Safe Haskell	None
Language	Haskell2010

Overloaded

Contents

Plugin
Overloaded:Symbols
Overloaded:Strings
Overloaded:Numerals
Overloaded:Naturals
Overloaded:Chars
Overloaded:Lists
Overloaded:If
Overloaded:Labels
Overloaded:CodeLabels
Overloaded:CodeStrings
Overloaded:TypeNats
Overloaded:TypeSymbols
Overloaded:Do
Overloaded:Categories
Overloaded:RecordFields

Description

Overloaded* language extensions as a source plugin.

Synopsis

plugin :: Plugin
class FromSymbol (s :: Symbol) a where
- fromSymbol :: a
class FromNumeral (n :: Nat) a where
- fromNumeral :: a
defaultFromNumeral :: forall n a. (KnownNat n, Integral a) => a
class FromNatural a where
- fromNatural :: Natural -> a
class FromChar a where
- fromChar :: Char -> a
class Nil a where
- nil :: a
class Cons x ys zs | zs -> x ys where
- cons :: x -> ys -> zs
class ToBool b where
- toBool :: b -> Bool
ifte :: ToBool b => b -> a -> a -> a
class IsCodeLabel (sym :: Symbol) a where
- codeFromLabel :: SpliceQ a
class IsCodeString a where
- codeFromString :: String -> SpliceQ a
class FromNatC a where
- type FromNat (n :: Nat) :: a
class FromTypeSymbolC a where
- type FromTypeSymbol (s :: Symbol) :: a
data DoMethod
- = Pure
- | Then
- | Bind
type Pure = 'Pure
type Then = 'Then
type Bind = 'Bind
class Monad' (method :: DoMethod) (ty :: Type) where
- monad :: ty
class Category (cat :: k -> k -> Type)
identity :: Category cat => cat a a
(%%) :: Category cat => cat b c -> cat a b -> cat a c
class Category cat => CartesianCategory (cat :: k -> k -> Type) where
- type Product cat :: k -> k -> k
- proj1 :: cat (Product cat a b) a
- proj2 :: cat (Product cat a b) b
- fanout :: cat a b -> cat a c -> cat a (Product cat b c)
class Category cat => CocartesianCategory (cat :: k -> k -> Type) where
- type Coproduct cat :: k -> k -> k
- inl :: cat a (Coproduct cat a b)
- inr :: cat b (Coproduct cat a b)
- fanin :: cat a c -> cat b c -> cat (Coproduct cat a b) c
class (CartesianCategory cat, CocartesianCategory cat) => BicartesianCategory cat where
- distr :: cat (Product cat (Coproduct cat a b) c) (Coproduct cat (Product cat a c) (Product cat b c))
class CartesianCategory cat => CCC (cat :: k -> k -> Type) where
- type Exponential cat :: k -> k -> k
- eval :: cat (Product cat (Exponential cat a b) a) b
- transpose :: cat (Product cat a b) c -> cat a (Exponential cat b c)

Plugin

plugin :: Plugin Source #

Overloaded plugin.

To enable plugin put the following at top of the module:

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:Symbols #-}

At least one option is required, multiple can given either using multiple -fplugin-opt options, or by separating options with colon:

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:Symbols:Numerals #-}

Options also take optional desugaring names, for example

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:Labels=Data.Generics.ProductFields.field #-}

to desugar OverloadedLabels directly into field from generics-lens (no need to import orphan instance!)

Supported options

Symbols desugars literal strings to fromSymbol @sym
Strings works like built-in OverloadedStrings (but you can use different method than fromString)
Numerals desugars literal numbers to fromNumeral @nat
Naturals desugars literal numbers to fromNatural nat (i.e. like fromString)
Chars desugars literal characters to fromChars c. Note: there isn't type-level alternative: we cannot promote Chars
Lists is not like built-in OverloadedLists, but desugars explicit lists to cons and nil
If desugars if-expressions to ifte b t e
Unit desugars ()-expressions to nil (but you can use different method, e.g. boring from Data.Boring)
Labels works like built-in OverloadedLabels (you should enable OverloadedLabels so parser recognises the syntax)
TypeNats and TypeSymbols desugar type-level literals into FromNat and FromTypeSymbol respectively
Do desugar in Local Do fashion. See examples.
Categories change Arrows desugaring to use "correct" category classes.
CodeLabels desugars OverloadedLabels into Typed Template Haskell splices
CodeStrings desugars string literals into Typed Template Haskell splices
RebindableApplication changes how juxtaposition is interpreted

Known limitations

Doesn't desugar inside patterns

RecordFields

WARNING the type-checker plugin is experimental, it's adviced to use

{-# OPTIONS_GHC -ddump-simpl #-}

to avoid surprising segfaults.

Usage

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:RecordFields #-}

Implementation bits

See Note [HasField instances] in ClsInst, the behavior of this plugin is similar.

The HasField class is defined in GHC.Records.Compat module of record-hasfield package:

class HasField {k} x r a | x r -> a where
    hasField :: r -> (a -> r, a)

Suppose we have

data R y = MkR { foo :: [y] }

and foo in scope. We will solve constraints like

HasField "foo" (R Int) a

by emitting a new wanted constraint

[Int] ~# a

and building a HasField dictionary out of selector foo appropriately cast.

Idiom brackets from TemplateHaskellQuotes

{-# LANGUAGE TemplateHaskellQuotes #-}
{-# OPTIONS_GHC -fplugin=Overloaded -fplugin-opt=Overloaded:IdiomBrackets #-}

data Tree a
    = Leaf a
    | Branch (Tree a) (Tree a)
  deriving (Show)

instance Functor Tree where
    fmap f (Leaf x)     = Leaf (f x)
    fmap f (Branch l r) = Branch (fmap f l) (fmap f r)

instance Traversable Tree where
    traverse f (Leaf x)     = [| Leaf (f x) |]
    traverse f (Branch l r) = [| Branch (traverse f l) (traverse f r) |]

RebindableApplication

Converts all f x applications into (f $ x) with whatever $ is in scope.

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:RebindableApplication #-}

let f = pure ((+) :: Int -> Int -> Int)
    x = Just 1
    y = Just 2

    z = let ($) = (<*>) in f x y
in z

Overloaded:Symbols

class FromSymbol (s :: Symbol) a where Source #

Another way to desugar overloaded string literals using this class.

A string literal "example" is desugared to

fromSymbol @"example"

Enabled with:

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:Symbols #-}

Methods

fromSymbol :: a Source #

Instances

Instances details

(KnownNat y, KnownNat m, KnownNat d, ParseDay s ~ '(y, m, d)) => FromSymbol s Day Source #
Instance details Defined in Overloaded.Symbols Methods fromSymbol :: Day Source #
(KnownSymbol s, SeqList (ToList s)) => FromSymbol s ByteString Source #
Instance details Defined in Overloaded.Symbols Methods fromSymbol :: ByteString Source #
(KnownSymbol s, SeqList (ToList s)) => FromSymbol s ByteString Source #
Instance details Defined in Overloaded.Symbols Methods fromSymbol :: ByteString Source #
KnownSymbol s => FromSymbol s Text Source #
Instance details Defined in Overloaded.Symbols Methods fromSymbol :: Text Source #
KnownSymbol s => FromSymbol s Text Source #
Instance details Defined in Overloaded.Symbols Methods fromSymbol :: Text Source #
(KnownSymbol s, a ~ Char) => FromSymbol s [a] Source #
Instance details Defined in Overloaded.Symbols Methods fromSymbol :: [a] Source #

Overloaded:Strings

See Data.String for fromString.

Overloaded:Numerals

class FromNumeral (n :: Nat) a where Source #

Another way to desugar numerals.

A numeric literal 123 is desugared to

fromNumeral @123

Enabled with:

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:Numerals #-}

One can do type-level computations with this.

Methods

fromNumeral :: a Source #

Instances

Instances details

(KnownNat n, (1 <=? n) ~ 'True) => FromNumeral n BinP Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: BinP Source #
KnownNat n => FromNumeral n Bin Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Bin Source #
KnownNat n => FromNumeral n Nat Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Nat Source #
(KnownNat n, OverflowCheck n "Word8" (n <=? 18446744073709551615)) => FromNumeral n Word64 Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Word64 Source #
(KnownNat n, OverflowCheck n "Word8" (n <=? 4294967295)) => FromNumeral n Word32 Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Word32 Source #
(KnownNat n, OverflowCheck n "Word8" (n <=? 65535)) => FromNumeral n Word16 Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Word16 Source #
(KnownNat n, OverflowCheck n "Word8" (n <=? 255)) => FromNumeral n Word8 Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Word8 Source #
KnownNat n => FromNumeral n Int Source #	TODO: currently there is no range check
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Int Source #
KnownNat n => FromNumeral n Integer Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Integer Source #
KnownNat n => FromNumeral n Natural Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Natural Source #
(PosFromNumeral (FromGHC n) b, IsLess n (ToGHC b)) => FromNumeral n (Pos ('BP b)) Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Pos ('BP b) Source #
(PosFromNumeral (FromGHC n) b, IsLess n (ToGHC b)) => FromNumeral n (PosP b) Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: PosP b Source #
(FinFromNumeral (FromGHC n) m, IsLess n (ToGHC m)) => FromNumeral n (Fin m) Source #
Instance details Defined in Overloaded.Numerals Methods fromNumeral :: Fin m Source #

defaultFromNumeral :: forall n a. (KnownNat n, Integral a) => a Source #

Default implementation of fromNumeral.

Usage example:

instance (KnownNat n, ...) => FromNumeral n MyType where
    fromNumeral = defaultFromNumeral @n

Overloaded:Naturals

class FromNatural a where Source #

Class for Natural-like datastructures

A numeric literal 42 is desugared to

fromNatural 42

Methods

fromNatural :: Natural -> a Source #

Instances

Instances details

FromNatural Integer Source #
Instance details Defined in Overloaded.Naturals Methods fromNatural :: Natural -> Integer Source #
FromNatural Natural Source #
Instance details Defined in Overloaded.Naturals Methods fromNatural :: Natural -> Natural Source #

Overloaded:Chars

class FromChar a where Source #

Class for Char-like datastructures

A character literal x is desugared to

fromChar 'x'

Methods

fromChar :: Char -> a Source #

Instances

Instances details

FromChar Char Source #
Instance details Defined in Overloaded.Chars Methods fromChar :: Char -> Char Source #

Overloaded:Lists

class Nil a where Source #

Class for nil, []

See test-suite for ways to define instances for Map. There are at-least two-ways.

Methods

nil :: a Source #

Instances

Instances details

Nil IntSet Source #	Since: 0.1.3
Instance details Defined in Overloaded.Lists Methods nil :: IntSet Source #
Nil [a] Source #
Instance details Defined in Overloaded.Lists Methods nil :: [a] Source #
Nil (IntMap v) Source #	Since: 0.2
Instance details Defined in Overloaded.Lists Methods nil :: IntMap v Source #
Nil (Seq a) Source #	Since: 0.2
Instance details Defined in Overloaded.Lists Methods nil :: Seq a Source #
Nil (Set a) Source #	Since: 0.1.3
Instance details Defined in Overloaded.Lists Methods nil :: Set a Source #
Nil (RAList a) Source #
Instance details Defined in Overloaded.Lists Methods nil :: RAList a Source #
Nil (Map k v) Source #	Since: 0.2
Instance details Defined in Overloaded.Lists Methods nil :: Map k v Source #
b ~ 'BZ => Nil (RAVec b a) Source #
Instance details Defined in Overloaded.Lists Methods nil :: RAVec b a Source #
n ~ 'Z => Nil (Vec n a) Source #
Instance details Defined in Overloaded.Lists Methods nil :: Vec n a Source #
xs ~ ('[] :: [k]) => Nil (NP f xs) Source #
Instance details Defined in Overloaded.Lists Methods nil :: NP f xs Source #
xs ~ ('[] :: [[k]]) => Nil (POP f xs) Source #
Instance details Defined in Overloaded.Lists Methods nil :: POP f xs Source #

class Cons x ys zs | zs -> x ys where Source #

Class for Cons :.

Methods

cons :: x -> ys -> zs infixr 5 Source #

Instances

Instances details

Cons Int IntSet IntSet Source #	Since: 0.1.3
Instance details Defined in Overloaded.Lists Methods cons :: Int -> IntSet -> IntSet Source #
(a ~ b, a ~ c) => Cons a (RAList b) (NERAList c) Source #
Instance details Defined in Overloaded.Lists Methods cons :: a -> RAList b -> NERAList c Source #
(a ~ b, a ~ c) => Cons a (RAList b) (RAList c) Source #
Instance details Defined in Overloaded.Lists Methods cons :: a -> RAList b -> RAList c Source #
(a ~ b, b ~ c) => Cons a (Seq b) (Seq c) Source #	Since: 0.2
Instance details Defined in Overloaded.Lists Methods cons :: a -> Seq b -> Seq c Source #
(Ord a, a ~ b, b ~ c) => Cons a (Set b) (Set c) Source #	Since: 0.1.3
Instance details Defined in Overloaded.Lists Methods cons :: a -> Set b -> Set c Source #
(a ~ b, b ~ c) => Cons a [b] (NonEmpty c) Source #
Instance details Defined in Overloaded.Lists Methods cons :: a -> [b] -> NonEmpty c Source #
(a ~ b, b ~ c) => Cons a [b] [c] Source #
Instance details Defined in Overloaded.Lists Methods cons :: a -> [b] -> [c] Source #
(bp ~ Pred b, b ~ Succ' bp) => Cons a (RAVec bp a) (NERAVec b a) Source #
Instance details Defined in Overloaded.Lists Methods cons :: a -> RAVec bp a -> NERAVec b a Source #
(b ~ 'BP bb, bp ~ Pred bb, bb ~ Succ' bp) => Cons a (RAVec bp a) (RAVec b a) Source #
Instance details Defined in Overloaded.Lists Methods cons :: a -> RAVec bp a -> RAVec b a Source #
(a ~ b, b ~ c, m ~ 'S n) => Cons a (Vec n b) (Vec m c) Source #
Instance details Defined in Overloaded.Lists Methods cons :: a -> Vec n b -> Vec m c Source #
(f ~ g, g ~ h, xxs ~ (x ': xs)) => Cons (f x) (NP g xs) (NP h xxs) Source #
Instance details Defined in Overloaded.Lists Methods cons :: f x -> NP g xs -> NP h xxs Source #
(i ~ Int, a ~ b, b ~ c) => Cons (i, a) (IntMap b) (IntMap c) Source #	Since: 0.2
Instance details Defined in Overloaded.Lists Methods cons :: (i, a) -> IntMap b -> IntMap c Source #
(Ord k, k ~ k1, k ~ k2, v ~ v1, v ~ v2) => Cons (k, v) (Map k1 v1) (Map k2 v2) Source #	Since: 0.2
Instance details Defined in Overloaded.Lists Methods cons :: (k, v) -> Map k1 v1 -> Map k2 v2 Source #
(f ~ g, g ~ h, xsxss ~ (xs ': xss)) => Cons (NP f xs) (POP g xss) (POP h xsxss) Source #
Instance details Defined in Overloaded.Lists Methods cons :: NP f xs -> POP g xss -> POP h xsxss Source #

Overloaded:If

class ToBool b where Source #

Class for Bool-like datastrucutres

An if--expression if b then t else e is desugared to

ifte (toBool b) t e

Enabled with:

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:If #-}

Methods

toBool :: b -> Bool Source #

Instances

Instances details

ToBool Bool Source #
Instance details Defined in Overloaded.If Methods toBool :: Bool -> Bool Source #
ToBool (Maybe a) Source #	`Just` is `True`
Instance details Defined in Overloaded.If Methods toBool :: Maybe a -> Bool Source #
ToBool (Either b a) Source #	`Right` is `True`
Instance details Defined in Overloaded.If Methods toBool :: Either b a -> Bool Source #

ifte :: ToBool b => b -> a -> a -> a Source #

ToBool overloaded if-expression.

Overloaded:Labels

See GHC.OverloadedLabels for fromLabel.

Overloaded:CodeLabels

class IsCodeLabel (sym :: Symbol) a where Source #

Class for auto-spliced labels

The labels #lbl is desugared into $$(codeFromlabel @"lbl") splice.

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:CodeLabels #-}

This feature is not very usable, see https://gitlab.haskell.org/ghc/ghc/-/issues/18211

Methods

codeFromLabel :: SpliceQ a Source #

Overloaded:CodeStrings

class IsCodeString a where Source #

Class for auto-spliced string literals

The string literals "beer" is desugared into $$(codeFromString @"beer") splice.

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:CodeLabels #-}

This feature is not very usable, see https://gitlab.haskell.org/ghc/ghc/-/issues/18211

Methods

codeFromString :: String -> SpliceQ a Source #

Instances

Instances details

IsCodeString ByteString Source #
Instance details Defined in Overloaded.CodeStrings Methods codeFromString :: String -> SpliceQ ByteString Source #
a ~ Char => IsCodeString [a] Source #
Instance details Defined in Overloaded.CodeStrings Methods codeFromString :: String -> SpliceQ [a] Source #

Overloaded:TypeNats

class FromNatC a Source #

A way to overload type level Nats.

A number type-literal 42 is desugared to

FromNat 42

Enabled with:

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:TypeNats #-}

Associated Types

type FromNat (n :: Nat) :: a Source #

Instances

Instances details

FromNatC Nat Source #
Instance details Defined in Overloaded.TypeNats Associated Types type FromNat n :: a Source #
FromNatC Nat Source #
Instance details Defined in Overloaded.TypeNats Associated Types type FromNat n :: a Source #
FromNatC Bin Source #
Instance details Defined in Overloaded.TypeNats Associated Types type FromNat n :: a Source #
FromNatC BinP Source #
Instance details Defined in Overloaded.TypeNats Associated Types type FromNat n :: a Source #

Overloaded:TypeSymbols

class FromTypeSymbolC a Source #

A way to overload type level Symbols.

A symbol type-literal "example" is desugared to

FromTypeSymbol "example"

Enabled with:

{-# OPTIONS -fplugin=Overloaded -fplugin-opt=Overloaded:TypeSymbols #-}

Associated Types

type FromTypeSymbol (s :: Symbol) :: a Source #

Instances

Instances details

FromTypeSymbolC Symbol Source #
Instance details Defined in Overloaded.TypeSymbols Associated Types type FromTypeSymbol s :: a Source #

Overloaded:Do

data DoMethod Source #

Constructors

Pure	`return`
Then	`>>`
Bind	`>>=`

type Pure = 'Pure Source #

type Then = 'Then Source #

type Bind = 'Bind Source #

class Monad' (method :: DoMethod) (ty :: Type) where Source #

Methods

monad :: ty Source #

Instances

Instances details

(ty ~ (a -> m a), Applicative m) => Monad' 'Pure ty Source #
Instance details Defined in Overloaded.Do Methods monad :: ty Source #
(ty ~ (m a -> m b -> m b), Applicative m) => Monad' 'Then ty Source #
Instance details Defined in Overloaded.Do Methods monad :: ty Source #
(ty ~ (m a -> (a -> m b) -> m b), Monad m) => Monad' 'Bind ty Source #
Instance details Defined in Overloaded.Do Methods monad :: ty Source #

Overloaded:Categories

class Category (cat :: k -> k -> Type) #

A class for categories. Instances should satisfy the laws

Right identity: f . id = f
Left identity: id . f = f
Associativity: f . (g . h) = (f . g) . h

Minimal complete definition

id, (.)

Instances

Instances details

Category (Coercion :: k -> k -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). Coercion a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). Coercion b c -> Coercion a b -> Coercion a c #
Category ((:~:) :: k -> k -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). a :~: a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~: c) -> (a :~: b) -> a :~: c #
Category ((:~~:) :: k -> k -> Type)	Since: base-4.10.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). a :~~: a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~~: c) -> (a :~~: b) -> a :~~: c #
Category arr => Category (WrappedArrow arr :: k -> k -> Type) Source #
Instance details Defined in Overloaded.Categories Methods id :: forall (a :: k0). WrappedArrow arr a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). WrappedArrow arr b c -> WrappedArrow arr a b -> WrappedArrow arr a c #
Category k2 => Category (Dual k2 :: k1 -> k1 -> Type)
Instance details Defined in Data.Semigroupoid.Dual Methods id :: forall (a :: k). Dual k2 a a # (.) :: forall (b :: k) (c :: k) (a :: k). Dual k2 b c -> Dual k2 a b -> Dual k2 a c #
Category p => Category (WrappedArrow p :: k -> k -> Type)
Instance details Defined in Data.Profunctor.Types Methods id :: forall (a :: k0). WrappedArrow p a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). WrappedArrow p b c -> WrappedArrow p a b -> WrappedArrow p a c #
(Category p, Category q) => Category (Product p q :: k -> k -> Type)
Instance details Defined in Data.Bifunctor.Product Methods id :: forall (a :: k0). Product p q a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). Product p q b c -> Product p q a b -> Product p q a c #
(Applicative f, Category p) => Category (Tannen f p :: k -> k -> Type)
Instance details Defined in Data.Bifunctor.Tannen Methods id :: forall (a :: k0). Tannen f p a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). Tannen f p b c -> Tannen f p a b -> Tannen f p a c #
Category Op
Instance details Defined in Data.Functor.Contravariant Methods id :: forall (a :: k). Op a a # (.) :: forall (b :: k) (c :: k) (a :: k). Op b c -> Op a b -> Op a c #
Monad m => Category (Kleisli m :: Type -> Type -> Type)	Since: base-3.0
Instance details Defined in Control.Arrow Methods id :: forall (a :: k). Kleisli m a a # (.) :: forall (b :: k) (c :: k) (a :: k). Kleisli m b c -> Kleisli m a b -> Kleisli m a c #
(Applicative f, Monad f) => Category (WhenMissing f :: Type -> Type -> Type)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods id :: forall (a :: k). WhenMissing f a a # (.) :: forall (b :: k) (c :: k) (a :: k). WhenMissing f b c -> WhenMissing f a b -> WhenMissing f a c #
Category ((->) :: Type -> Type -> Type)	Since: base-3.0
Instance details Defined in Control.Category Methods id :: forall (a :: k). a -> a # (.) :: forall (b :: k) (c :: k) (a :: k). (b -> c) -> (a -> b) -> a -> c #
(Monad f, Applicative f) => Category (WhenMatched f x :: Type -> Type -> Type)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods id :: forall (a :: k). WhenMatched f x a a # (.) :: forall (b :: k) (c :: k) (a :: k). WhenMatched f x b c -> WhenMatched f x a b -> WhenMatched f x a c #
(Applicative f, Monad f) => Category (WhenMissing f k :: Type -> Type -> Type)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods id :: forall (a :: k0). WhenMissing f k a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). WhenMissing f k b c -> WhenMissing f k a b -> WhenMissing f k a c #
Monad f => Category (Star f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Types Methods id :: forall (a :: k). Star f a a # (.) :: forall (b :: k) (c :: k) (a :: k). Star f b c -> Star f a b -> Star f a c #
(Monad f, Applicative f) => Category (WhenMatched f k x :: Type -> Type -> Type)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods id :: forall (a :: k0). WhenMatched f k x a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). WhenMatched f k x b c -> WhenMatched f k x a b -> WhenMatched f k x a c #

identity :: Category cat => cat a a Source #

A non-clashing name for id.

(%%) :: Category cat => cat b c -> cat a b -> cat a c infixr 9 Source #

A non-clashing name for (.).

class Category cat => CartesianCategory (cat :: k -> k -> Type) where Source #

Cartesian category is a monoidal category where monoidal product is the categorical product.

Associated Types

type Product cat :: k -> k -> k Source #

Methods

proj1 :: cat (Product cat a b) a Source #

proj2 :: cat (Product cat a b) b Source #

fanout :: cat a b -> cat a c -> cat a (Product cat b c) Source #

fanout f g is written as $\langle f, g \rangle$ in category theory literature.

Instances

Instances details

CocartesianCategory cat => CartesianCategory (Dual cat :: k -> k -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Product (Dual cat) :: k -> k -> k Source # Methods proj1 :: forall (a :: k0) (b :: k0). Dual cat (Product (Dual cat) a b) a Source # proj2 :: forall (a :: k0) (b :: k0). Dual cat (Product (Dual cat) a b) b Source # fanout :: forall (a :: k0) (b :: k0) (c :: k0). Dual cat a b -> Dual cat a c -> Dual cat a (Product (Dual cat) b c) Source #
CartesianCategory Op Source #
Instance details Defined in Overloaded.Categories Associated Types type Product Op :: k -> k -> k Source # Methods proj1 :: forall (a :: k) (b :: k). Op (Product Op a b) a Source # proj2 :: forall (a :: k) (b :: k). Op (Product Op a b) b Source # fanout :: forall (a :: k) (b :: k) (c :: k). Op a b -> Op a c -> Op a (Product Op b c) Source #
Monad m => CartesianCategory (Kleisli m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Product (Kleisli m) :: k -> k -> k Source # Methods proj1 :: forall (a :: k) (b :: k). Kleisli m (Product (Kleisli m) a b) a Source # proj2 :: forall (a :: k) (b :: k). Kleisli m (Product (Kleisli m) a b) b Source # fanout :: forall (a :: k) (b :: k) (c :: k). Kleisli m a b -> Kleisli m a c -> Kleisli m a (Product (Kleisli m) b c) Source #
CartesianCategory ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Product (->) :: k -> k -> k Source # Methods proj1 :: forall (a :: k) (b :: k). Product (->) a b -> a Source # proj2 :: forall (a :: k) (b :: k). Product (->) a b -> b Source # fanout :: forall (a :: k) (b :: k) (c :: k). (a -> b) -> (a -> c) -> a -> Product (->) b c Source #
Monad m => CartesianCategory (Star m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Product (Star m) :: k -> k -> k Source # Methods proj1 :: forall (a :: k) (b :: k). Star m (Product (Star m) a b) a Source # proj2 :: forall (a :: k) (b :: k). Star m (Product (Star m) a b) b Source # fanout :: forall (a :: k) (b :: k) (c :: k). Star m a b -> Star m a c -> Star m a (Product (Star m) b c) Source #
Arrow arr => CartesianCategory (WrappedArrow arr :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Product (WrappedArrow arr) :: k -> k -> k Source # Methods proj1 :: forall (a :: k) (b :: k). WrappedArrow arr (Product (WrappedArrow arr) a b) a Source # proj2 :: forall (a :: k) (b :: k). WrappedArrow arr (Product (WrappedArrow arr) a b) b Source # fanout :: forall (a :: k) (b :: k) (c :: k). WrappedArrow arr a b -> WrappedArrow arr a c -> WrappedArrow arr a (Product (WrappedArrow arr) b c) Source #

class Category cat => CocartesianCategory (cat :: k -> k -> Type) where Source #

Cocartesian category is a monoidal category where monoidal product is the categorical coproduct.

Associated Types

type Coproduct cat :: k -> k -> k Source #

Methods

inl :: cat a (Coproduct cat a b) Source #

inr :: cat b (Coproduct cat a b) Source #

fanin :: cat a c -> cat b c -> cat (Coproduct cat a b) c Source #

fanin f g is written as $[f, g]$ in category theory literature.

Instances

Instances details

CartesianCategory cat => CocartesianCategory (Dual cat :: k -> k -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Coproduct (Dual cat) :: k -> k -> k Source # Methods inl :: forall (a :: k0) (b :: k0). Dual cat a (Coproduct (Dual cat) a b) Source # inr :: forall (b :: k0) (a :: k0). Dual cat b (Coproduct (Dual cat) a b) Source # fanin :: forall (a :: k0) (c :: k0) (b :: k0). Dual cat a c -> Dual cat b c -> Dual cat (Coproduct (Dual cat) a b) c Source #
CocartesianCategory Op Source #
Instance details Defined in Overloaded.Categories Associated Types type Coproduct Op :: k -> k -> k Source # Methods inl :: forall (a :: k) (b :: k). Op a (Coproduct Op a b) Source # inr :: forall (b :: k) (a :: k). Op b (Coproduct Op a b) Source # fanin :: forall (a :: k) (c :: k) (b :: k). Op a c -> Op b c -> Op (Coproduct Op a b) c Source #
Monad m => CocartesianCategory (Kleisli m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Coproduct (Kleisli m) :: k -> k -> k Source # Methods inl :: forall (a :: k) (b :: k). Kleisli m a (Coproduct (Kleisli m) a b) Source # inr :: forall (b :: k) (a :: k). Kleisli m b (Coproduct (Kleisli m) a b) Source # fanin :: forall (a :: k) (c :: k) (b :: k). Kleisli m a c -> Kleisli m b c -> Kleisli m (Coproduct (Kleisli m) a b) c Source #
CocartesianCategory ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Coproduct (->) :: k -> k -> k Source # Methods inl :: forall (a :: k) (b :: k). a -> Coproduct (->) a b Source # inr :: forall (b :: k) (a :: k). b -> Coproduct (->) a b Source # fanin :: forall (a :: k) (c :: k) (b :: k). (a -> c) -> (b -> c) -> Coproduct (->) a b -> c Source #
Monad m => CocartesianCategory (Star m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Coproduct (Star m) :: k -> k -> k Source # Methods inl :: forall (a :: k) (b :: k). Star m a (Coproduct (Star m) a b) Source # inr :: forall (b :: k) (a :: k). Star m b (Coproduct (Star m) a b) Source # fanin :: forall (a :: k) (c :: k) (b :: k). Star m a c -> Star m b c -> Star m (Coproduct (Star m) a b) c Source #
ArrowChoice arr => CocartesianCategory (WrappedArrow arr :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Coproduct (WrappedArrow arr) :: k -> k -> k Source # Methods inl :: forall (a :: k) (b :: k). WrappedArrow arr a (Coproduct (WrappedArrow arr) a b) Source # inr :: forall (b :: k) (a :: k). WrappedArrow arr b (Coproduct (WrappedArrow arr) a b) Source # fanin :: forall (a :: k) (c :: k) (b :: k). WrappedArrow arr a c -> WrappedArrow arr b c -> WrappedArrow arr (Coproduct (WrappedArrow arr) a b) c Source #

class (CartesianCategory cat, CocartesianCategory cat) => BicartesianCategory cat where Source #

Bicartesian category is category which is both cartesian and cocartesian.

We also require distributive morpism.

Methods

distr :: cat (Product cat (Coproduct cat a b) c) (Coproduct cat (Product cat a c) (Product cat b c)) Source #

Instances

Instances details

Monad m => BicartesianCategory (Kleisli m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Methods distr :: forall (a :: k) (b :: k) (c :: k). Kleisli m (Product (Kleisli m) (Coproduct (Kleisli m) a b) c) (Coproduct (Kleisli m) (Product (Kleisli m) a c) (Product (Kleisli m) b c)) Source #
BicartesianCategory ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Methods distr :: forall (a :: k) (b :: k) (c :: k). Product (->) (Coproduct (->) a b) c -> Coproduct (->) (Product (->) a c) (Product (->) b c) Source #
Monad m => BicartesianCategory (Star m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Methods distr :: forall (a :: k) (b :: k) (c :: k). Star m (Product (Star m) (Coproduct (Star m) a b) c) (Coproduct (Star m) (Product (Star m) a c) (Product (Star m) b c)) Source #
ArrowChoice arr => BicartesianCategory (WrappedArrow arr :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Methods distr :: forall (a :: k) (b :: k) (c :: k). WrappedArrow arr (Product (WrappedArrow arr) (Coproduct (WrappedArrow arr) a b) c) (Coproduct (WrappedArrow arr) (Product (WrappedArrow arr) a c) (Product (WrappedArrow arr) b c)) Source #

class CartesianCategory cat => CCC (cat :: k -> k -> Type) where Source #

Closed cartesian category.

Associated Types

type Exponential cat :: k -> k -> k Source #

Exponential cat a b represents $B^A$. This is due how (->) works.

Methods

eval :: cat (Product cat (Exponential cat a b) a) b Source #

transpose :: cat (Product cat a b) c -> cat a (Exponential cat b c) Source #

Instances

Instances details

Monad m => CCC (Kleisli m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Exponential (Kleisli m) :: k -> k -> k Source # Methods eval :: forall (a :: k) (b :: k). Kleisli m (Product (Kleisli m) (Exponential (Kleisli m) a b) a) b Source # transpose :: forall (a :: k) (b :: k) (c :: k). Kleisli m (Product (Kleisli m) a b) c -> Kleisli m a (Exponential (Kleisli m) b c) Source #
CCC ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Exponential (->) :: k -> k -> k Source # Methods eval :: forall (a :: k) (b :: k). Product (->) (Exponential (->) a b) a -> b Source # transpose :: forall (a :: k) (b :: k) (c :: k). (Product (->) a b -> c) -> a -> Exponential (->) b c Source #
Monad m => CCC (Star m :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Exponential (Star m) :: k -> k -> k Source # Methods eval :: forall (a :: k) (b :: k). Star m (Product (Star m) (Exponential (Star m) a b) a) b Source # transpose :: forall (a :: k) (b :: k) (c :: k). Star m (Product (Star m) a b) c -> Star m a (Exponential (Star m) b c) Source #
ArrowApply arr => CCC (WrappedArrow arr :: Type -> Type -> Type) Source #
Instance details Defined in Overloaded.Categories Associated Types type Exponential (WrappedArrow arr) :: k -> k -> k Source # Methods eval :: forall (a :: k) (b :: k). WrappedArrow arr (Product (WrappedArrow arr) (Exponential (WrappedArrow arr) a b) a) b Source # transpose :: forall (a :: k) (b :: k) (c :: k). WrappedArrow arr (Product (WrappedArrow arr) a b) c -> WrappedArrow arr a (Exponential (WrappedArrow arr) b c) Source #

Overloaded:RecordFields

See GHC.Records.Compat from record-hasfield package.