Control.Auto.Switch

A collection of versatile switching mechanisms. Switching is really a core mechanic at the heart of how to structure a lot of program logics. Switching from one "mode" to another, from dead to alive, from room to room, menu to menu...switching between Autos is a core part about how many programs are built.

All of the switches here take advantage of either blip semantics (from Control.Auto.Blip) or Interval semantics (from Control.Auto.Interval)...so this is where maintaining semantically meaningful blip streams and intervals pays off!

Each switch here has various examples, and you'll find many of these in use in the example projects.

Note the naming convention going on here (also used in Control.Auto.Serialize): A switch "from" a blip stream is triggered "internally" by the Auto being switched itself; a switch "on" a blip stream is triggered "externally" by an Auto that is not swiched.

Sequential switching

(-->) infixr 1

Arguments

:: Monad m

=> Interval m a b

initial behavior

-> Auto m a b

final behavior, when the initial behavior turns off.

-> Auto m a b

"This, then that". Behave like the first Interval (and run its effects) as long as it is "on" (outputting Just). As soon as it turns off (is 'Nothing), it'll "switch over" and begin behaving like the second Auto forever, running the effects of the second Auto, too. Works well if the Autos follow interval semantics from Control.Auto.Interval.

>>> let a1 = whileI (<= 4) --> pure 0
>>> streamAuto' a1 [1..10]
[1, 2, 3, 4, 0, 0, 0, 0, 0, 0]

(whileI only lets items satisfying the predicate pass through as "on", and is "off" otherwise; pure is the Auto that always produces the same output)

Association works in a way that you can "chain" -->s, as long as you have an appropriate Auto (and not Interval) at the end:

>>> let a2 = onFor 3 . sumFrom 0
         --> onFor 3 . sumFrom 100
         --> pure 0
>>> streamAuto' a2 [1..10]
[1,3,6,104,109,115,0,0,0,0]

a --> b --> c associates as a --> (b --> c)

This is pretty invaluable for having Autos "step" through a series of different Autos, progressing their state from one stage to the next. Autos can control when they want to be "moved on" from by turning "off" (outputting Nothing).

Note that recursive bindings work just fine, so:

>>> let a3 = onFor 2 . pure "hello"
         --> onFor 2 . pure "goodbye"
         --> a3
>>> let (res3, _) = stepAutoN' 8 a3 ()
>>> res3
["hello", "hello", "world", "world", "hello", "hello", "world", "world"]

the above represents an infinite loop between outputting "hello" and outputting "world".

For serialization, an extra byte cost is incurred per invocation of -->. For cyclic switches like a3, every time the cycle "completes", it adds another layer of --> byte costs. For example, initially, saving a3 incurs a cost for the two -->s. After a3 loops once, it incurs a cost for another two -->s, so it costs four -->s. After a3 loops another time, it is like a cost of six -->s. So be aware that for cyclic bindings like a3, space for serialization grows at O(n).

By the way, it might be worth contrasting this with <|!> and <|?> from Control.Auto.Interval, which have the same type signatures. Those alternative-y operators always feed the input to both sides, run both sides, and output the first Just. With <|!>, you can "switch back and forth" to the first Auto as soon as the first Auto is "on" (Just) again.

-->, in contrast, runs only the first Auto until it is off (Nothing)...then runs only the second Auto. This transition is one-way, as well.

(-?>) infixr 1

Arguments

:: Monad m

=> Interval m a b

initial behavior

-> Interval m a b

final behavior, when the initial behavior turns off.

-> Interval m a b

A variation of -->, where the right hand side can also be an interval/Maybe. The entire result is, then, a Maybe. Probably less useful than --> in most situations.

Arbitrary switching

switchFrom_

Arguments

:: Monad m

=> Auto m a (b, Blip (Auto m a b))

Auto outputting a normal output (b) and a blip stream containing the Auto to replace itself with.

-> Auto m a b

Takes an Auto who has both a normal output stream and a blip stream output stream, where the blip stream emits new Autos.

You can imagine switchFrom_ as a box containing a single Auto like the one just described. It feeds its input into the contained Auto, and its output stream is the "normal value" output stream of the contained Auto.

However, as soon as the blip stream of the contained Auto emits a new Auto...it immediately replaces the contained Auto with the new one. And the whole thing starts all over again.

switchFrom_ a0 will "start" with a0 already in the box.

This is mostly useful to allow Autos to "replace themselves" or control their own destiny, or the behavior of their successors.

In the following example, a1 is an Auto that behaves like a cumulative sum but also outputs a blip stream that will emit an Auto containing pure 100 (the Auto that always emits 100) after three steps.

a1 :: Auto' Int (Int, Blip (Auto' Int Int))
a1 = proc x -> do
    sums       <- sumFrom 0 -< x
    switchBlip <- inB 4     -< pure 100
    id -< (sums, switchBlip)

-- alternatively
a1' = sumFrom 0 &&& (tagBlips (pure 100) . inB 4)

So, switchFrom_ a1 will be the output of count for three steps, and then switch to pure 100 afterwards (when the blip stream emits):

>>> streamAuto' (switchFrom_ a1) [1..10]
[1,3,6,10,100,100,100,100,100,100]

This is fun to use with recursion, so you can get looping switches:

a2 :: Auto' Int (Int, Blip (Auto' Int Int))
a2 = proc x -> do
    sums       <- sumFrom 0 -< x
    switchBlip <- inB 3     -< switchFrom_ a2
    id -< (c, switchBlip)

-- alternatively
a2' = sumFrom 0 &&& (tagBlips (switchFrom_ a2') . inB 3)

>>> streamAuto' (switchFrom_ a2) [101..112]
[ 101, 203, 306  -- first 'sumFrom', on first three items
, 104, 209, 315  -- second 'sumFrom', on second three items
, 107, 215, 324  -- third 'sumFrom', on third three items (107, 108, 109)
, 110, 221, 333] -- final 'sumFrom', on fourht three items (110, 111, 112)

Note that this combinator is inherently unserializable, so you are going to lose all serialization capabilities if you use this. So sad, I know! :( This fact is reflected in the underscore suffix, as per convention.

If you want to use switching and have serialization, you can use the perfectly serialization-safe alternative, switchFromF, which slightly less powerful in ways that are unlikely to be missed in practical usage. That is, almost all non-contrived real life usages of switchFrom_ can be recovered using switchFromF.

switchOn_

Arguments

:: Monad m

=> Auto m a b

initial Auto

-> Auto m (a, Blip (Auto m a b)) b

You can think of this as a little box containing a single Auto inside. Takes two input streams: an input stream of normal values, and a blip stream containing Autos. It feeds the input stream into the contained Auto...but every time the input blip stream emits with a new Auto, replaces the contained Auto with the emitted one. Then starts the cycle all over, immediately giving the new Auto the received input.

Useful for being able to externally "swap out" Autos for a given situation by just emitting a new Auto in the blip stream.

For example, here we push several Autos one after the other into the box: sumFrom 0, productFrom 1, and count. eachAt_ 4 emits each Auto in the given list every four steps, starting on the fourth.

newAutos :: Auto' Int (Blip (Auto' Int Int))
newAutos = eachAt_ 4 [sumFrom 0, productFrom 1, count]

a :: Auto' Int Int
a = proc i -> do
    blipAutos <- newAutos -< ()
    switchOn_ (pure 0)    -< (i, blipAutos)

-- alternatively
a' = switchOn_ (pure 0) . (id &&& newAutos)

>>> streamAuto' a [1..12]
[ 1,  3,   6           -- output from sumFrom 0
, 4, 20, 120           -- output from productFrom 1
, 0,  1,   2, 3, 4, 5] -- output from count

Like switchFrom_, this combinator is inherently unserializable. So if you use it, you give up serialization for your Autos. This is reflected in the underscore suffix.

If you wish to have the same switching devices but keep serialization, you can use switchOnF, which is slightly less powerful, but should be sufficient for all practical use cases.

Function-based switches

switchOnF

Arguments

:: (Monad m, Serialize c)

=> (c -> Auto m a b)

function to generate the next Auto to behave like

-> Auto m a b

initial starting Auto to behave like

-> Auto m (a, Blip c) b

Essentially identical to switchOn_, except instead of taking in a blip stream of new Autos to put into the box, takes a blip stream of c --- and switchOnF uses the c to create the new Auto to put in the box.

Here is the equivalent of the two examples from switchOn_, implemented with switchOnF; see the documentatino for switchOn_ for a description of what they are to do.

newAuto :: Int -> Auto' Int Int
newAuto 1 = sumFrom 0
newAuto 2 = productFrom 1
newAuto 3 = count
newAuto _ = error "Do you expect rigorous error handling from a toy example?"

a :: Auto' Int Int
a = proc i -> do
    blipAutos <- eachAt 4 [1,2,3] -< ()
    switchOnF_ newAuto (pure 0) -< (i, blipAutos)

>>> streamAuto' a [1..12]
[ 1,  3,   6           -- output from sumFrom 0
, 4, 20, 120           -- output from productFrom 1
, 0,  1,   2, 3, 4, 5] -- output from count

Instead of sending in the "replacement Auto", sends in a number, which corresponds to a specific replacement Auto.

As you can see, all of the simple examples from switchOn_ can be implemented in switchOnF...and so can most real-life examples. The advantage is that switchOnF is serializable, and switchOn_ is not.

switchOnF_

Arguments

:: Monad m

=> (c -> Auto m a b)

function to generate the next Auto to behave like

-> Auto m a b

initial starting Auto to behave like

-> Auto m (a, Blip c) b

The non-serializing/non-resuming version of switchOnF. You sort of might as well use switchOn_; this version might give rise to more "disciplined" code, however, by being more restricted in power.

switchFromF

Arguments

:: (Monad m, Serialize c)

=> (c -> Auto m a (b, Blip c))

function to generate the next Auto to behave like

-> Auto m a (b, Blip c)

initial Auto. the b is the output, and the blip stream triggers new Autos to replace this one.

-> Auto m a b

Essentially identical to switchFrom_, except insead of the Auto outputting a blip stream of new Autos to replace itself with, it emits a blip stream of c --- and switchFromF uses the c to create the new Auto.

Here is the equivalent of the two examples from switchFrom_, implemented with switchFromF; see the documentatino for switchFrom_ for a description of what they are to do.

a1 :: Auto' Int (Int, Blip Int)
a1 = proc x -> do
    sums       <- sumFrom 0 -< x
    switchBlip <- inB 4     -< 100
    id -< (sums, switchBlip)

-- alternatively
a1' = sumFrom 0 &&& (tagBlips 100 . inB 4)

>>> streamAuto' (switchFrom_ pure a1) [1..10]
[1,3,6,10,100,100,100,100,100,100]

a2 :: Auto' Int (Int, Blip ())
a2 = proc x -> do
    sums       <- sumFrom 0 -< x
    switchBlip <- inB 3     -< ()
    id -< (c, switchBlip)

-- alternatively
a2' = sumFrom 0 &&& (tagBlips () . inB 3)

>>> streamAuto' (switchFromF (const a2) a2) [101..112]
[ 101, 203, 306  -- first 'sumFrom', on first three items
, 104, 209, 315  -- second 'sumFrom', on second three items
, 107, 215, 324  -- third 'sumFrom', on third three items (107, 108, 109)
, 110, 221, 333] -- final 'sumFrom', on fourht three items (110, 111, 112)

Or, if you're only ever going to use a2 in switching form:

a2s :: Auto' Int Int
a2s = switchFromF (const a2s) $ proc x -> do
          sums       <- sumFrom 0 -< x
          switchBlip <- inB 3     -< ()
          id -< (c, swichBlip)

-- or
a2s' = switchFromF (const a2s')
     $ sumFrom 0 &&& (tagBlips () . inB 3)

>>> streamAuto' a2s [101..112]
[101, 203, 306, 104, 209, 315, 107, 215, 324, 110, 221, 333]

As you can see, all of the simple examples from switchFrom_ can be implemented in switchFromF...and so can most real-life examples. The advantage is that switchFromF is serializable, and switchFrom_ is not.

Note that for the examples above, instead of using const, we could have actually used the input parameter to create a new Auto based on what we outputted.

switchFromF_

Arguments

:: Monad m

=> (c -> Auto m a (b, Blip c))

function to generate the next Auto to behave like

-> Auto m a (b, Blip c)

initial Auto. the b is the output, and the blip stream triggers new Autos to replace this one.

-> Auto m a b

The non-serializing/non-resuming version of switchFromF. You sort of might as well use switchFrom_; this version might give rise to more "disciplined" code, however, by being more restricted in power.

Resetting

resetOn

Arguments

:: Monad m

=> Auto m a b

Auto to repeatedly reset

-> Auto m (a, Blip c) b

Takes an innocent Auto and wraps a "reset button" around it. It behaves just like the original Auto at first, but when the input blip stream emits, the internal Auto is reset back to the beginning.

Here we have sumFrom wrapped around a reset button, and we send in a blip stream that emits every 4 steps; so every 4th step, the whole summer resets.

>>> let a = resetOn (sumFrom 0) . (id &&& every 4)
>>> streamAuto' a [101..112]
[ 101, 203, 306
, 104, 209, 315  -- resetted!
, 107, 215, 324  -- resetted!
, 110, 221, 333] -- resetted!

resetFrom

Arguments

:: Monad m

=> Auto m a (b, Blip c)

The self-resetting Auto

-> Auto m a b

Gives an Auto the ability to "reset" itself on command

Basically acts like fmap fst

fmap fst :: Monad m => Auto m a (b, Blip c) -> Auto m a b

But...whenever the blip stream emits..."resets" the Auto back to the original state, as if nothing ever happened.

Note that this resetting happens on the step after the blip stream emits.

Here is a summer that sends out a signal to reset itself whenever the cumulative sum reaches 10 or higher:

limitSummer :: Auto' Int (Int, Blip ())
limitSummer = (id &&& became (>= 10)) . sumFrom 0

And now we throw it into resetFrom:

resettingSummer :: Auto' Int Int
resettingSummer = resetFrom limitSummer

>>> streamAuto' resettingSummer [1..10]
[ 1, 3, 6, 10    -- and...reset!
, 5, 11          -- and...reset!
, 7, 15          -- and...reset!
, 9, 19 ]