Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Validity

Contents

Helper functions to define validate
- Helpers for specific types
Utilities
- Utilities for validity checking
- Utilities for validation
Re-exports

Description

Validity is used to specify additional invariants upon values that are not enforced by the type system.

Let's take an example. Suppose we were to implement a type Prime that represents prime integers.

If you were to completely enforce the invariant that the represented number is a prime, then we could use Natural and only store the index of the given prime in the infinite sequence of prime numbers. This is very safe but also very expensive if we ever want to use the number, because we would have to calculcate all the prime numbers until that index.

Instead we choose to implement Prime by a newtype Prime = Prime Int. Now we have to maintain the invariant that the Int that we use to represent the prime is in fact positive and a prime.

The Validity typeclass allows us to specify this invariant (and enables testing via the genvalidity libraries: https://hackage.haskell.org/package/genvalidity ):

instance Validity Prime where
    validate (Prime n) = check (isPrime n) "The 'Int' is prime."

If certain typeclass invariants exist, you can make these explicit in the validity instance as well. For example, 'Fixed a' is only valid if a has an HasResolution instance, so the correct validity instance is HasResolution a => Validity (Fixed a).

Synopsis

class Validity a where
- validate :: a -> Validation
trivialValidation :: a -> Validation
genericValidate :: (Generic a, GValidity (Rep a)) => a -> Validation
check :: Bool -> String -> Validation
declare :: String -> Bool -> Validation
annotate :: Validity a => a -> String -> Validation
delve :: Validity a => String -> a -> Validation
decorate :: String -> Validation -> Validation
decorateList :: [a] -> (a -> Validation) -> Validation
decorateString :: String -> (Char -> Validation) -> Validation
invalid :: String -> Validation
valid :: Validation
validateCharNotUtf16SurrogateCodePoint :: Char -> Validation
isUtf16SurrogateCodePoint :: Char -> Bool
validateCharNotLineSeparator :: Char -> Validation
isLineSeparator :: Char -> Bool
validateStringSingleLine :: String -> Validation
isSingleLine :: String -> Bool
validateNotNaN :: RealFloat a => a -> Validation
validateNotInfinite :: RealFloat a => a -> Validation
validateRatioNotNaN :: Integral a => Ratio a -> Validation
validateRatioNotInfinite :: Integral a => Ratio a -> Validation
validateRatioNormalised :: Integral a => Ratio a -> Validation
isValid :: Validity a => a -> Bool
isInvalid :: Validity a => a -> Bool
constructValid :: Validity a => a -> Maybe a
constructValidUnsafe :: (Show a, Validity a) => a -> a
newtype Validation = Validation {
- unValidation :: [ValidationChain]
}
data ValidationChain
- = Violated String
- | Location String ValidationChain
checkValidity :: Validity a => a -> Either [ValidationChain] a
validationIsValid :: Validation -> Bool
prettyValidate :: Validity a => a -> Either String a
prettyValidation :: Validation -> Maybe String
class Semigroup a => Monoid a where
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
class Semigroup a where
- (<>) :: a -> a -> a
- sconcat :: NonEmpty a -> a
- stimes :: Integral b => b -> a -> a

Documentation

class Validity a where Source #

A class of types that have additional invariants defined upon them

Minimal complete definition

Nothing

Methods

validate :: a -> Validation Source #

default validate :: (Generic a, GValidity (Rep a)) => a -> Validation Source #

Instances

Instances details

Validity Int16 Source #
Instance details Defined in Data.Validity Methods validate :: Int16 -> Validation Source #
Validity Int32 Source #
Instance details Defined in Data.Validity Methods validate :: Int32 -> Validation Source #
Validity Int64 Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: Int64 -> Validation Source #
Validity Int8 Source #
Instance details Defined in Data.Validity Methods validate :: Int8 -> Validation Source #
Validity Word16 Source #
Instance details Defined in Data.Validity Methods validate :: Word16 -> Validation Source #
Validity Word32 Source #
Instance details Defined in Data.Validity Methods validate :: Word32 -> Validation Source #
Validity Word64 Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: Word64 -> Validation Source #
Validity Word8 Source #
Instance details Defined in Data.Validity Methods validate :: Word8 -> Validation Source #
Validity Ordering Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: Ordering -> Validation Source #
Validity ValidationChain Source #
Instance details Defined in Data.Validity Methods validate :: ValidationChain -> Validation Source #
Validity Integer Source #	Trivially valid Integer is not trivially valid under the hood, but instantiating `Validity` correctly would force validity to depend on a specific (big integer library `integer-gmp` versus `integer-simple`). This is rather impractical so for the time being we have opted for assuming that an `Integer` is always valid. Even though this is not technically sound, it is good enough for now.
Instance details Defined in Data.Validity Methods validate :: Integer -> Validation Source #
Validity Natural Source #	Valid according to `isValidNatural`
Instance details Defined in Data.Validity Methods validate :: Natural -> Validation Source #
Validity () Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: () -> Validation Source #
Validity Bool Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: Bool -> Validation Source #
Validity Char Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: Char -> Validation Source #
Validity Double Source #	Trivially valid:
Instance details Defined in Data.Validity Methods validate :: Double -> Validation Source #
Validity Float Source #	Trivially valid:
Instance details Defined in Data.Validity Methods validate :: Float -> Validation Source #
Validity Int Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: Int -> Validation Source #
Validity Word Source #	Trivially valid
Instance details Defined in Data.Validity Methods validate :: Word -> Validation Source #
Validity a => Validity (Identity a) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: Identity a -> Validation Source #
Validity a => Validity (First a) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: First a -> Validation Source #
Validity a => Validity (Last a) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: Last a -> Validation Source #
Validity a => Validity (First a) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: First a -> Validation Source #
Validity a => Validity (Last a) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: Last a -> Validation Source #
Validity a => Validity (Dual a) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: Dual a -> Validation Source #
Validity a => Validity (NonEmpty a) Source #	A nonempty list is valid if all the elements are valid. See the instance for 'Validity [a]' for more information.
Instance details Defined in Data.Validity Methods validate :: NonEmpty a -> Validation Source #
(Validity a, Ord a, Num a, Integral a) => Validity (Ratio a) Source #	Valid if the contained numbers are valid and the denominator is strictly positive.
Instance details Defined in Data.Validity Methods validate :: Ratio a -> Validation Source #
Validity a => Validity (Maybe a) Source #	A Maybe thing is valid if the thing inside is valid or it's nothing It makes sense to assume that `Nothing` is valid. If Nothing wasn't valid, you wouldn't have used a Maybe in the datastructure.
Instance details Defined in Data.Validity Methods validate :: Maybe a -> Validation Source #
Validity a => Validity [a] Source #	A list of things is valid if all of the things are valid. This means that the empty list is considered valid. If the empty list should not be considered valid as part of your custom data type, make sure to write a custom `Validity instance`
Instance details Defined in Data.Validity Methods validate :: [a] -> Validation Source #
(Validity a, Validity b) => Validity (Either a b) Source #	Any Either of things is valid if the contents are valid in either of the cases.
Instance details Defined in Data.Validity Methods validate :: Either a b -> Validation Source #
HasResolution a => Validity (Fixed a) Source #	Valid according to the contained `Integer`.
Instance details Defined in Data.Validity Methods validate :: Fixed a -> Validation Source #
(Validity a, Validity b) => Validity (a, b) Source #	Any tuple of things is valid if both of its elements are valid
Instance details Defined in Data.Validity Methods validate :: (a, b) -> Validation Source #
Validity a => Validity (Const a b) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: Const a b -> Validation Source #
Validity (f a) => Validity (Alt f a) Source #	Valid values the same as it's base type:
Instance details Defined in Data.Validity Methods validate :: Alt f a -> Validation Source #
(Validity a, Validity b, Validity c) => Validity (a, b, c) Source #	Any triple of things is valid if all three of its elements are valid
Instance details Defined in Data.Validity Methods validate :: (a, b, c) -> Validation Source #
(Validity a, Validity b, Validity c, Validity d) => Validity (a, b, c, d) Source #	Any quadruple of things is valid if all four of its elements are valid
Instance details Defined in Data.Validity Methods validate :: (a, b, c, d) -> Validation Source #
(Validity a, Validity b, Validity c, Validity d, Validity e) => Validity (a, b, c, d, e) Source #	Any quintuple of things is valid if all five of its elements are valid
Instance details Defined in Data.Validity Methods validate :: (a, b, c, d, e) -> Validation Source #
(Validity a, Validity b, Validity c, Validity d, Validity e, Validity f) => Validity (a, b, c, d, e, f) Source #	Any sextuple of things is valid if all six of its elements are valid
Instance details Defined in Data.Validity Methods validate :: (a, b, c, d, e, f) -> Validation Source #

Helper functions to define `validate`

trivialValidation :: a -> Validation Source #

Declare any value to be valid in validation

trivialValidation a = seq a mempty

genericValidate :: (Generic a, GValidity (Rep a)) => a -> Validation Source #

check :: Bool -> String -> Validation Source #

Check that a given invariant holds.

The given string should describe the invariant, not the violation.

Example:

check (x < 5) "x is strictly smaller than 5"

instead of

check (x < 5) "x is greater than 5"

declare :: String -> Bool -> Validation Source #

check, but with the arguments flipped

annotate :: Validity a => a -> String -> Validation Source #

Declare a sub-part as a necessary part for validation, and annotate it with a name.

Example:

validate (a, b) =
    mconcat
        [ annotate a "The first element of the tuple"
        , annotate b "The second element of the tuple"
        ]

delve :: Validity a => String -> a -> Validation Source #

annotate, but with the arguments flipped.

decorate :: String -> Validation -> Validation Source #

Decorate a validation with a location

decorateList :: [a] -> (a -> Validation) -> Validation Source #

Decorate a piecewise validation of a list with their location in the list

decorateString :: String -> (Char -> Validation) -> Validation Source #

decorateList, but specifically for Strings

decorateString = decorateList

invalid :: String -> Validation Source #

Construct a trivially invalid Validation

Example:

data Wrong
    = Wrong
    | Fine
    deriving (Show, Eq)

instance Validity Wrong where
    validate w =
        case w of
            Wrong -> invalid "Wrong"
            Fine -> valid

valid :: Validation Source #

Helpers for specific types

Utilities

Utilities for validity checking

isValid :: Validity a => a -> Bool Source #

Check whether a value is valid.

isInvalid :: Validity a => a -> Bool Source #

Check whether a value is not valid.

isInvalid = not . isValid

constructValid :: Validity a => a -> Maybe a Source #

Construct a valid element from an unchecked element

constructValidUnsafe :: (Show a, Validity a) => a -> a Source #

Construct a valid element from an unchecked element, throwing error on invalid elements.

Utilities for validation

newtype Validation Source #

The result of validating a value.

mempty means the value was valid.

This type intentionally doesn't have a Validity instance to make sure you can never accidentally use annotate or delve twice.

Constructors

Validation
Fields unValidation :: [ValidationChain]

Instances

Instances details

Monoid Validation Source #
Instance details Defined in Data.Validity Methods mempty :: Validation Source # mappend :: Validation -> Validation -> Validation Source # mconcat :: [Validation] -> Validation Source #
Semigroup Validation Source #
Instance details Defined in Data.Validity Methods (<>) :: Validation -> Validation -> Validation Source # sconcat :: NonEmpty Validation -> Validation Source # stimes :: Integral b => b -> Validation -> Validation Source #
Generic Validation Source #
Instance details Defined in Data.Validity Associated Types type Rep Validation :: Type -> Type Source # Methods from :: Validation -> Rep Validation x Source # to :: Rep Validation x -> Validation Source #
Show Validation Source #
Instance details Defined in Data.Validity Methods showsPrec :: Int -> Validation -> ShowS Source # show :: Validation -> String Source # showList :: [Validation] -> ShowS Source #
Eq Validation Source #
Instance details Defined in Data.Validity Methods (==) :: Validation -> Validation -> Bool Source # (/=) :: Validation -> Validation -> Bool Source #
type Rep Validation Source #
Instance details Defined in Data.Validity type Rep Validation = D1 ('MetaData "Validation" "Data.Validity" "validity-0.12.1.0-Lsh2VBI3jRIHJToqWDw5jy" 'True) (C1 ('MetaCons "Validation" 'PrefixI 'True) (S1 ('MetaSel ('Just "unValidation") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [ValidationChain])))

data ValidationChain Source #

Constructors

Violated String
Location String ValidationChain

Instances

Instances details

Generic ValidationChain Source #
Instance details Defined in Data.Validity Associated Types type Rep ValidationChain :: Type -> Type Source # Methods from :: ValidationChain -> Rep ValidationChain x Source # to :: Rep ValidationChain x -> ValidationChain Source #
Show ValidationChain Source #
Instance details Defined in Data.Validity Methods showsPrec :: Int -> ValidationChain -> ShowS Source # show :: ValidationChain -> String Source # showList :: [ValidationChain] -> ShowS Source #
Eq ValidationChain Source #
Instance details Defined in Data.Validity Methods (==) :: ValidationChain -> ValidationChain -> Bool Source # (/=) :: ValidationChain -> ValidationChain -> Bool Source #
Validity ValidationChain Source #
Instance details Defined in Data.Validity Methods validate :: ValidationChain -> Validation Source #
type Rep ValidationChain Source #
Instance details Defined in Data.Validity type Rep ValidationChain = D1 ('MetaData "ValidationChain" "Data.Validity" "validity-0.12.1.0-Lsh2VBI3jRIHJToqWDw5jy" 'False) (C1 ('MetaCons "Violated" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String)) :+: C1 ('MetaCons "Location" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 ValidationChain)))

checkValidity :: Validity a => a -> Either [ValidationChain] a Source #

validate a given value.

This function returns either all the reasons why the given value is invalid, in the form of a list of ValidationChains, or it returns Right with the input value, as evidence that it is valid.

Note: You may want to use prettyValidation instead, if you want to display these ValidationChains to a user.

validationIsValid :: Validation -> Bool Source #

Check if a Validation concerns a valid value.

prettyValidate :: Validity a => a -> Either String a Source #

Validate a given value

This function will return a nice error if the value is invalid. It will return the original value in Right if it was valid, as evidence that it has been validated.

prettyValidation :: Validation -> Maybe String Source #

Render a Validation in a somewhat pretty way.

This function will return Nothing if the Validation concerned a valid value.

Re-exports

class Semigroup a => Monoid a where Source #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

Right identity: x <> mempty = x
Left identity: mempty <> x = x
Associativity: x <> (y <> z) = (x <> y) <> z (Semigroup law)
Concatenation: mconcat = foldr (<>) mempty

You can alternatively define mconcat instead of mempty, in which case the laws are:

Unit: mconcat (pure x) = x
Multiplication: mconcat (join xss) = mconcat (fmap mconcat xss)
Subclass: mconcat (toList xs) = sconcat xs

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.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty | mconcat

Methods

mempty :: a Source #

Identity of mappend

Examples

Expand

>>> "Hello world" <> mempty
"Hello world"

>>> mempty <> [1, 2, 3]
[1,2,3]

mappend :: a -> a -> a Source #

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: [a] -> a Source #

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Instances

Instances details

Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid Validation Source #
Instance details Defined in Data.Validity Methods mempty :: Validation Source # mappend :: Validation -> Validation -> Validation Source # mconcat :: [Validation] -> Validation Source #
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
FiniteBits a => Monoid (And a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: And a Source # mappend :: And a -> And a -> And a Source # mconcat :: [And a] -> And a Source #
FiniteBits a => Monoid (Iff a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Iff a Source # mappend :: Iff a -> Iff a -> Iff a Source # mconcat :: [Iff a] -> Iff a Source #
Bits a => Monoid (Ior a)	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Ior a Source # mappend :: Ior a -> Ior a -> Ior a Source # mconcat :: [Ior a] -> Ior a Source #
Bits a => Monoid (Xor a)	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Xor a Source # mappend :: Xor a -> Xor a -> Xor a Source # mconcat :: [Xor a] -> Xor a Source #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a Source # mappend :: Identity a -> Identity a -> Identity a Source # mconcat :: [Identity a] -> Identity a Source #
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
(Ord a, Bounded a) => Monoid (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
(Ord a, Bounded a) => Monoid (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
(Generic a, Monoid (Rep a ())) => Monoid (Generically a)	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods mempty :: Generically a Source # mappend :: Generically a -> Generically a -> Generically a Source # mconcat :: [Generically a] -> Generically a Source #
Monoid p => Monoid (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p Source # mappend :: Par1 p -> Par1 p -> Par1 p Source # mconcat :: [Par1 p] -> Par1 p Source #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source # mappend :: Maybe a -> Maybe a -> Maybe a Source # mconcat :: [Maybe a] -> Maybe a Source #
Monoid a => Monoid (a)	Since: base-4.15
Instance details Defined in GHC.Base Methods mempty :: (a) Source # mappend :: (a) -> (a) -> (a) Source # mconcat :: [(a)] -> (a) Source #
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Monoid (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p Source # mappend :: U1 p -> U1 p -> U1 p Source # mconcat :: [U1 p] -> U1 p Source #
(Monoid a, Monoid b) => Monoid (a, b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
Monoid b => Monoid (a -> b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source # mappend :: (a -> b) -> (a -> b) -> a -> b Source # mconcat :: [a -> b] -> a -> b Source #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b Source # mappend :: Const a b -> Const a b -> Const a b Source # mconcat :: [Const a b] -> Const a b Source #
(Applicative f, Monoid a) => Monoid (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source # mappend :: Ap f a -> Ap f a -> Ap f a Source # mconcat :: [Ap f a] -> Ap f a Source #
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source # mappend :: Alt f a -> Alt f a -> Alt f a Source # mconcat :: [Alt f a] -> Alt f a Source #
Monoid (f p) => Monoid (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p Source # mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source # mconcat :: [Rec1 f p] -> Rec1 f p Source #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) Source # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # mconcat :: [(a, b, c)] -> (a, b, c) Source #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p Source # mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p Source # mconcat :: [(f :: g) p] -> (f :: g) p Source #
Monoid c => Monoid (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p Source # mappend :: K1 i c p -> K1 i c p -> K1 i c p Source # mconcat :: [K1 i c p] -> K1 i c p Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #
Monoid (f (g p)) => Monoid ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p Source # mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source # mconcat :: [(f :.: g) p] -> (f :.: g) p Source #
Monoid (f p) => Monoid (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p Source # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source # mconcat :: [M1 i c f p] -> M1 i c f p Source #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

class Semigroup a where Source #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity: x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit: sconcat (pure x) = x
Multiplication: sconcat (join xss) = sconcat (fmap sconcat xss)

Since: base-4.9.0.0

Minimal complete definition

(<>) | sconcat

Methods

(<>) :: a -> a -> a infixr 6 Source #

An associative operation.

Examples

Expand

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

>>> Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]

>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!

sconcat :: NonEmpty a -> a Source #

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

Examples

Expand

For the following examples, we will assume that we have:

>>> import Data.List.NonEmpty (NonEmpty (..))

>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

>>> sconcat $ Just [1, 2, 3] :| [Nothing, Just [4, 5, 6]]
Just [1,2,3,4,5,6]

>>> sconcat $ Left 1 :| [Right 2, Left 3, Right 4]
Right 2

stimes :: Integral b => b -> a -> a Source #

Repeat a value n times.

The default definition will raise an exception for a multiplier that is <= 0. This may be overridden with an implementation that is total. For monoids it is preferred to use stimesMonoid.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

Examples

Expand

>>> stimes 4 [1]
[1,1,1,1]

>>> stimes 5 (putStr "hi!")
hi!hi!hi!hi!hi!

>>> stimes 3 (Right ":)")
Right ":)"

Instances

Instances details

Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Semigroup Void	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Void -> Void -> Void Source # sconcat :: NonEmpty Void -> Void Source # stimes :: Integral b => b -> Void -> Void Source #
Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering Source # sconcat :: NonEmpty Ordering -> Ordering Source # stimes :: Integral b => b -> Ordering -> Ordering Source #
Semigroup Validation Source #
Instance details Defined in Data.Validity Methods (<>) :: Validation -> Validation -> Validation Source # sconcat :: NonEmpty Validation -> Validation Source # stimes :: Integral b => b -> Validation -> Validation Source #
Semigroup ()	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () Source # sconcat :: NonEmpty () -> () Source # stimes :: Integral b => b -> () -> () Source #
Bits a => Semigroup (And a)	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: And a -> And a -> And a Source # sconcat :: NonEmpty (And a) -> And a Source # stimes :: Integral b => b -> And a -> And a Source #
FiniteBits a => Semigroup (Iff a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Iff a -> Iff a -> Iff a Source # sconcat :: NonEmpty (Iff a) -> Iff a Source # stimes :: Integral b => b -> Iff a -> Iff a Source #
Bits a => Semigroup (Ior a)	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a Source # sconcat :: NonEmpty (Ior a) -> Ior a Source # stimes :: Integral b => b -> Ior a -> Ior a Source #
Bits a => Semigroup (Xor a)	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a Source # sconcat :: NonEmpty (Xor a) -> Xor a Source # stimes :: Integral b => b -> Xor a -> Xor a Source #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a Source # sconcat :: NonEmpty (Identity a) -> Identity a Source # stimes :: Integral b => b -> Identity a -> Identity a Source #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Ord a => Semigroup (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a Source # sconcat :: NonEmpty (Max a) -> Max a Source # stimes :: Integral b => b -> Max a -> Max a Source #
Ord a => Semigroup (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a Source # sconcat :: NonEmpty (Min a) -> Min a Source # stimes :: Integral b => b -> Min a -> Min a Source #
Monoid m => Semigroup (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source #
Semigroup a => Semigroup (Dual a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Semigroup (Endo a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Semigroup (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source #
(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Generically a -> Generically a -> Generically a Source # sconcat :: NonEmpty (Generically a) -> Generically a Source # stimes :: Integral b => b -> Generically a -> Generically a Source #
Semigroup p => Semigroup (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Par1 p -> Par1 p -> Par1 p Source # sconcat :: NonEmpty (Par1 p) -> Par1 p Source # stimes :: Integral b => b -> Par1 p -> Par1 p Source #
Semigroup a => Semigroup (IO a)	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a Source # sconcat :: NonEmpty (IO a) -> IO a Source # stimes :: Integral b => b -> IO a -> IO a Source #
Semigroup a => Semigroup (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a Source # sconcat :: NonEmpty (Maybe a) -> Maybe a Source # stimes :: Integral b => b -> Maybe a -> Maybe a Source #
Semigroup a => Semigroup (a)	Since: base-4.15
Instance details Defined in GHC.Base Methods (<>) :: (a) -> (a) -> (a) Source # sconcat :: NonEmpty (a) -> (a) Source # stimes :: Integral b => b -> (a) -> (a) Source #
Semigroup [a]	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] Source # sconcat :: NonEmpty [a] -> [a] Source # stimes :: Integral b => b -> [a] -> [a] Source #
Semigroup (Either a b)	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #
Semigroup (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p Source # sconcat :: NonEmpty (U1 p) -> U1 p Source # stimes :: Integral b => b -> U1 p -> U1 p Source #
Semigroup (V1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p Source # sconcat :: NonEmpty (V1 p) -> V1 p Source # stimes :: Integral b => b -> V1 p -> V1 p Source #
(Semigroup a, Semigroup b) => Semigroup (a, b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source # sconcat :: NonEmpty (a, b) -> (a, b) Source # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #
Semigroup b => Semigroup (a -> b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source # sconcat :: NonEmpty (a -> b) -> a -> b Source # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b Source # sconcat :: NonEmpty (Const a b) -> Const a b Source # stimes :: Integral b0 => b0 -> Const a b -> Const a b Source #
(Applicative f, Semigroup a) => Semigroup (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a Source # sconcat :: NonEmpty (Ap f a) -> Ap f a Source # stimes :: Integral b => b -> Ap f a -> Ap f a Source #
Alternative f => Semigroup (Alt f a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a Source # sconcat :: NonEmpty (Alt f a) -> Alt f a Source # stimes :: Integral b => b -> Alt f a -> Alt f a Source #
Semigroup (f p) => Semigroup (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p Source # sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p Source # stimes :: Integral b => b -> Rec1 f p -> Rec1 f p Source #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :: g) p -> (f :: g) p -> (f :: g) p Source # sconcat :: NonEmpty ((f :: g) p) -> (f :: g) p Source # stimes :: Integral b => b -> (f :: g) p -> (f :*: g) p Source #
Semigroup c => Semigroup (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: K1 i c p -> K1 i c p -> K1 i c p Source # sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source # stimes :: Integral b => b -> K1 i c p -> K1 i c p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source #
Semigroup (f (g p)) => Semigroup ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source # sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source # stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source #
Semigroup (f p) => Semigroup (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

Documentation

Instances

Helper functions to define validate

Helpers for specific types

Char

RealFloat (Double)

Ratio

Utilities

Utilities for validity checking

Utilities for validation

Instances

Instances

Re-exports

Examples

Instances

Examples

Examples

Examples

Instances

Helper functions to define `validate`