deepcontrol

A Haskell library that enables more deeper level style programming than the usual Control.xxx modules provide, especially for Applicative and Monad.

Installing with Stack

If you haven't installed Stack yet, install Stack.

If you have never even used Stack, launch the terminal and go to your working directory:

.../yourworkingdirectory$

To create your own Stack new project folder, type as below:

../yourworkingdirectory$ stack new yourproject simple
Downloading template "simple" to create project "yourproject" in yourproject/ ...
...

Go into your project folder:

../yourworkingdirectory$ cd yourproject/

To install GHC on your Stack project folder, type as below:

.../yourproject$ stack setup
stack will use a locally installed GHC

Now start ghci and see if it works well.

.../yourproject$ stack ghci
...
Prelude>

Fetch from Stackage

Add deepcontrol to your .cabal file:

yourproject.cabal:

  ...
  build-depends:       ...
                     , deepcontrol

On your project folder run "stack build" to get Stack to install deepcontrol into your project.

.../yourproject$ stack build

If Stack yields a messeage below, it means that deepcontrol failed to be resolved on yourproject's Stack resolver. Probably you will get this message since deepcontrol is just one of miner libraries yet.

.../yourproject$ stack build
While constructing the BuildPlan the following exceptions were encountered:
...

If you want to try other resolver, type as below:

.../yourproject$ stack init
Refusing to overwrite existing stack.yaml, please delete before running stack init or if you are sure use "--force"

Please follow the message direction.

Fetch from Hackage

Ok, I(you) got deepcontrol isn't in Stackage. Then let's fetch deepcontrol from Hackage. Add deepcontrol-0.3.3.0 to your extra-deps field in stack.yaml too:

stack.yaml:

extra-deps:
...
- deepcontrol-0.3.3.0

And type as below:

.../yourproject$ stack build

Stack must fetch and install deepcontrol automatically.

../yourproject$ stack build
deepcontrol-0.3.3.0: configure
...

Now start ghci and see if it works well.

.../yourproject$ stack ghci
...
Prelude> :m DeepControl.Applicative

Installing with Cabal

deepcontrol is available from Hackage.

Launch the terminal and go to your project folder:

.../yourproject$

If you haven't done setup cabal sandbox on your project folder yet, type as below so that deepcontrol will be installed locally on your project folder:

.../yourproject$ cabal sandbox init
Writing a default package environment file to
...

To install deepcontrol on your project folder, type as below:

.../yourproject$ cabal update
Downloading the latest package list from hackage.haskell.org
...
.../yourproject$ cabal install deepcontrol
Resolving dependencies...
...

Now start ghci and see if it works well.

.../yourproject$ cabal repl
...

Prelude> :m DeepControl.Applicative

Examples

Applicative

This module enables you to program in applicative style for more deeper level than the usual Applicative module expresses. You would soon realize exactly what more deeper level means by reading the example codes below in order.

Prelude> :m DeepControl.Applicative

Level-0

bra-ket notation:

> (1+) |> 2
3
> 1 <| (+2)
3

> 1 <|(+)|> 2
3
> 1 <|(+)|> 2 <|(*)|> 3
9

> 1 <|(,)|> 2
(1,2)

Level-1

bra-ket notation:

> (1+) |$> [2]
[3]
> [1] <$| (+2)
[3]
> ("<"++)|$> ["a","b"] <$|(++">")
["<a>","<b>"]

> [(1+)] |*> [2]
[3]

> [1] <$|(+)|*> [2]
[3]
> [1] <$|(+)|*> [0,1,2]
[1,2,3]
> [0,1] <$|(+)|*> [2,3] <$|(+)|*> [4,5]
[6,7,7,8,7,8,8,9]

> foldr (\x acc -> x <$|(:)|*> acc) ((*:) []) [Just 1, Just 2,  Just 3]
Just [1,2,3]
> foldr (\x acc -> x <$|(:)|*> acc) ((*:) []) [Just 1, Nothing, Just 3]
Nothing

> filter (even <$|(&&)|*> (10 >)) [1..100]
[2,4,6,8]
> filter (even <$|(&&)|*> (10 >) <$|(&&)|*> (5 <)) [1..100]
[6,8]

braket-cover notation

> [(1+)] |* 2
[3]
> [1] <$|(+)|* 2
[3]
> [1] <$|(+)|* 2 <$|(*)|* 3
[9]

> Just 1 <$|(,)|* 2
Just (1,2)

> 1 *| [(+2)]
[3]
> 1 *| [(+)] |* 2
[3]
> 1 *|[(+),(-),(*),(^)]|* 2
[3,-1,2,1]

> 1 *|Just (,)|* 2
Just (1,2)

Level-2

bra-ket notation:

> (+1) |$>> [[2]]
[[3]]
> [[2]] <<$| (+1)
[[3]]

> [Just 1] <<$|(+)|*>> [Just 2]
[Just 3]
> [Just 1] <<$|(,)|*>> [Just 2]
[Just (1,2)]

> [[1]] <<$|(+)|*>> [[2]] <<$|(-)|*>> [[3]]
[[0]]

> foldr (\n acc -> n <<$|(+)|*>> acc) ((**:) 0) [Right (Just 1), Right (Just 2), Right (Just 3)] :: Either () (Maybe Int)
Right (Just 6)
> foldr (\n acc -> n <<$|(+)|*>> acc) ((**:) 0) [Right (Just 1), Right Nothing, Right (Just 3)] :: Either () (Maybe Int)
Right Nothing
> foldr (\n acc -> n <<$|(+)|*>> acc) ((**:) 0) [Right (Just 1), Right Nothing, Left ()]
Left ()

braket-cover notation:

> [Just 1] <<$|(+)|** 2
[Just 3]
> 1 **|(+)|$>> [Just 2]
[Just 3]
> 1 **|[Just (+)]|**  2
[Just 3]
> 1 **|[Just (+), Just (-), Just (*), Nothing]|** 2
[Just 3,Just (-1),Just 2,Nothing]

> [Just 1] <<$|(+)|-* [2]
[Just 3]
> [Just 1] <<$|(+)|*- Just 2
[Just 3]
>      [1]  -*|(+)|$>> [Just 2]
[Just 3]
>   Just 1  *-|(+)|$>> [Just 2]
[Just 3]
>   Just 1  *-|[Just (+)]|** 2
[Just 3]
>   Just 1  *-|[Just (+)]|*- Just 2
[Just 3]
>      [1]  -*|[Just (+)]|*- Just 2
[Just 3]
>      [1]  -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2
[Just 3,Just (-1),Just 2,Nothing]
>    [0,1]  -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2
[Just 2,Just 3,Just (-2),Just (-1),Just 0,Just 2,Nothing,Nothing]

Level-3

Work well likewise.

Level-4, Level-5

Not completely written up yet.

Monad

This module enables you to program in Monad for more deeper level than the usual Monad module expresses. You would soon realize exactly what more deeper level means by reading the example codes below in order.

Level-2

import DeepControl.Applicative ((**:))
import DeepControl.Monad

listlist :: [[String]]             -- List-List Monad
listlist = [["a","b"]] >>== \x ->
           [[0],[1,2]] >>== \y ->
           (**:) $ x ++ show y

-- > listlist
-- [["a0","b0"],["a0","b1","b2"],["a1","a2","b0"],["a1","a2","b1","b2"]]

import DeepControl.Applicative
import DeepControl.Monad
import DeepControl.Monad.Trans.Writer

factorial :: Int ->
             Maybe (Writer [Int] Int)  -- Maybe-Writer Monad
factorial n | n < 0  = (-*) Nothing
            | n == 0 = (*:) $ tell [0] >> return 1
            | n > 0  = factorial (n-1) >>== \v ->
                       tell [v] ->~
                       (**:) (n * v)

-- > runWriter |$> factorial 5
-- Just (120,[0,1,1,2,6,24])

Level-3

import DeepControl.Applicative
import DeepControl.Monad
import DeepControl.Monad.Trans.Writer

factorial :: Int ->
             IO (Maybe (Writer [Int] Int))    -- IO-Maybe-Writer Monad
factorial n | n < 0  = (*-*) Nothing
            | n == 0 = (**:) $ tell [0] >> return 1
            | n > 0  = factorial (n-1) >>>== \v ->
                       print v >--~
                       tell [v] -->~
                       (***:) (n * v)

-- > runWriter |$>> factorial 5
-- 1
-- 1
-- 2
-- 6
-- 24
-- Just (120,[0,1,1,2,6,24])

Monad-Transformer

Level-2

Here is a monad transformer example how to implement Ackermann function, improved to stop within a certain limit of time, with ReaderT-IdentityT2-IO-Maybe monad, a level-2 monad-transformation.

import DeepControl.Applicative
import DeepControl.Commutative (commute)
import DeepControl.Monad ((>-))
import DeepControl.Monad.Morph ((|>|))
import DeepControl.Monad.Trans (liftTT2, transfold2, untransfold2)
import DeepControl.Monad.Trans.Identity
import DeepControl.Monad.Trans.Reader
import Control.Monad.Trans.Maybe

import System.Timeout (timeout)

type TimeLimit = Int

ackermannTimeLimit :: TimeLimit -> Int -> Int -> 
                      IO (Maybe Int)                     -- IO-Maybe Monad
ackermannTimeLimit timelimit x y = timeout timelimit (ackermannIO x y)
  where
    ackermannIO :: Int -> Int -> IO Int
    ackermannIO 0 n = (*:) $ n + 1
    ackermannIO m n | m > 0 && n == 0 = ackermannIO (m-1) 1
                    | m > 0 && n > 0  = ackermannIO m (n-1) >>= ackermannIO (m-1)
 
ackermann :: Int -> Int -> 
             ReaderT TimeLimit (IdentityT2 IO Maybe) Int -- ReaderT-IdentityT2-IO-Maybe monad
ackermann x y = do
    timelimit <- ask
    liftTT2 $ ackermannTimeLimit timelimit x y           -- lift IO-Maybe function to ReaderT-IdentityT2-IO-Maybe function

calc_ackermann :: TimeLimit -> Int -> Int -> IO (Maybe Int)
calc_ackermann timelimit x y = ackermann x y >- \r -> runReaderT r timelimit
                                             >- runIdentityT2

-- λ> commute $ calc_ackermann 1000 |$> [0..4] |* 4
-- [Just 5,Just 6,Just 11,Just 125,Nothing]

ackermann' :: Int -> Int -> 
              ReaderT TimeLimit (MaybeT IO) Int                -- ReaderT-MaybeT-IO monad
ackermann' x y = (runIdentityT . transfold2) |>| ackermann x y -- You can get usual ReaderT-MaybeT-IO function from ReaderT-IdentityT2-IO-Maybe function

ackermann'' :: Int -> Int -> 
               ReaderT TimeLimit (IdentityT2 IO Maybe) Int      -- ReaderT-IdentityT2-IO-Maybe monad
ackermann'' x y = (untransfold2 . IdentityT) |>| ackermann' x y -- You can get ReaderT-IdentityT2-IO-Maybe function from usual ReaderT-MaybeT-IO function

Here is a monad transformer example showing that the monad morph is usable.

import DeepControl.Applicative ((|$>))
import DeepControl.Monad (Monad2)
import DeepControl.Monad.Morph ((|>|))
import DeepControl.Monad.Trans (liftT, (|*|), (|-*|), (|*-|))
import DeepControl.Monad.Trans.Writer
import DeepControl.Monad.Trans.Identity
import DeepControl.Monad.Trans.State

tick :: State Int ()
tick = modify (+1)

tock                         ::                   StateT Int IO ()
tock = do
    (|*|) tick               :: (Monad      m) => StateT Int m  ()
    liftT $ putStrLn "Tock!" :: (MonadTrans t) => t          IO ()

-- λ> runStateT tock 0
-- Tock!
-- ((),1)

save    :: StateT Int (Writer [Int]) ()
save = do
    n <- get
    liftT $ tell [n]

program ::               StateT Int (IdentityT2 IO (Writer [Int])) ()
program = replicateM_ 4 $ do
    ((|-*|).liftT) |>| tock
        :: (Monad2 m) => StateT Int (IdentityT2 IO m             ) ()
    ((|*-|).liftT) |>| save
        :: (Monad  m) => StateT Int (IdentityT2 m  (Writer [Int])) ()

-- λ> execWriter |$> runIdentityT2 (runStateT program 0)
-- Tock!
-- Tock!
-- Tock!
-- Tock!
-- [1,2,3,4]

Level-3, Level-4 and Level-5

Work well likewise.

Monad-Morph

Here is a monad-morph example, a level-2 monad-morph.

import DeepControl.Monad.Morph
import DeepControl.Monad.Trans.State
import DeepControl.Monad.Trans.Writer

-- i.e. :: StateT Int Identity ()
tick    :: State Int ()
tick = modify (+1)

tock                        ::                   StateT Int IO ()
tock = do
    generalize |>| tick     :: (Monad      m) => StateT Int m  ()
    lift $ putStrLn "Tock!" :: (MonadTrans t) => t          IO ()

-- λ> runStateT tock 0
-- Tock!
-- ((),1)

-- i.e. :: StateT Int (WriterT [Int] Identity) ()
save    :: StateT Int (Writer  [Int]) ()
save = do
    n <- get
    lift $ tell [n]

program ::                   StateT Int (WriterT [Int] IO) ()
program = replicateM_ 4 $ do
    lift |>| tock
        :: (MonadTrans t) => StateT Int (t             IO) ()
    generalize |>>| save
        :: (Monad      m) => StateT Int (WriterT [Int] m ) ()

-- λ> execWriterT (runStateT program 0)
-- Tock!
-- Tock!
-- Tock!
-- Tock!
-- [1,2,3,4]

Commutative

Arrow