Injection

Documentation

class Injection from into where

Injection describes a lossless conversion that includes one type in another.

The sole method of this class,

inject :: from -> into

takes a value input :: from and returns a value output :: into which preserves all the information contained in the input. Specifically, each input is mapped to a unique output. In mathematical terminology, inject is injective:

inject a ≡ inject b → a ≡ b

The name of the class is derived from the mathematical term.

Injection models the "is-a" relationship used in languages with subtypes (such as in object-oriented programming), but an explicit cast with inject is required in Haskell.

Although it is often possible to infer the type parameters of this class, it is advisable to specify one or both of the parameters to inject using a type signature or the TypeApplications language extension. Specifying the type parameters will give clearer error messages from the type checker in any case.

Methods

inject :: from -> into

Instances

Injection Bool All

Defined in Injection

Methods

inject :: Bool -> All

Injection Bool Any

Defined in Injection

Methods

inject :: Bool -> Any

Injection Natural Integer

Defined in Injection

Methods

inject :: Natural -> Integer

Typeable a => Injection a Dynamic

Defined in Injection

Methods

inject :: a -> Dynamic

Injection a a

Defined in Injection

Methods

inject :: a -> a

Injection Void any

Defined in Injection

Methods

inject :: Void -> any

Injection All Bool

Defined in Injection

Methods

inject :: All -> Bool

Injection Any Bool

Defined in Injection

Methods

inject :: Any -> Bool

Injection Text String

unpack is the canonical injection Text -> String. There is no injection in the other direction because String can represent invalid surrogate code points, but Text cannot; for details, see Data.Text.Lazy.

Defined in Injection

Methods

inject :: Text -> String

Injection Text Text

Defined in Injection

Methods

inject :: Text0 -> Text

Injection Text String

unpack is the canonical injection Text -> String. There is no injection in the other direction because String can represent invalid surrogate code points, but Text cannot; for details, see Data.Text.

Defined in Injection

Methods

inject :: Text -> String

Injection Text Text

Defined in Injection

Methods

inject :: Text -> Text0

Injection Integer (Ratio Integer)

Defined in Injection

Methods

inject :: Integer -> Ratio Integer

Injection a (Min a)

Defined in Injection

Methods

inject :: a -> Min a

Injection a (Max a)

Defined in Injection

Methods

inject :: a -> Max a

Injection a (Last a)

Defined in Injection

Methods

inject :: a -> Last a

Injection a (First a)

Defined in Injection

Methods

inject :: a -> First a

Injection a (First a)

Defined in Injection

Methods

inject :: a -> First a

Injection a (Last a)

Defined in Injection

Methods

inject :: a -> Last a

Injection a (Dual a)

Defined in Injection

Methods

inject :: a -> Dual a

Injection a (Sum a)

Defined in Injection

Methods

inject :: a -> Sum a

Injection a (Product a)

Defined in Injection

Methods

inject :: a -> Product a

Injection a (Down a)

Defined in Injection

Methods

inject :: a -> Down a

Injection a (Identity a)

Defined in Injection

Methods

inject :: a -> Identity a

Num a => Injection a (Complex a)

Defined in Injection

Methods

inject :: a -> Complex a

Injection a b => Injection a (Maybe b)

Defined in Injection

Methods

inject :: a -> Maybe b

HasResolution a => Injection Integer (Fixed a)

Defined in Injection

Methods

inject :: Integer -> Fixed a

Injection a (r -> a)

Defined in Injection

Methods

inject :: a -> r -> a

Injection a (Const a b)

Defined in Injection

Methods

inject :: a -> Const a b

Injection (Min a) a

Defined in Injection

Methods

inject :: Min a -> a

Injection (Max a) a

Defined in Injection

Methods

inject :: Max a -> a

Injection (First a) a

Defined in Injection

Methods

inject :: First a -> a

Injection (Last a) a

Defined in Injection

Methods

inject :: Last a -> a

Injection (Identity a) a

Defined in Injection

Methods

inject :: Identity a -> a

Injection (Dual a) a

Defined in Injection

Methods

inject :: Dual a -> a

Injection (Sum a) a

Defined in Injection

Methods

inject :: Sum a -> a

Injection (Product a) a

Defined in Injection

Methods

inject :: Product a -> a

Injection (Down a) a

Defined in Injection

Methods

inject :: Down a -> a

Injection a b => Injection (Maybe a) [b]

Defined in Injection

Methods

inject :: Maybe a -> [b]

Injection (NonEmpty a) [a]

Defined in Injection

Methods

inject :: NonEmpty a -> [a]

Injection (Const a b) a

Defined in Injection

Methods

inject :: Const a b -> a

class Injection from into => Retraction from into where

Retraction undoes an Injection.

Because Injection is a lossless conversion, we can define a Retraction which undoes it. The method

retract :: into -> Maybe from

is the (left) inverse of inject:

retract (inject x) = Just x

retract is partial (returns Maybe) because the type into may be larger than the type from; that is, there may be values in into which are not inject-ed from from, and in that case retract may return Nothing.

Although it is often possible to infer the type parameters of this class, it is advisable to specify one or both of the parameters to retract using a type signature or the TypeApplications language extension. Specifying the type parameters will give clearer error messages from the type checker in any case.

Methods

retract :: into -> Maybe from

Instances

Retraction Natural Integer

Defined in Injection

Methods

retract :: Integer -> Maybe Natural

Typeable a => Retraction a Dynamic

Defined in Injection

Methods

retract :: Dynamic -> Maybe a

Retraction a a

Defined in Injection

Methods

retract :: a -> Maybe a

Retraction Integer (Ratio Integer)

Defined in Injection

Methods

retract :: Ratio Integer -> Maybe Integer

Retraction a (First a)

Defined in Injection

Methods

retract :: First a -> Maybe a

Retraction a (Last a)

Defined in Injection

Methods

retract :: Last a -> Maybe a

(Eq a, Num a) => Retraction a (Complex a)

Defined in Injection

Methods

retract :: Complex a -> Maybe a

Retraction a b => Retraction a (Maybe b)

Defined in Injection

Methods

retract :: Maybe b -> Maybe a

HasResolution a => Retraction Integer (Fixed a)

Defined in Injection

Methods

retract :: Fixed a -> Maybe Integer

Retraction a b => Retraction (Maybe a) [b]

Defined in Injection

Methods

retract :: [b] -> Maybe (Maybe a)

Retraction (NonEmpty a) [a]

Defined in Injection

Methods

retract :: [a] -> Maybe (NonEmpty a)