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Language	Haskell2010

Data.PartialSemigroup.Generics

Contents

The generic PartialSemigroup operator
Implementation details
Re-exports

Description

If a type derives Generic and all of its fields have PartialSemigroup instances, you can get a PartialSemigroup for free using genericPartialSemigroupOp.

Example

For this demonstration we'll define a contrived example type T with two constructors, A and B.

>>> data T = A String (Either String String) | B String deriving (Generic, Show)

And then define its PartialSemigroup instance using genericPartialSemigroupOp.

>>> instance PartialSemigroup T where (<>?) = genericPartialSemigroupOp

This gives us an implementation of <>? which combines values only if they have the same structure.

>>> A "s" (Left "x") <>? A "t" (Left "y")
Just (A "st" (Left "xy"))

>>> B "x" <>? B "y"
Just (B "xy")

For values that do not have the same structure, <>? produces Nothing.

>>> A "s" (Left "x") <>? A "t" (Right "y")
Nothing

>>> A "x" (Left "y") <>? B "z"
Nothing

Synopsis

genericPartialSemigroupOp :: (Generic a, PartialSemigroupRep (Rep a)) => a -> a -> Maybe a
class PartialSemigroupRep rep where
- repPartialSemigroupOp :: rep a -> rep a -> Maybe (rep a)
class Generic a
class PartialSemigroup a where
- (<>?) :: a -> a -> Maybe a

The generic PartialSemigroup operator

genericPartialSemigroupOp :: (Generic a, PartialSemigroupRep (Rep a)) => a -> a -> Maybe a Source #

Implementation details

class PartialSemigroupRep rep where Source #

The class of generic type Reps for which we can automatically derive PartialSemigroup:

K1 - a single value
M1 - a value with some additional metadata (which we simply discard)
:+: - sum types
:*: - product types

Methods

repPartialSemigroupOp :: rep a -> rep a -> Maybe (rep a) Source #

Instances

PartialSemigroup a => PartialSemigroupRep (K1 i a :: Type -> Type) Source #
Instance details Defined in Data.PartialSemigroup.Generics Methods repPartialSemigroupOp :: K1 i a a0 -> K1 i a a0 -> Maybe (K1 i a a0) Source #
(PartialSemigroupRep rep1, PartialSemigroupRep rep2) => PartialSemigroupRep (rep1 :+: rep2) Source #
Instance details Defined in Data.PartialSemigroup.Generics Methods repPartialSemigroupOp :: (rep1 :+: rep2) a -> (rep1 :+: rep2) a -> Maybe ((rep1 :+: rep2) a) Source #
(PartialSemigroupRep rep1, PartialSemigroupRep rep2) => PartialSemigroupRep (rep1 :*: rep2) Source #
Instance details Defined in Data.PartialSemigroup.Generics Methods repPartialSemigroupOp :: (rep1 :: rep2) a -> (rep1 :: rep2) a -> Maybe ((rep1 :*: rep2) a) Source #
PartialSemigroupRep rep => PartialSemigroupRep (M1 i meta rep) Source #
Instance details Defined in Data.PartialSemigroup.Generics Methods repPartialSemigroupOp :: M1 i meta rep a -> M1 i meta rep a -> Maybe (M1 i meta rep a) Source #

Re-exports

class Generic a #

Representable types of kind *. This class is derivable in GHC with the DeriveGeneric flag on.

A Generic instance must satisfy the following laws:

from . to ≡ id
to . from ≡ id

Minimal complete definition

from, to

Instances

Generic Bool
Instance details Defined in GHC.Generics Associated Types type Rep Bool :: Type -> Type # Methods from :: Bool -> Rep Bool x # to :: Rep Bool x -> Bool #
Generic Ordering
Instance details Defined in GHC.Generics Associated Types type Rep Ordering :: Type -> Type # Methods from :: Ordering -> Rep Ordering x # to :: Rep Ordering x -> Ordering #
Generic ()
Instance details Defined in GHC.Generics Associated Types type Rep () :: Type -> Type # Methods from :: () -> Rep () x # to :: Rep () x -> () #
Generic All
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep All :: Type -> Type # Methods from :: All -> Rep All x # to :: Rep All x -> All #
Generic Any
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep Any :: Type -> Type # Methods from :: Any -> Rep Any x # to :: Rep Any x -> Any #
Generic Fixity
Instance details Defined in GHC.Generics Associated Types type Rep Fixity :: Type -> Type # Methods from :: Fixity -> Rep Fixity x # to :: Rep Fixity x -> Fixity #
Generic Associativity
Instance details Defined in GHC.Generics Associated Types type Rep Associativity :: Type -> Type # Methods from :: Associativity -> Rep Associativity x # to :: Rep Associativity x -> Associativity #
Generic SourceUnpackedness
Instance details Defined in GHC.Generics Associated Types type Rep SourceUnpackedness :: Type -> Type # Methods from :: SourceUnpackedness -> Rep SourceUnpackedness x # to :: Rep SourceUnpackedness x -> SourceUnpackedness #
Generic SourceStrictness
Instance details Defined in GHC.Generics Associated Types type Rep SourceStrictness :: Type -> Type # Methods from :: SourceStrictness -> Rep SourceStrictness x # to :: Rep SourceStrictness x -> SourceStrictness #
Generic DecidedStrictness
Instance details Defined in GHC.Generics Associated Types type Rep DecidedStrictness :: Type -> Type # Methods from :: DecidedStrictness -> Rep DecidedStrictness x # to :: Rep DecidedStrictness x -> DecidedStrictness #
Generic [a]
Instance details Defined in GHC.Generics Associated Types type Rep [a] :: Type -> Type # Methods from :: [a] -> Rep [a] x # to :: Rep [a] x -> [a] #
Generic (Maybe a)
Instance details Defined in GHC.Generics Associated Types type Rep (Maybe a) :: Type -> Type # Methods from :: Maybe a -> Rep (Maybe a) x # to :: Rep (Maybe a) x -> Maybe a #
Generic (Par1 p)
Instance details Defined in GHC.Generics Associated Types type Rep (Par1 p) :: Type -> Type # Methods from :: Par1 p -> Rep (Par1 p) x # to :: Rep (Par1 p) x -> Par1 p #
Generic (Min a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Min a) :: Type -> Type # Methods from :: Min a -> Rep (Min a) x # to :: Rep (Min a) x -> Min a #
Generic (Max a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Max a) :: Type -> Type # Methods from :: Max a -> Rep (Max a) x # to :: Rep (Max a) x -> Max a #
Generic (First a)
Instance details Defined in Data.Semigroup Associated Types type Rep (First a) :: Type -> Type # Methods from :: First a -> Rep (First a) x # to :: Rep (First a) x -> First a #
Generic (Last a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Last a) :: Type -> Type # Methods from :: Last a -> Rep (Last a) x # to :: Rep (Last a) x -> Last a #
Generic (WrappedMonoid m)
Instance details Defined in Data.Semigroup Associated Types type Rep (WrappedMonoid m) :: Type -> Type # Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x # to :: Rep (WrappedMonoid m) x -> WrappedMonoid m #
Generic (Option a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Option a) :: Type -> Type # Methods from :: Option a -> Rep (Option a) x # to :: Rep (Option a) x -> Option a #
Generic (ZipList a)
Instance details Defined in Control.Applicative Associated Types type Rep (ZipList a) :: Type -> Type # Methods from :: ZipList a -> Rep (ZipList a) x # to :: Rep (ZipList a) x -> ZipList a #
Generic (Identity a)
Instance details Defined in Data.Functor.Identity Associated Types type Rep (Identity a) :: Type -> Type # Methods from :: Identity a -> Rep (Identity a) x # to :: Rep (Identity a) x -> Identity a #
Generic (First a)
Instance details Defined in Data.Monoid Associated Types type Rep (First a) :: Type -> Type # Methods from :: First a -> Rep (First a) x # to :: Rep (First a) x -> First a #
Generic (Last a)
Instance details Defined in Data.Monoid Associated Types type Rep (Last a) :: Type -> Type # Methods from :: Last a -> Rep (Last a) x # to :: Rep (Last a) x -> Last a #
Generic (Dual a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Dual a) :: Type -> Type # Methods from :: Dual a -> Rep (Dual a) x # to :: Rep (Dual a) x -> Dual a #
Generic (Endo a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Endo a) :: Type -> Type # Methods from :: Endo a -> Rep (Endo a) x # to :: Rep (Endo a) x -> Endo a #
Generic (Sum a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Sum a) :: Type -> Type # Methods from :: Sum a -> Rep (Sum a) x # to :: Rep (Sum a) x -> Sum a #
Generic (Product a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Product a) :: Type -> Type # Methods from :: Product a -> Rep (Product a) x # to :: Rep (Product a) x -> Product a #
Generic (Down a)
Instance details Defined in GHC.Generics Associated Types type Rep (Down a) :: Type -> Type # Methods from :: Down a -> Rep (Down a) x # to :: Rep (Down a) x -> Down a #
Generic (NonEmpty a)
Instance details Defined in GHC.Generics Associated Types type Rep (NonEmpty a) :: Type -> Type # Methods from :: NonEmpty a -> Rep (NonEmpty a) x # to :: Rep (NonEmpty a) x -> NonEmpty a #
Generic (Either a b)
Instance details Defined in GHC.Generics Associated Types type Rep (Either a b) :: Type -> Type # Methods from :: Either a b -> Rep (Either a b) x # to :: Rep (Either a b) x -> Either a b #
Generic (V1 p)
Instance details Defined in GHC.Generics Associated Types type Rep (V1 p) :: Type -> Type # Methods from :: V1 p -> Rep (V1 p) x # to :: Rep (V1 p) x -> V1 p #
Generic (U1 p)
Instance details Defined in GHC.Generics Associated Types type Rep (U1 p) :: Type -> Type # Methods from :: U1 p -> Rep (U1 p) x # to :: Rep (U1 p) x -> U1 p #
Generic (a, b)
Instance details Defined in GHC.Generics Associated Types type Rep (a, b) :: Type -> Type # Methods from :: (a, b) -> Rep (a, b) x # to :: Rep (a, b) x -> (a, b) #
Generic (Arg a b)
Instance details Defined in Data.Semigroup Associated Types type Rep (Arg a b) :: Type -> Type # Methods from :: Arg a b -> Rep (Arg a b) x # to :: Rep (Arg a b) x -> Arg a b #
Generic (WrappedMonad m a)
Instance details Defined in Control.Applicative Associated Types type Rep (WrappedMonad m a) :: Type -> Type # Methods from :: WrappedMonad m a -> Rep (WrappedMonad m a) x # to :: Rep (WrappedMonad m a) x -> WrappedMonad m a #
Generic (Proxy t)
Instance details Defined in GHC.Generics Associated Types type Rep (Proxy t) :: Type -> Type # Methods from :: Proxy t -> Rep (Proxy t) x # to :: Rep (Proxy t) x -> Proxy t #
Generic (Rec1 f p)
Instance details Defined in GHC.Generics Associated Types type Rep (Rec1 f p) :: Type -> Type # Methods from :: Rec1 f p -> Rep (Rec1 f p) x # to :: Rep (Rec1 f p) x -> Rec1 f p #
Generic (URec (Ptr ()) p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec (Ptr ()) p) :: Type -> Type # Methods from :: URec (Ptr ()) p -> Rep (URec (Ptr ()) p) x # to :: Rep (URec (Ptr ()) p) x -> URec (Ptr ()) p #
Generic (URec Char p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Char p) :: Type -> Type # Methods from :: URec Char p -> Rep (URec Char p) x # to :: Rep (URec Char p) x -> URec Char p #
Generic (URec Double p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Double p) :: Type -> Type # Methods from :: URec Double p -> Rep (URec Double p) x # to :: Rep (URec Double p) x -> URec Double p #
Generic (URec Float p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Float p) :: Type -> Type # Methods from :: URec Float p -> Rep (URec Float p) x # to :: Rep (URec Float p) x -> URec Float p #
Generic (URec Int p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Int p) :: Type -> Type # Methods from :: URec Int p -> Rep (URec Int p) x # to :: Rep (URec Int p) x -> URec Int p #
Generic (URec Word p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Word p) :: Type -> Type # Methods from :: URec Word p -> Rep (URec Word p) x # to :: Rep (URec Word p) x -> URec Word p #
Generic (a, b, c)
Instance details Defined in GHC.Generics Associated Types type Rep (a, b, c) :: Type -> Type # Methods from :: (a, b, c) -> Rep (a, b, c) x # to :: Rep (a, b, c) x -> (a, b, c) #
Generic (WrappedArrow a b c)
Instance details Defined in Control.Applicative Associated Types type Rep (WrappedArrow a b c) :: Type -> Type # Methods from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x # to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c #
Generic (Ap f a)
Instance details Defined in Data.Monoid Associated Types type Rep (Ap f a) :: Type -> Type # Methods from :: Ap f a -> Rep (Ap f a) x # to :: Rep (Ap f a) x -> Ap f a #
Generic (Alt f a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Alt f a) :: Type -> Type # Methods from :: Alt f a -> Rep (Alt f a) x # to :: Rep (Alt f a) x -> Alt f a #
Generic (K1 i c p)
Instance details Defined in GHC.Generics Associated Types type Rep (K1 i c p) :: Type -> Type # Methods from :: K1 i c p -> Rep (K1 i c p) x # to :: Rep (K1 i c p) x -> K1 i c p #
Generic ((f :+: g) p)
Instance details Defined in GHC.Generics Associated Types type Rep ((f :+: g) p) :: Type -> Type # Methods from :: (f :+: g) p -> Rep ((f :+: g) p) x # to :: Rep ((f :+: g) p) x -> (f :+: g) p #
Generic ((f :*: g) p)
Instance details Defined in GHC.Generics Associated Types type Rep ((f :: g) p) :: Type -> Type # Methods from :: (f :: g) p -> Rep ((f :: g) p) x # to :: Rep ((f :: g) p) x -> (f :*: g) p #
Generic (a, b, c, d)
Instance details Defined in GHC.Generics Associated Types type Rep (a, b, c, d) :: Type -> Type # Methods from :: (a, b, c, d) -> Rep (a, b, c, d) x # to :: Rep (a, b, c, d) x -> (a, b, c, d) #
Generic (M1 i c f p)
Instance details Defined in GHC.Generics Associated Types type Rep (M1 i c f p) :: Type -> Type # Methods from :: M1 i c f p -> Rep (M1 i c f p) x # to :: Rep (M1 i c f p) x -> M1 i c f p #
Generic ((f :.: g) p)
Instance details Defined in GHC.Generics Associated Types type Rep ((f :.: g) p) :: Type -> Type # Methods from :: (f :.: g) p -> Rep ((f :.: g) p) x # to :: Rep ((f :.: g) p) x -> (f :.: g) p #
Generic (a, b, c, d, e)
Instance details Defined in GHC.Generics Associated Types type Rep (a, b, c, d, e) :: Type -> Type # Methods from :: (a, b, c, d, e) -> Rep (a, b, c, d, e) x # to :: Rep (a, b, c, d, e) x -> (a, b, c, d, e) #
Generic (a, b, c, d, e, f)
Instance details Defined in GHC.Generics Associated Types type Rep (a, b, c, d, e, f) :: Type -> Type # Methods from :: (a, b, c, d, e, f) -> Rep (a, b, c, d, e, f) x # to :: Rep (a, b, c, d, e, f) x -> (a, b, c, d, e, f) #
Generic (a, b, c, d, e, f, g)
Instance details Defined in GHC.Generics Associated Types type Rep (a, b, c, d, e, f, g) :: Type -> Type # Methods from :: (a, b, c, d, e, f, g) -> Rep (a, b, c, d, e, f, g) x # to :: Rep (a, b, c, d, e, f, g) x -> (a, b, c, d, e, f, g) #

class PartialSemigroup a where Source #

A PartialSemigroup is like a Semigroup, but with an operator returning Maybe a rather than a.

For comparison:

(<>)  :: Semigroup a        => a -> a -> a
(<>?) :: PartialSemigroup a => a -> a -> Maybe a

The associativity axiom for partial semigroups

For all x, y, z:

If x <>? y = Just xy and y <>? z = Just yz, then
- x <>? yz = xy <>? z.

Relationship to the semigroup associativity axiom

The partial semigroup associativity axiom is a natural adaptation of the semigroup associativity axiom

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

with a slight modification to accommodate situations where <> is undefined. We may gain some insight into the connection between Semigroup and PartialSemigroup by rephrasing the partial semigroup associativity in terms of a partial <> operator thusly:

For all x, y, z:

If x <> y and y <> z are both defined, then
- x <> (y <> z) is defined if and only if (x <> y) <> z is defined, and
- if these things are all defined, then the axiom for total semigroups x <> (y <> z) = (x <> y) <> z must hold.

Methods

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

Instances

PartialSemigroup () Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: () -> () -> Maybe () Source #
PartialSemigroup [a] Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: [a] -> [a] -> Maybe [a] Source #
PartialSemigroup a => PartialSemigroup (ZipList a) Source #	`partialZip`
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: ZipList a -> ZipList a -> Maybe (ZipList a) Source #
PartialSemigroup a => PartialSemigroup (Identity a) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: Identity a -> Identity a -> Maybe (Identity a) Source #
Num a => PartialSemigroup (Sum a) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: Sum a -> Sum a -> Maybe (Sum a) Source #
Num a => PartialSemigroup (Product a) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: Product a -> Product a -> Maybe (Product a) Source #
Semigroup a => PartialSemigroup (Total a) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: Total a -> Total a -> Maybe (Total a) Source #
(PartialSemigroup a, PartialSemigroup b) => PartialSemigroup (Either a b) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: Either a b -> Either a b -> Maybe (Either a b) Source #
(PartialSemigroup a, PartialSemigroup b) => PartialSemigroup (a, b) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: (a, b) -> (a, b) -> Maybe (a, b) Source #
PartialSemigroup b => PartialSemigroup (AppendRight a b) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: AppendRight a b -> AppendRight a b -> Maybe (AppendRight a b) Source #
PartialSemigroup a => PartialSemigroup (AppendLeft a b) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: AppendLeft a b -> AppendLeft a b -> Maybe (AppendLeft a b) Source #
(PartialSemigroup a, PartialSemigroup b, PartialSemigroup c) => PartialSemigroup (a, b, c) Source #
Instance details Defined in Data.PartialSemigroup Methods (<>?) :: (a, b, c) -> (a, b, c) -> Maybe (a, b, c) Source #