| License | BSD-style |
|---|---|
| Maintainer | Vincent Hanquez <vincent@snarc.org> |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | None |
| Language | Haskell2010 |
Foundation
Contents
Description
I tried to picture clusters of information As they moved through the computer What do they look like?
Alternative Prelude
- ($) :: (a -> b) -> a -> b
- ($!) :: (a -> b) -> a -> b
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- (.) :: Category k cat => forall b c a. cat b c -> cat a b -> cat a c
- not :: Bool -> Bool
- otherwise :: Bool
- data Tuple2 a b = Tuple2 !a !b
- data Tuple3 a b c = Tuple3 !a !b !c
- data Tuple4 a b c d = Tuple4 !a !b !c !d
- class Fstable a where
- type FstTy a
- class Sndable a where
- type SndTy a
- class Thdable a where
- type ThdTy a
- id :: Category k cat => forall a. cat a a
- maybe :: b -> (a -> b) -> Maybe a -> b
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- flip :: (a -> b -> c) -> b -> a -> c
- const :: a -> b -> a
- error :: HasCallStack => [Char] -> a
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- getArgs :: IO [String]
- uncurry :: (a -> b -> c) -> (a, b) -> c
- curry :: ((a, b) -> c) -> a -> b -> c
- swap :: (a, b) -> (b, a)
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a -> a -> a
- undefined :: HasCallStack => a
- seq :: a -> b -> b
- class Show a where
- class Eq a => Ord a where
- class Eq a where
- class Bounded a where
- class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
- class Functor f where
- class Functor f => Applicative f where
- class Applicative m => Monad m where
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- class IsString a where
- fromString :: String -> a
- class IsList l where
- class (Eq a, Ord a, Num a, Enum a, Additive a, Subtractive a, Difference a ~ a, Multiplicative a, Divisible a) => Number a where
- class Number a => Signed a where
- class Additive a where
- class Subtractive a where
- type Difference a
- class Multiplicative a where
- data Maybe a :: * -> *
- data Ordering :: *
- data Bool :: *
- data Char :: *
- data IO a :: * -> *
- data Either a b :: * -> * -> *
- data Int8 :: *
- data Int16 :: *
- data Int32 :: *
- data Int64 :: *
- data Word8 :: *
- data Word16 :: *
- data Word32 :: *
- data Word64 :: *
- data Word :: *
- data Int :: *
- data Integer :: *
- type Rational = Ratio Integer
- data Float :: *
- data Double :: *
- data UArray ty
- class Eq ty => PrimType ty
- data Array a
- data String
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- class Monoid a where
- (<>) :: Monoid m => m -> m -> m
- class Foldable t
- asum :: (Foldable t, Alternative f) => t (f a) -> f a
- class (Functor t, Foldable t) => Traversable t
- mapMaybe :: (a -> Maybe b) -> [a] -> [b]
- catMaybes :: [Maybe a] -> [a]
- fromMaybe :: a -> Maybe a -> a
- isJust :: Maybe a -> Bool
- isNothing :: Maybe a -> Bool
- listToMaybe :: [a] -> Maybe a
- maybeToList :: Maybe a -> [a]
- partitionEithers :: [Either a b] -> ([a], [b])
- lefts :: [Either a b] -> [a]
- rights :: [Either a b] -> [b]
- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- (<|>) :: Alternative f => forall a. f a -> f a -> f a
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- class (Typeable * e, Show e) => Exception e where
- toException :: e -> SomeException
- fromException :: SomeException -> Maybe e
- displayException :: e -> String
- class Typeable k a
- data SomeException :: *
- data IOException :: *
- data Proxy k t :: forall k. k -> * = Proxy
- asProxyTypeOf :: a -> Proxy * a -> a
- data Partial a
- partial :: a -> Partial a
- data PartialError
- fromPartial :: Partial a -> a
- type LString = String
Standard
Operators
($) :: (a -> b) -> a -> b infixr 0 #
Application operator. This operator is redundant, since ordinary
application (f x) means the same as (f . However, $ x)$ has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as map ($ 0) xszipWith ($) fs xs
($!) :: (a -> b) -> a -> b infixr 0 #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
Functions
Strict tuple (a,b)
Constructors
| Tuple2 !a !b |
Instances
| (Eq a, Eq b) => Eq (Tuple2 a b) Source # | |
| (Data a, Data b) => Data (Tuple2 a b) Source # | |
| (Ord a, Ord b) => Ord (Tuple2 a b) Source # | |
| (Show a, Show b) => Show (Tuple2 a b) Source # | |
| Generic (Tuple2 a b) Source # | |
| Sndable (Tuple2 a b) Source # | |
| Fstable (Tuple2 a b) Source # | |
| type Rep (Tuple2 a b) Source # | |
| type SndTy (Tuple2 a b) Source # | |
| type FstTy (Tuple2 a b) Source # | |
Strict tuple (a,b,c)
Constructors
| Tuple3 !a !b !c |
Instances
| (Eq a, Eq b, Eq c) => Eq (Tuple3 a b c) Source # | |
| (Data a, Data b, Data c) => Data (Tuple3 a b c) Source # | |
| (Ord a, Ord b, Ord c) => Ord (Tuple3 a b c) Source # | |
| (Show a, Show b, Show c) => Show (Tuple3 a b c) Source # | |
| Generic (Tuple3 a b c) Source # | |
| Thdable (Tuple3 a b c) Source # | |
| Sndable (Tuple3 a b c) Source # | |
| Fstable (Tuple3 a b c) Source # | |
| type Rep (Tuple3 a b c) Source # | |
| type ThdTy (Tuple3 a b c) Source # | |
| type SndTy (Tuple3 a b c) Source # | |
| type FstTy (Tuple3 a b c) Source # | |
Strict tuple (a,b,c,d)
Constructors
| Tuple4 !a !b !c !d |
Instances
| (Eq a, Eq b, Eq c, Eq d) => Eq (Tuple4 a b c d) Source # | |
| (Data a, Data b, Data c, Data d) => Data (Tuple4 a b c d) Source # | |
| (Ord a, Ord b, Ord c, Ord d) => Ord (Tuple4 a b c d) Source # | |
| (Show a, Show b, Show c, Show d) => Show (Tuple4 a b c d) Source # | |
| Generic (Tuple4 a b c d) Source # | |
| Thdable (Tuple4 a b c d) Source # | |
| Sndable (Tuple4 a b c d) Source # | |
| Fstable (Tuple4 a b c d) Source # | |
| type Rep (Tuple4 a b c d) Source # | |
| type ThdTy (Tuple4 a b c d) Source # | |
| type SndTy (Tuple4 a b c d) Source # | |
| type FstTy (Tuple4 a b c d) Source # | |
class Fstable a where Source #
Class of product types that have a first element
Minimal complete definition
class Sndable a where Source #
Class of product types that have a second element
Minimal complete definition
class Thdable a where Source #
Class of product types that have a third element
Minimal complete definition
maybe :: b -> (a -> b) -> Maybe a -> b #
The maybe function takes a default value, a function, and a Maybe
value. If the Maybe value is Nothing, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just and returns the result.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed,
return twice the integer; that is, apply (*2) to it. If instead
we fail to parse an integer, return 0 by default:
>>>import Text.Read ( readMaybe )>>>maybe 0 (*2) (readMaybe "5")10>>>maybe 0 (*2) (readMaybe "")0
Apply show to a Maybe Int. If we have Just n, we want to show
the underlying Int n. But if we have Nothing, we return the
empty string instead of (for example) "Nothing":
>>>maybe "" show (Just 5)"5">>>maybe "" show Nothing""
either :: (a -> c) -> (b -> c) -> Either a b -> c #
Case analysis for the Either type.
If the value is Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft constructor and another using the Right constructor. Then
we apply "either" the length function (if we have a String)
or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
flip :: (a -> b -> c) -> b -> a -> c #
flip ff.
const x is a unary function which evaluates to x for all inputs.
For instance,
>>>map (const 42) [0..3][42,42,42,42]
error :: HasCallStack => [Char] -> a #
error stops execution and displays an error message.
getArgs :: IO [String] Source #
Returns a list of the program's command line arguments (not including the program name).
uncurry :: (a -> b -> c) -> (a, b) -> c #
uncurry converts a curried function to a function on pairs.
until :: (a -> Bool) -> (a -> a) -> a -> a #
until p ff until p holds.
undefined :: HasCallStack => a #
The value of seq a b is bottom if a is bottom, and
otherwise equal to b. seq is usually introduced to
improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does
not guarantee that a will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
Type classes
Conversion of values to readable Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show is equivalent to
instance (Show a) => Show (Tree a) where
showsPrec d (Leaf m) = showParen (d > app_prec) $
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10
showsPrec d (u :^: v) = showParen (d > up_prec) $
showsPrec (up_prec+1) u .
showString " :^: " .
showsPrec (up_prec+1) v
where up_prec = 5Note that right-associativity of :^: is ignored. For example,
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Instances
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined
datatype whose constituent types are in Ord. The declared order
of the constructors in the data declaration determines the ordering
in derived Ord instances. The Ordering datatype allows a single
comparison to determine the precise ordering of two objects.
Minimal complete definition: either compare or <=.
Using compare can be more efficient for complex types.
Instances
The Eq class defines equality (==) and inequality (/=).
All the basic datatypes exported by the Prelude are instances of Eq,
and Eq may be derived for any datatype whose constituents are also
instances of Eq.
Instances
| Eq Bool | |
| Eq Char | |
| Eq Double | |
| Eq Float | |
| Eq Int | |
| Eq Int8 | |
| Eq Int16 | |
| Eq Int32 | |
| Eq Int64 | |
| Eq Integer | |
| Eq Ordering | |
| Eq Word | |
| Eq Word8 | |
| Eq Word16 | |
| Eq Word32 | |
| Eq Word64 | |
| Eq TypeRep | |
| Eq () | |
| Eq TyCon | |
| Eq BigNat | |
| Eq SpecConstrAnnotation | |
| Eq Void | |
| Eq Constr | Equality of constructors |
| Eq DataRep | |
| Eq ConstrRep | |
| Eq Fixity | |
| Eq Version | |
| Eq HandlePosn | |
| Eq CDev | |
| Eq CIno | |
| Eq CMode | |
| Eq COff | |
| Eq CPid | |
| Eq CSsize | |
| Eq CGid | |
| Eq CNlink | |
| Eq CUid | |
| Eq CCc | |
| Eq CSpeed | |
| Eq CTcflag | |
| Eq CRLim | |
| Eq Fd | |
| Eq ThreadId | |
| Eq BlockReason | |
| Eq ThreadStatus | |
| Eq Errno | |
| Eq AsyncException | |
| Eq ArrayException | |
| Eq ExitCode | |
| Eq IOErrorType | |
| Eq Handle | |
| Eq BufferMode | |
| Eq Newline | |
| Eq NewlineMode | |
| Eq WordPtr | |
| Eq IntPtr | |
| Eq CChar | |
| Eq CSChar | |
| Eq CUChar | |
| Eq CShort | |
| Eq CUShort | |
| Eq CInt | |
| Eq CUInt | |
| Eq CLong | |
| Eq CULong | |
| Eq CLLong | |
| Eq CULLong | |
| Eq CFloat | |
| Eq CDouble | |
| Eq CPtrdiff | |
| Eq CSize | |
| Eq CWchar | |
| Eq CSigAtomic | |
| Eq CClock | |
| Eq CTime | |
| Eq CUSeconds | |
| Eq CSUSeconds | |
| Eq CIntPtr | |
| Eq CUIntPtr | |
| Eq CIntMax | |
| Eq CUIntMax | |
| Eq IODeviceType | |
| Eq SeekMode | |
| Eq All | |
| Eq Any | |
| Eq Fixity | |
| Eq Associativity | |
| Eq SourceUnpackedness | |
| Eq SourceStrictness | |
| Eq DecidedStrictness | |
| Eq MaskingState | |
| Eq IOException | |
| Eq ErrorCall | |
| Eq ArithException | |
| Eq SomeNat | |
| Eq SomeSymbol | |
| Eq IOMode | |
| Eq SrcLoc | |
| Eq Sign # | |
| Eq PartialError # | |
| Eq Bitmap # | |
| Eq Encoding # | |
| Eq ValidationFailure # | |
| Eq String # | |
| Eq FileName # | |
| Eq FilePath # | |
| Eq Relativity # | |
| Eq Endianness # | |
| Eq OS # | |
| Eq a => Eq [a] | |
| Eq a => Eq (Maybe a) | |
| Eq a => Eq (Ratio a) | |
| Eq (Ptr a) | |
| Eq (FunPtr a) | |
| Eq (V1 p) | |
| Eq (U1 p) | |
| Eq p => Eq (Par1 p) | |
| Eq a => Eq (Identity a) | |
| Eq a => Eq (Min a) | |
| Eq a => Eq (Max a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Last a) | |
| Eq m => Eq (WrappedMonoid m) | |
| Eq a => Eq (Option a) | |
| Eq a => Eq (NonEmpty a) | |
| Eq a => Eq (ZipList a) | |
| Eq (TVar a) | |
| Eq (ForeignPtr a) | |
| Eq a => Eq (Dual a) | |
| Eq a => Eq (Sum a) | |
| Eq a => Eq (Product a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Last a) | |
| Eq (IORef a) | |
| (PrimType ty, Eq ty) => Eq (UArray ty) # | |
| Eq a => Eq (Array a) # | |
| (Eq a, Eq b) => Eq (Either a b) | |
| Eq (f p) => Eq (Rec1 f p) | |
| Eq (URec Char p) | |
| Eq (URec Double p) | |
| Eq (URec Float p) | |
| Eq (URec Int p) | |
| Eq (URec Word p) | |
| Eq (URec (Ptr ()) p) | |
| (Eq a, Eq b) => Eq (a, b) | |
| (Ix i, Eq e) => Eq (Array i e) | |
| Eq a => Eq (Arg a b) | |
| Eq (Proxy k s) | |
| Eq (STRef s a) | |
| (Eq a, Eq b) => Eq (Tuple2 a b) # | |
| Eq c => Eq (K1 i c p) | |
| (Eq (f p), Eq (g p)) => Eq ((:+:) f g p) | |
| (Eq (f p), Eq (g p)) => Eq ((:*:) f g p) | |
| Eq (f (g p)) => Eq ((:.:) f g p) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| Eq (STArray s i e) | |
| Eq a => Eq (Const k a b) | |
| Eq (f a) => Eq (Alt k f a) | |
| Eq (Coercion k a b) | |
| Eq ((:~:) k a b) | |
| (Eq a, Eq b, Eq c) => Eq (Tuple3 a b c) # | |
| Eq (f p) => Eq (M1 i c f p) | |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| (Eq a, Eq b, Eq c, Eq d) => Eq (Tuple4 a b c d) # | |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
The Bounded class is used to name the upper and lower limits of a
type. Ord is not a superclass of Bounded since types that are not
totally ordered may also have upper and lower bounds.
The Bounded class may be derived for any enumeration type;
minBound is the first constructor listed in the data declaration
and maxBound is the last.
Bounded may also be derived for single-constructor datatypes whose
constituent types are in Bounded.
Instances
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum from 0 through n-1.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum,
the following should hold:
- The calls
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBoundInstances
The Functor class is used for types that can be mapped over.
Instances of Functor should satisfy the following laws:
fmap id == id fmap (f . g) == fmap f . fmap g
The instances of Functor for lists, Maybe and IO
satisfy these laws.
Minimal complete definition
Instances
| Functor [] | |
| Functor Maybe | |
| Functor IO | |
| Functor V1 | |
| Functor U1 | |
| Functor Par1 | |
| Functor Id | |
| Functor Identity | |
| Functor Min | |
| Functor Max | |
| Functor First | |
| Functor Last | |
| Functor Option | |
| Functor NonEmpty | |
| Functor ZipList | |
| Functor Handler | |
| Functor STM | |
| Functor Dual | |
| Functor Sum | |
| Functor Product | |
| Functor First | |
| Functor Last | |
| Functor Partial # | |
| Functor Array # | |
| Functor ((->) r) | |
| Functor (Either a) | |
| Functor f => Functor (Rec1 f) | |
| Functor (URec Char) | |
| Functor (URec Double) | |
| Functor (URec Float) | |
| Functor (URec Int) | |
| Functor (URec Word) | |
| Functor (URec (Ptr ())) | |
| Functor ((,) a) | |
| Functor (StateL s) | |
| Functor (StateR s) | |
| Functor (Array i) | |
| Functor (Arg a) | |
| Monad m => Functor (WrappedMonad m) | |
| Arrow a => Functor (ArrowMonad a) | |
| Functor (Proxy *) | |
| Functor (ST s) | |
| Functor (K1 i c) | |
| (Functor f, Functor g) => Functor ((:+:) f g) | |
| (Functor f, Functor g) => Functor ((:*:) f g) | |
| (Functor f, Functor g) => Functor ((:.:) f g) | |
| Arrow a => Functor (WrappedArrow a b) | |
| Functor (Const * m) | |
| Functor f => Functor (Alt * f) | |
| Functor f => Functor (M1 i c f) | |
class Functor f => Applicative f where #
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying the following laws:
- identity
pureid<*>v = v- composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- homomorphism
puref<*>purex =pure(f x)- interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Instances
| Applicative [] | |
| Applicative Maybe | |
| Applicative IO | |
| Applicative U1 | |
| Applicative Par1 | |
| Applicative Id | |
| Applicative Identity | |
| Applicative Min | |
| Applicative Max | |
| Applicative First | |
| Applicative Last | |
| Applicative Option | |
| Applicative NonEmpty | |
| Applicative ZipList | |
| Applicative STM | |
| Applicative Dual | |
| Applicative Sum | |
| Applicative Product | |
| Applicative First | |
| Applicative Last | |
| Applicative Partial # | |
| Applicative ((->) a) | |
| Applicative (Either e) | |
| Applicative f => Applicative (Rec1 f) | |
| Monoid a => Applicative ((,) a) | |
| Applicative (StateL s) | |
| Applicative (StateR s) | |
| Monad m => Applicative (WrappedMonad m) | |
| Arrow a => Applicative (ArrowMonad a) | |
| Applicative (Proxy *) | |
| Applicative (ST s) | |
| (Applicative f, Applicative g) => Applicative ((:*:) f g) | |
| (Applicative f, Applicative g) => Applicative ((:.:) f g) | |
| Arrow a => Applicative (WrappedArrow a b) | |
| Monoid m => Applicative (Const * m) | |
| Applicative f => Applicative (Alt * f) | |
| Applicative f => Applicative (M1 i c f) | |
class Applicative m => Monad m where #
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad should satisfy the following laws:
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Instances
| Monad [] | |
| Monad Maybe | |
| Monad IO | |
| Monad U1 | |
| Monad Par1 | |
| Monad Identity | |
| Monad Min | |
| Monad Max | |
| Monad First | |
| Monad Last | |
| Monad Option | |
| Monad NonEmpty | |
| Monad STM | |
| Monad Dual | |
| Monad Sum | |
| Monad Product | |
| Monad First | |
| Monad Last | |
| Monad Partial # | |
| Monad ((->) r) | |
| Monad (Either e) | |
| Monad f => Monad (Rec1 f) | |
| Monoid a => Monad ((,) a) | |
| Monad m => Monad (WrappedMonad m) | |
| ArrowApply a => Monad (ArrowMonad a) | |
| Monad (Proxy *) | |
| Monad (ST s) | |
| (Monad f, Monad g) => Monad ((:*:) f g) | |
| Monad f => Monad (Alt * f) | |
| Monad f => Monad (M1 i c f) | |
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=, but with the arguments interchanged.
Class for string-like datastructures; used by the overloaded string extension (-XOverloadedStrings in GHC).
The IsList class and its methods are intended to be used in
conjunction with the OverloadedLists extension.
Since: 4.7.0.0
Associated Types
The Item type function returns the type of items of the structure
l.
Instances
Numeric type classes
class (Eq a, Ord a, Num a, Enum a, Additive a, Subtractive a, Difference a ~ a, Multiplicative a, Divisible a) => Number a where Source #
Number literals, convertible through the generic Integer type.
all number are Enum'erable, meaning that you can move to next element
Minimal complete definition
class Additive a where Source #
Represent class of things that can be added together, contains a neutral element and is commutative.
- x + azero = x
- azero + x = x
- x + y = y + x
class Subtractive a where Source #
Represent class of things that can be subtracted.
Note that the result is not necessary of the same type as the operand depending on the actual type.
For example: e.g. (-) :: Int -> Int -> Int (-) :: DateTime -> DateTime -> Seconds (-) :: Ptr a -> Ptr a -> PtrDiff
Minimal complete definition
Associated Types
type Difference a Source #
Methods
(-) :: a -> a -> Difference a infixl 6 Source #
Instances
class Multiplicative a where Source #
Represent class of things that can be multiplied together
- x * midentity = x
- midentity * x = x
Methods
Identity element over multiplication
(*) :: a -> a -> a infixl 7 Source #
Multiplication of 2 elements that result in another element
(^) :: Number n => a -> n -> a infixr 8 Source #
Raise to power, repeated multiplication e.g. > a ^ 2 = a * a > a ^ 10 = (a ^ 5) * (a ^ 5) ..
Instances
Data types
The Maybe type encapsulates an optional value. A value of type
Maybe aa (represented as Just aNothing). Using Maybe is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as error.
The Maybe type is also a monad. It is a simple kind of error
monad, where all errors are represented by Nothing. A richer
error monad can be built using the Either type.
Instances
| Monad Maybe | |
| Functor Maybe | |
| Applicative Maybe | |
| Foldable Maybe | |
| Traversable Maybe | |
| Generic1 Maybe | |
| Alternative Maybe | |
| MonadPlus Maybe | |
| Eq a => Eq (Maybe a) | |
| Data a => Data (Maybe a) | |
| Ord a => Ord (Maybe a) | |
| Show a => Show (Maybe a) | |
| Generic (Maybe a) | |
| Semigroup a => Semigroup (Maybe a) | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| SingI (Maybe a) (Nothing a) | |
| SingKind a (KProxy a) => SingKind (Maybe a) (KProxy (Maybe a)) | |
| SingI a a1 => SingI (Maybe a) (Just a a1) | |
| type Rep1 Maybe | |
| type Rep (Maybe a) | |
| data Sing (Maybe a) | |
| type (==) (Maybe k) a b | |
| type DemoteRep (Maybe a) (KProxy (Maybe a)) | |
The character type Char is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) characters (see
http://www.unicode.org/ for details). This set extends the ISO 8859-1
(Latin-1) character set (the first 256 characters), which is itself an extension
of the ASCII character set (the first 128 characters). A character literal in
Haskell has type Char.
To convert a Char to or from the corresponding Int value defined
by Unicode, use toEnum and fromEnum from the
Enum class respectively (or equivalently ord and chr).
Instances
| Bounded Char | |
| Enum Char | |
| Eq Char | |
| Data Char | |
| Ord Char | |
| Show Char | |
| Ix Char | |
| PrimType Char Source # | |
| Functor (URec Char) | |
| Foldable (URec Char) | |
| Traversable (URec Char) | |
| Generic1 (URec Char) | |
| Eq (URec Char p) | |
| Ord (URec Char p) | |
| Show (URec Char p) | |
| Generic (URec Char p) | |
| data URec Char | Used for marking occurrences of |
| type Rep1 (URec Char) | |
| type Rep (URec Char p) | |
A value of type IO aa.
There is really only one way to "perform" an I/O action: bind it to
Main.main in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the IO monad and called
at some point, directly or indirectly, from Main.main.
IO is a monad, so IO actions can be combined using either the do-notation
or the >> and >>= operations from the Monad class.
data Either a b :: * -> * -> * #
The Either type represents values with two possibilities: a value of
type Either a bLeft aRight b
The Either type is sometimes used to represent a value which is
either correct or an error; by convention, the Left constructor is
used to hold an error value and the Right constructor is used to
hold a correct value (mnemonic: "right" also means "correct").
Examples
The type Either String IntString or an Int. The Left constructor can be used only on
Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: Either String Int
The fmap from our Functor instance will ignore Left values, but
will apply the supplied function to values contained in a Right:
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>fmap (*2) sLeft "foo">>>fmap (*2) nRight 6
The Monad instance for Either allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int from a Char, or fail.
>>>import Data.Char ( digitToInt, isDigit )>>>:{let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>:}
The following should work, since both '1' and '2' can be
parsed as Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 3
But the following should fail overall, since the first operation where
we attempt to parse 'm' as an Int will fail:
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleLeft "parse error"
Instances
| Monad (Either e) | |
| Functor (Either a) | |
| Applicative (Either e) | |
| Foldable (Either a) | |
| Traversable (Either a) | |
| Generic1 (Either a) | |
| (Eq a, Eq b) => Eq (Either a b) | |
| (Data a, Data b) => Data (Either a b) | |
| (Ord a, Ord b) => Ord (Either a b) | |
| (Read a, Read b) => Read (Either a b) | |
| (Show a, Show b) => Show (Either a b) | |
| Generic (Either a b) | |
| Semigroup (Either a b) | |
| type Rep1 (Either a) | |
| type Rep (Either a b) | |
| type (==) (Either k k1) a b | |
Numbers
8-bit signed integer type
Instances
16-bit signed integer type
Instances
32-bit signed integer type
Instances
64-bit signed integer type
Instances
8-bit unsigned integer type
Instances
16-bit unsigned integer type
Instances
32-bit unsigned integer type
Instances
64-bit unsigned integer type
Instances
Instances
| Bounded Word | |
| Enum Word | |
| Eq Word | |
| Integral Word | |
| Data Word | |
| Num Word | |
| Ord Word | |
| Real Word | |
| Show Word | |
| Ix Word | |
| Bits Word | |
| FiniteBits Word | |
| Divisible Word Source # | |
| Subtractive Word Source # | |
| Multiplicative Word Source # | |
| Additive Word Source # | |
| Number Word Source # | |
| Functor (URec Word) | |
| Foldable (URec Word) | |
| Traversable (URec Word) | |
| Generic1 (URec Word) | |
| Eq (URec Word p) | |
| Ord (URec Word p) | |
| Show (URec Word p) | |
| Generic (URec Word p) | |
| data URec Word | Used for marking occurrences of |
| type Difference Word Source # | |
| type Rep1 (URec Word) | |
| type Rep (URec Word p) | |
A fixed-precision integer type with at least the range [-2^29 .. 2^29-1].
The exact range for a given implementation can be determined by using
minBound and maxBound from the Bounded class.
Instances
| Bounded Int | |
| Enum Int | |
| Eq Int | |
| Integral Int | |
| Data Int | |
| Num Int | |
| Ord Int | |
| Real Int | |
| Show Int | |
| Ix Int | |
| Bits Int | |
| FiniteBits Int | |
| Divisible Int Source # | |
| Subtractive Int Source # | |
| Multiplicative Int Source # | |
| Additive Int Source # | |
| Signed Int Source # | |
| Number Int Source # | |
| Functor (URec Int) | |
| Foldable (URec Int) | |
| Traversable (URec Int) | |
| Generic1 (URec Int) | |
| Eq (URec Int p) | |
| Ord (URec Int p) | |
| Show (URec Int p) | |
| Generic (URec Int p) | |
| data URec Int | Used for marking occurrences of |
| type Difference Int Source # | |
| type Rep1 (URec Int) | |
| type Rep (URec Int p) | |
Invariant: Jn# and Jp# are used iff value doesn't fit in S#
Useful properties resulting from the invariants:
Instances
Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.
Instances
| Eq Float | |
| Floating Float | |
| Data Float | |
| Ord Float | |
| RealFloat Float | |
| PrimType Float Source # | |
| Functor (URec Float) | |
| Foldable (URec Float) | |
| Traversable (URec Float) | |
| Generic1 (URec Float) | |
| Eq (URec Float p) | |
| Ord (URec Float p) | |
| Show (URec Float p) | |
| Generic (URec Float p) | |
| data URec Float | Used for marking occurrences of |
| type Rep1 (URec Float) | |
| type Rep (URec Float p) | |
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
Instances
| Eq Double | |
| Floating Double | |
| Data Double | |
| Ord Double | |
| RealFloat Double | |
| PrimType Double Source # | |
| Functor (URec Double) | |
| Foldable (URec Double) | |
| Traversable (URec Double) | |
| Generic1 (URec Double) | |
| Eq (URec Double p) | |
| Ord (URec Double p) | |
| Show (URec Double p) | |
| Generic (URec Double p) | |
| data URec Double | Used for marking occurrences of |
| type Rep1 (URec Double) | |
| type Rep (URec Double p) | |
Collection types
An array of type built on top of GHC primitive.
The elements need to have fixed sized and the representation is a packed contiguous array in memory that can easily be passed to foreign interface
Instances
| PrimType ty => IsList (UArray ty) Source # | |
| (PrimType ty, Eq ty) => Eq (UArray ty) Source # | |
| (PrimType ty, Ord ty) => Ord (UArray ty) Source # | |
| (PrimType ty, Show ty) => Show (UArray ty) Source # | |
| PrimType ty => Monoid (UArray ty) Source # | |
| PrimType ty => Foldable (UArray ty) Source # | |
| PrimType ty => IndexedCollection (UArray ty) Source # | |
| PrimType ty => InnerFunctor (UArray ty) Source # | |
| PrimType ty => Sequential (UArray ty) Source # | |
| PrimType ty => Zippable (UArray ty) Source # | |
| type Item (UArray ty) Source # | |
| type Element (UArray ty) Source # | |
class Eq ty => PrimType ty Source #
Represent the accessor for types that can be stored in the UArray and MUArray.
Types need to be a instance of storable and have fixed sized.
Minimal complete definition
primSizeInBytes, primBaIndex, primMbaRead, primMbaWrite, primAddrIndex, primAddrRead, primAddrWrite
Array of a
Instances
| Functor Array Source # | |
| IsList (Array ty) Source # | |
| Eq a => Eq (Array a) Source # | |
| Ord a => Ord (Array a) Source # | |
| Show a => Show (Array a) Source # | |
| Monoid (Array a) Source # | |
| IndexedCollection (Array ty) Source # | |
| InnerFunctor (Array ty) Source # | |
| Sequential (Array ty) Source # | |
| BoxedZippable (Array ty) Source # | |
| Zippable (Array ty) Source # | |
| type Item (Array ty) Source # | |
| type Element (Array ty) Source # | |
Opaque packed array of characters in the UTF8 encoding
Numeric functions
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
Monoids
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
mappend mempty x = x
mappend x mempty = x
mappend x (mappend y z) = mappend (mappend x y) z
mconcat =
foldrmappend mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtypes and make those instances
of Monoid, e.g. Sum and Product.
Instances
| Monoid Ordering | |
| Monoid () | |
| Monoid All | |
| Monoid Any | |
| Monoid Bitmap # | |
| Monoid String # | |
| Monoid FileName # | |
| Monoid [a] | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| Monoid a => Monoid (IO a) | |
| Ord a => Monoid (Max a) | |
| Ord a => Monoid (Min a) | |
| Monoid a => Monoid (Identity a) | |
| (Ord a, Bounded a) => Monoid (Min a) | |
| (Ord a, Bounded a) => Monoid (Max a) | |
| Monoid m => Monoid (WrappedMonoid m) | |
| Semigroup a => Monoid (Option a) | |
| Monoid a => Monoid (Dual a) | |
| Monoid (Endo a) | |
| Num a => Monoid (Sum a) | |
| Num a => Monoid (Product a) | |
| Monoid (First a) | |
| Monoid (Last a) | |
| PrimType ty => Monoid (UArray ty) # | |
| Monoid (Array a) # | |
| Monoid b => Monoid (a -> b) | |
| (Monoid a, Monoid b) => Monoid (a, b) | |
| Monoid (Proxy k s) | |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |
| Monoid a => Monoid (Const k a b) | |
| Alternative f => Monoid (Alt * f a) | |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | |
Folds and traversals
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed
to satisfy the monoid laws. Alternatively, one could define foldr:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
sum, product, maximum, and minimum should all be essentially
equivalent to foldMap forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a Functor instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
Instances
| Foldable [] | |
| Foldable Maybe | |
| Foldable V1 | |
| Foldable U1 | |
| Foldable Par1 | |
| Foldable Identity | |
| Foldable Min | |
| Foldable Max | |
| Foldable First | |
| Foldable Last | |
| Foldable Option | |
| Foldable NonEmpty | |
| Foldable ZipList | |
| Foldable Dual | |
| Foldable Sum | |
| Foldable Product | |
| Foldable First | |
| Foldable Last | |
| Foldable (Either a) | |
| Foldable f => Foldable (Rec1 f) | |
| Foldable (URec Char) | |
| Foldable (URec Double) | |
| Foldable (URec Float) | |
| Foldable (URec Int) | |
| Foldable (URec Word) | |
| Foldable (URec (Ptr ())) | |
| Foldable ((,) a) | |
| Foldable (Array i) | |
| Foldable (Arg a) | |
| Foldable (Proxy *) | |
| Foldable (K1 i c) | |
| (Foldable f, Foldable g) => Foldable ((:+:) f g) | |
| (Foldable f, Foldable g) => Foldable ((:*:) f g) | |
| (Foldable f, Foldable g) => Foldable ((:.:) f g) | |
| Foldable (Const * m) | |
| Foldable f => Foldable (M1 i c f) | |
asum :: (Foldable t, Alternative f) => t (f a) -> f a #
The sum of a collection of actions, generalizing concat.
class (Functor t, Foldable t) => Traversable t #
Functors representing data structures that can be traversed from left to right.
A definition of traverse must satisfy the following laws:
- naturality
t .for every applicative transformationtraversef =traverse(t . f)t- identity
traverseIdentity = Identity- composition
traverse(Compose .fmapg . f) = Compose .fmap(traverseg) .traversef
A definition of sequenceA must satisfy the following laws:
- naturality
t .for every applicative transformationsequenceA=sequenceA.fmaptt- identity
sequenceA.fmapIdentity = Identity- composition
sequenceA.fmapCompose = Compose .fmapsequenceA.sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative operations, i.e.
and the identity functor Identity and composition of functors Compose
are defined as
newtype Identity a = Identity a
instance Functor Identity where
fmap f (Identity x) = Identity (f x)
instance Applicative Identity where
pure x = Identity x
Identity f <*> Identity x = Identity (f x)
newtype Compose f g a = Compose (f (g a))
instance (Functor f, Functor g) => Functor (Compose f g) where
fmap f (Compose x) = Compose (fmap (fmap f) x)
instance (Applicative f, Applicative g) => Applicative (Compose f g) where
pure x = Compose (pure (pure x))
Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)(The naturality law is implied by parametricity.)
Instances are similar to Functor, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*>
imply a form of associativity.
The superclass instances should satisfy the following:
- In the
Functorinstance,fmapshould be equivalent to traversal with the identity applicative functor (fmapDefault). - In the
Foldableinstance,foldMapshould be equivalent to traversal with a constant applicative functor (foldMapDefault).
Instances
| Traversable [] | |
| Traversable Maybe | |
| Traversable V1 | |
| Traversable U1 | |
| Traversable Par1 | |
| Traversable Identity | |
| Traversable Min | |
| Traversable Max | |
| Traversable First | |
| Traversable Last | |
| Traversable Option | |
| Traversable NonEmpty | |
| Traversable ZipList | |
| Traversable Dual | |
| Traversable Sum | |
| Traversable Product | |
| Traversable First | |
| Traversable Last | |
| Traversable (Either a) | |
| Traversable f => Traversable (Rec1 f) | |
| Traversable (URec Char) | |
| Traversable (URec Double) | |
| Traversable (URec Float) | |
| Traversable (URec Int) | |
| Traversable (URec Word) | |
| Traversable (URec (Ptr ())) | |
| Traversable ((,) a) | |
| Ix i => Traversable (Array i) | |
| Traversable (Arg a) | |
| Traversable (Proxy *) | |
| Traversable (K1 i c) | |
| (Traversable f, Traversable g) => Traversable ((:+:) f g) | |
| (Traversable f, Traversable g) => Traversable ((:*:) f g) | |
| (Traversable f, Traversable g) => Traversable ((:.:) f g) | |
| Traversable (Const * m) | |
| Traversable f => Traversable (M1 i c f) | |
Maybe
mapMaybe :: (a -> Maybe b) -> [a] -> [b] #
The mapMaybe function is a version of map which can throw
out elements. In particular, the functional argument returns
something of type Maybe bNothing, no element
is added on to the result list. If it is Just bb is
included in the result list.
Examples
Using mapMaybe f xcatMaybes $ map f x
>>>import Text.Read ( readMaybe )>>>let readMaybeInt = readMaybe :: String -> Maybe Int>>>mapMaybe readMaybeInt ["1", "Foo", "3"][1,3]>>>catMaybes $ map readMaybeInt ["1", "Foo", "3"][1,3]
If we map the Just constructor, the entire list should be returned:
>>>mapMaybe Just [1,2,3][1,2,3]
catMaybes :: [Maybe a] -> [a] #
The catMaybes function takes a list of Maybes and returns
a list of all the Just values.
Examples
Basic usage:
>>>catMaybes [Just 1, Nothing, Just 3][1,3]
When constructing a list of Maybe values, catMaybes can be used
to return all of the "success" results (if the list is the result
of a map, then mapMaybe would be more appropriate):
>>>import Text.Read ( readMaybe )>>>[readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ][Just 1,Nothing,Just 3]>>>catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ][1,3]
fromMaybe :: a -> Maybe a -> a #
The fromMaybe function takes a default value and and Maybe
value. If the Maybe is Nothing, it returns the default values;
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 Text.Read ( readMaybe )>>>fromMaybe 0 (readMaybe "5")5>>>fromMaybe 0 (readMaybe "")0
listToMaybe :: [a] -> Maybe a #
The listToMaybe function returns Nothing on an empty list
or Just aa is the first element of the list.
Examples
Basic usage:
>>>listToMaybe []Nothing
>>>listToMaybe [9]Just 9
>>>listToMaybe [1,2,3]Just 1
Composing maybeToList with listToMaybe should be the identity
on singleton/empty lists:
>>>maybeToList $ listToMaybe [5][5]>>>maybeToList $ listToMaybe [][]
But not on lists with more than one element:
>>>maybeToList $ listToMaybe [1,2,3][1]
maybeToList :: Maybe a -> [a] #
The maybeToList function returns an empty list when given
Nothing or a singleton list when not given Nothing.
Examples
Basic usage:
>>>maybeToList (Just 7)[7]
>>>maybeToList Nothing[]
One can use maybeToList to avoid pattern matching when combined
with a function that (safely) works on lists:
>>>import Text.Read ( readMaybe )>>>sum $ maybeToList (readMaybe "3")3>>>sum $ maybeToList (readMaybe "")0
Either
partitionEithers :: [Either a b] -> ([a], [b]) #
Partitions a list of Either into two lists.
All the Left elements are extracted, in order, to the first
component of the output. Similarly the Right elements are extracted
to the second component of the output.
Examples
Basic usage:
>>>let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]>>>partitionEithers list(["foo","bar","baz"],[3,7])
The pair returned by partitionEithers x(:lefts x, rights x)
>>>let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]>>>partitionEithers list == (lefts list, rights list)True
Function
Applicative
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
An infix synonym for fmap.
The name of this operator is an allusion to $.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
(<|>) :: Alternative f => forall a. f a -> f a -> f a #
An associative binary operation
Monad
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #
Left-to-right Kleisli composition of monads.
Exceptions
class (Typeable * e, Show e) => Exception e where #
Any type that you wish to throw or catch as an exception must be an
instance of the Exception class. The simplest case is a new exception
type directly below the root:
data MyException = ThisException | ThatException
deriving (Show, Typeable)
instance Exception MyExceptionThe default method definitions in the Exception class do what we need
in this case. You can now throw and catch ThisException and
ThatException as exceptions:
*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
Caught ThisException
In more complicated examples, you may wish to define a whole hierarchy of exceptions:
---------------------------------------------------------------------
-- Make the root exception type for all the exceptions in a compiler
data SomeCompilerException = forall e . Exception e => SomeCompilerException e
deriving Typeable
instance Show SomeCompilerException where
show (SomeCompilerException e) = show e
instance Exception SomeCompilerException
compilerExceptionToException :: Exception e => e -> SomeException
compilerExceptionToException = toException . SomeCompilerException
compilerExceptionFromException :: Exception e => SomeException -> Maybe e
compilerExceptionFromException x = do
SomeCompilerException a <- fromException x
cast a
---------------------------------------------------------------------
-- Make a subhierarchy for exceptions in the frontend of the compiler
data SomeFrontendException = forall e . Exception e => SomeFrontendException e
deriving Typeable
instance Show SomeFrontendException where
show (SomeFrontendException e) = show e
instance Exception SomeFrontendException where
toException = compilerExceptionToException
fromException = compilerExceptionFromException
frontendExceptionToException :: Exception e => e -> SomeException
frontendExceptionToException = toException . SomeFrontendException
frontendExceptionFromException :: Exception e => SomeException -> Maybe e
frontendExceptionFromException x = do
SomeFrontendException a <- fromException x
cast a
---------------------------------------------------------------------
-- Make an exception type for a particular frontend compiler exception
data MismatchedParentheses = MismatchedParentheses
deriving (Typeable, Show)
instance Exception MismatchedParentheses where
toException = frontendExceptionToException
fromException = frontendExceptionFromExceptionWe can now catch a MismatchedParentheses exception as
MismatchedParentheses, SomeFrontendException or
SomeCompilerException, but not other types, e.g. IOException:
*Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: SomeFrontendException)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: SomeCompilerException)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: IOException)) *** Exception: MismatchedParentheses
Minimal complete definition
Nothing
Instances
The class Typeable allows a concrete representation of a type to
be calculated.
Minimal complete definition
data SomeException :: * #
The SomeException type is the root of the exception type hierarchy.
When an exception of type e is thrown, behind the scenes it is
encapsulated in a SomeException.
Instances
data IOException :: * #
Exceptions that occur in the IO monad.
An IOException records a more specific error type, a descriptive
string and maybe the handle that was used when the error was
flagged.
Instances
Proxy
data Proxy k t :: forall k. k -> * #
A concrete, poly-kinded proxy type
Constructors
| Proxy |
Instances
| Monad (Proxy *) | |
| Functor (Proxy *) | |
| Applicative (Proxy *) | |
| Foldable (Proxy *) | |
| Traversable (Proxy *) | |
| Generic1 (Proxy *) | |
| Alternative (Proxy *) | |
| MonadPlus (Proxy *) | |
| Bounded (Proxy k s) | |
| Enum (Proxy k s) | |
| Eq (Proxy k s) | |
| Data t => Data (Proxy * t) | |
| Ord (Proxy k s) | |
| Read (Proxy k s) | |
| Show (Proxy k s) | |
| Ix (Proxy k s) | |
| Generic (Proxy k t) | |
| Semigroup (Proxy k s) | |
| Monoid (Proxy k s) | |
| type Rep1 (Proxy *) | |
| type Rep (Proxy k t) | |
asProxyTypeOf :: a -> Proxy * a -> a #
asProxyTypeOf is a type-restricted version of const.
It is usually used as an infix operator, and its typing forces its first
argument (which is usually overloaded) to have the same type as the tag
of the second.
Partial
Partialiality wrapper.
partial :: a -> Partial a Source #
Create a value that is partial. this can only be
unwrap using the fromPartial function
data PartialError Source #
An error related to the evaluation of a Partial value that failed.
it contains the name of the function and the reason for failure
Instances
fromPartial :: Partial a -> a Source #
Dewrap a possible partial value