rightClicked)
    {
       if (leftClicked.boolValue) {
           return @(-1);
       } else  if (leftClicked.boolValue) {
           return @(1);
       } else {
           return @(0);
       }
    }];

   // resubscribe the original signal
   RACSignal* bSign = [bSignTemp concat:bSignTemp];