PlutusPrelude

Enumerate all the values of an Enum, from minBound to maxBound.

enumerate == [False, True]

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

'join bss' can be understood as the do expression

do bs <- bss
   bs

Examples

>>> join [[1, 2, 3], [4, 5, 6], [7, 8, 9]][1,2,3,4,5,6,7,8,9]

>>> join (Just (Just 3))Just 3

A common use of join is to run an IO computation returned from an GHC.Conc.STM transaction, since GHC.Conc.STM transactions can't perform IO directly. Recall that

GHC.Internal.Conc.atomically :: STM a -> IO a

is used to run GHC.Conc.STM transactions atomically. So, by specializing the types of GHC.Internal.Conc.atomically and join to

GHC.Internal.Conc.atomically :: STM (IO b) -> IO (IO b)
join       :: IO (IO b)  -> IO b

we can compose them as

join . GHC.Internal.Conc.atomically :: STM (IO b) -> IO b

to run an GHC.Conc.STM transaction and the IO action it returns.

Left-to-right composition. This is useful if you want to write a morphism as a pipeline going from left to right.

Right-to-left composition of Kleisli arrows. (>=>), with the arguments flipped.

Note how this operator resembles function composition (.):

(.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c

Left-to-right composition of Kleisli arrows.

'(bs >=> cs) a' can be understood as the do expression

do b <- bs a
   cs b

or in terms of (>>=) as

bs a >>= cs

Conditional failure of Alternative computations. Defined by

guard True  = pure ()
guard False = empty

Examples

Common uses of guard include conditionally signalling an error in an error monad and conditionally rejecting the current choice in an Alternative-based parser.

As an example of signalling an error in the error monad Maybe, consider a safe division function safeDiv x y that returns Nothing when the denominator y is zero and Just (x `div` y) otherwise. For example:

>>> safeDiv 4 0Nothing

>>> safeDiv 4 2Just 2

A definition of safeDiv using guards, but not guard:

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y | y /= 0    = Just (x `div` y)
            | otherwise = Nothing

A definition of safeDiv using guard and Monad do-notation:

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y = do
  guard (y /= 0)
  return (x `div` y)

Return the contents of a Right-value or a default value otherwise.

Examples

Basic usage:

>>> fromRight 1 (Right 3)3>>> fromRight 1 (Left "foo")1

Return True if the given value is a Left-value, False otherwise.

Examples

Basic usage:

>>> isLeft (Left "foo")True>>> isLeft (Right 3)False

Assuming a Left value signifies some sort of error, we can use isLeft to write a very simple error-reporting function that does absolutely nothing in the case of success, and outputs "ERROR" if any error occurred.

This example shows how isLeft might be used to avoid pattern matching when one does not care about the value contained in the constructor:

>>> import Control.Monad ( when )>>> let report e = when (isLeft e) $ putStrLn "ERROR">>> report (Right 1)>>> report (Left "parse error")ERROR

Return True if the given value is a Right-value, False otherwise.

Examples

Basic usage:

>>> isRight (Left "foo")False>>> isRight (Right 3)True

Assuming a Left value signifies some sort of error, we can use isRight to write a very simple reporting function that only outputs "SUCCESS" when a computation has succeeded.

This example shows how isRight might be used to avoid pattern matching when one does not care about the value contained in the constructor:

>>> import Control.Monad ( when )>>> let report e = when (isRight e) $ putStrLn "SUCCESS">>> report (Left "parse error")>>> report (Right 1)SUCCESS

for_ is traverse_ with its arguments flipped. For a version that doesn't ignore the results see for. This is forM_ generalised to Applicative actions.

for_ is just like forM_, but generalised to Applicative actions.

Examples

Basic usage:

>>> for_ [1..4] print1234

Map each element of a structure to an Applicative action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see traverse.

traverse_ is just like mapM_, but generalised to Applicative actions.

Examples

Basic usage:

>>> traverse_ print ["Hello", "world", "!"]"Hello""world""!"

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

This is a version of flip id, where id is specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is (a -> b) -> a -> b. flipping this yields a -> (a -> b) -> b which is the type signature of &

Examples

>>> 5 & (+1) & show"6"

>>> sqrt $ [1 / n^2 | n <- [1..1000]] & sum & (*6)3.1406380562059946

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

(op `on` f) x y = f x `op` f y

Examples

>>> sortBy (compare `on` length) [[0, 1, 2], [0, 1], [], [0]][[],[0],[0,1],[0,1,2]]

>>> ((+) `on` length) [1, 2, 3] [-1]4

>>> ((,) `on` (*2)) 2 3(4,6)

Algebraic properties

• (*) `on` id = (*) -- (if (*) ∉ {⊥, const ⊥})

• ((*) `on` f) `on` g = (*) `on` (f . g)

• flip on f . flip on g = flip on (g . f)

Flipped version of <$.

Examples

Replace the contents of a Maybe Int with a constant String:

>>> Nothing $> "foo"Nothing

>>> Just 90210 $> "foo"Just "foo"

Replace the contents of an Either Int Int with a constant String, resulting in an Either Int String:

>>> Left 8675309 $> "foo"Left 8675309

>>> Right 8675309 $> "foo"Right "foo"

Replace each element of a list with a constant String:

>>> [1,2,3] $> "foo"["foo","foo","foo"]

Replace the second element of a pair with a constant String:

>>> (1,2) $> "foo"(1,"foo")

Flipped version of <$>.

(<&>) = flip fmap

Examples

Apply (+1) to a list, a Just and a Right:

>>> Just 2 <&> (+1)Just 3

>>> [1,2,3] <&> (+1)[2,3,4]

>>> Right 3 <&> (+1)Right 4

void value discards or ignores the result of evaluation, such as the return value of an System.IO.IO action.

Examples

Replace the contents of a Maybe Int with unit:

>>> void NothingNothing

>>> void (Just 3)Just ()

Replace the contents of an Either Int Int with unit, resulting in an Either Int ():

>>> void (Left 8675309)Left 8675309

>>> void (Right 8675309)Right ()

Replace every element of a list with unit:

>>> void [1,2,3][(),(),()]

Replace the second element of a pair with unit:

>>> void (1,2)(1,())

Discard the result of an System.IO.IO action:

>>> mapM print [1,2]12[(),()]

>>> void $ mapM print [1,2]12

The fromMaybe function takes a default value and a Maybe value. If the Maybe is Nothing, it returns the default value; otherwise, it returns the value contained in the Maybe.

Examples

Basic usage:

>>> fromMaybe "" (Just "Hello, World!")"Hello, World!"

>>> fromMaybe "" Nothing""

Read an integer from a string using readMaybe. If we fail to parse an integer, we want to return 0 by default:

>>> import GHC.Internal.Text.Read ( readMaybe )>>> fromMaybe 0 (readMaybe "5")5>>> fromMaybe 0 (readMaybe "")0

isJust x returns True when x is of the form Just _ and False otherwise.

Examples

Basic usage:

>>> isJust (Just 3)True

>>> isJust (Just ())True

>>> isJust NothingFalse

Only the outer constructor is taken into consideration:

>>> isJust (Just Nothing)True

isNothing x returns True when x is Nothing and False otherwise.

Examples

Basic usage:

>>> isNothing (Just 3)False

>>> isNothing (Just ())False

>>> isNothing NothingTrue

Only the outer constructor is taken into consideration:

>>> isNothing (Just Nothing)False

for is traverse with its arguments flipped. For a version that ignores the results see for_.

The trace function outputs the trace message given as its first argument, before returning the second argument as its result.

For example, this returns the value of f x and outputs the message to stderr. Depending on your terminal (settings), they may or may not be mixed.

>>> let x = 123; f = show>>> trace ("calling f with x = " ++ show x) (f x)calling f with x = 123"123"

The trace function should only be used for debugging, or for monitoring execution. The function is not referentially transparent: its type indicates that it is a pure function but it has the side effect of outputting the trace message.

Like traceShow but returns the shown value instead of a third value.

>>> traceShowId (1+2+3, "hello" ++ "world")(6,"helloworld")(6,"helloworld")

Throw an exception. Exceptions may be thrown from purely functional code, but may only be caught within the IO monad.

WARNING: You may want to use throwIO instead so that your pure code stays exception-free.

View the value pointed to by a Getter or Lens or the result of folding over all the results of a Control.Lens.Fold.Fold or Control.Lens.Traversal.Traversal that points at a monoidal values.

This is the same operation as view with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (Prelude..).

>>> (a,b)^._2b

>>> ("hello","world")^._2"world"

>>> import Data.Complex>>> ((0, 1 :+ 2), 3)^._1._2.to magnitude2.23606797749979

(^.) ::             s -> Getter s a     -> a
(^.) :: Monoid m => s -> Control.Lens.Fold.Fold s m       -> m
(^.) ::             s -> Control.Lens.Iso.Iso' s a       -> a
(^.) ::             s -> Lens' s a      -> a
(^.) :: Monoid m => s -> Control.Lens.Traversal.Traversal' s m -> m

View the value pointed to by a Getter, Control.Lens.Iso.Iso or Lens or the result of folding over all the results of a Fold or Control.Lens.Traversal.Traversal that points at a monoidal value.

view . to ≡ id

>>> view (to f) af a

>>> view _2 (1,"hello")"hello"

>>> view (to succ) 56

>>> view (_2._1) ("hello",("world","!!!"))"world"

As view is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

view ::             Getter s a     -> s -> a
view :: Monoid m => Fold s m       -> s -> m
view ::             Control.Lens.Iso.Iso' s a       -> s -> a
view ::             Lens' s a      -> s -> a
view :: Monoid m => Control.Lens.Traversal.Traversal' s m -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

view :: MonadReader s m             => Getter s a     -> m a
view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
view :: MonadReader s m             => Control.Lens.Iso.Iso' s a       -> m a
view :: MonadReader s m             => Lens' s a      -> m a
view :: (MonadReader s m, Monoid a) => Control.Lens.Traversal.Traversal' s a -> m a

Build a Lens from a getter and a setter.

lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t

>>> s ^. lens getter settergetter s

>>> s & lens getter setter .~ bsetter s b

>>> s & lens getter setter %~ fsetter s (f (getter s))

lens :: (s -> a) -> (s -> a -> s) -> Lens' s a

Modifies the target of a Lens or all of the targets of a Setter or Traversal with a user supplied function.

This is an infix version of over.

fmap f ≡ mapped %~ f
fmapDefault f ≡ traverse %~ f

>>> (a,b,c) & _3 %~ f(a,b,f c)

>>> (a,b) & both %~ f(f a,f b)

>>> _2 %~ length $ (1,"hello")(1,5)

>>> traverse %~ f $ [a,b,c][f a,f b,f c]

>>> traverse %~ even $ [1,2,3][False,True,False]

>>> traverse.traverse %~ length $ [["hello","world"],["!!!"]][[5,5],[3]]

(%~) :: Setter s t a b    -> (a -> b) -> s -> t
(%~) :: Iso s t a b       -> (a -> b) -> s -> t
(%~) :: Lens s t a b      -> (a -> b) -> s -> t
(%~) :: Traversal s t a b -> (a -> b) -> s -> t

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

This is an infix version of set, provided for consistency with (.=).

f <$ a ≡ mapped .~ f $ a

>>> (a,b,c,d) & _4 .~ e(a,b,c,e)

>>> (42,"world") & _1 .~ "hello"("hello","world")

>>> (a,b) & both .~ c(c,c)

(.~) :: Setter s t a b    -> b -> s -> t
(.~) :: Iso s t a b       -> b -> s -> t
(.~) :: Lens s t a b      -> b -> s -> t
(.~) :: Traversal s t a b -> b -> s -> t

Modify the target of a Lens or all the targets of a Setter or Traversal with a function.

fmap ≡ over mapped
fmapDefault ≡ over traverse
sets . over ≡ id
over . sets ≡ id

Given any valid Setter l, you can also rely on the law:

over l f . over l g = over l (f . g)

e.g.

>>> over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]True

Another way to view over is to say that it transforms a Setter into a "semantic editor combinator".

>>> over mapped f (Just a)Just (f a)

>>> over mapped (*10) [1,2,3][10,20,30]

>>> over _1 f (a,b)(f a,b)

>>> over _1 show (10,20)("10",20)

over :: Setter s t a b -> (a -> b) -> s -> t
over :: ASetter s t a b -> (a -> b) -> s -> t

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

(<$) ≡ set mapped

>>> set _2 "hello" (1,())(1,"hello")

>>> set mapped () [1,2,3,4][(),(),(),()]

Note: Attempting to set a Fold or Getter will fail at compile time with an relatively nice error message.

set :: Setter s t a b    -> b -> s -> t
set :: Iso s t a b       -> b -> s -> t
set :: Lens s t a b      -> b -> s -> t
set :: Traversal s t a b -> b -> s -> t

Pretty-print and render a value as a string type.

The function coerce allows you to safely convert between values of types that have the same representation with no run-time overhead. In the simplest case you can use it instead of a newtype constructor, to go from the newtype's concrete type to the abstract type. But it also works in more complicated settings, e.g. converting a list of newtypes to a list of concrete types.

When used in conversions involving a newtype wrapper, make sure the newtype constructor is in scope.

This function is representation-polymorphic, but the RuntimeRep type argument is marked as Inferred, meaning that it is not available for visible type application. This means the typechecker will accept coerce @Int @Age 42.

Examples

>>> newtype TTL = TTL Int deriving (Eq, Ord, Show)>>> newtype Age = Age Int deriving (Eq, Ord, Show)>>> coerce (Age 42) :: TTLTTL 42>>> coerce (+ (1 :: Int)) (Age 42) :: TTLTTL 43>>> coerce (map (+ (1 :: Int))) [Age 42, Age 24] :: [TTL][TTL 43,TTL 25]

Map covariantly over the first argument.

first f ≡ bimap f id

Examples

>>> first toUpper ('j', 3)('J',3)

>>> first toUpper (Left 'j')Left 'J'

Map covariantly over the second argument.

second ≡ bimap id

Examples

>>> second (+1) ('j', 3)('j',4)

>>> second (+1) (Right 3)Right 4

A class for types with a default value.

A class of types that can be fully evaluated.