Safe Haskell	Safe
Language	Haskell2010

Data.PolyKinded

Contents

Lists of types and application
- Singleton for list of types
Splitting types

Synopsis

data LoT k where
- LoT0 :: LoT *
- (:&&:) :: k -> LoT ks -> LoT (k -> ks)
type family (f :: k) :@@: (tys :: LoT k) :: * where ...
type LoT1 a = a :&&: LoT0
type LoT2 a b = a :&&: (b :&&: LoT0)
type family HeadLoT (tys :: LoT (k -> k')) :: k where ...
type family TailLoT (tys :: LoT (k -> k')) :: LoT k' where ...
type family SpineLoT (ts :: LoT k) :: LoT k where ...
data SLoT (l :: LoT k) where
- SLoT0 :: SLoT LoT0
- SLoTA :: Proxy t -> SLoT ts -> SLoT (t :&&: ts)
class SForLoT (l :: LoT k) where
- slot :: SLoT l
data Proxy (t :: k) :: forall k. k -> Type = Proxy
type SplitF (t :: d) (f :: k) = SplitF' t f LoT0
data Nat
- = Z
- | S Nat
data TyEnv where
- TyEnv :: forall k. k -> LoT k -> TyEnv
type family SplitN (n :: Nat) t :: TyEnv where ...

Lists of types and application

data LoT k where Source #

LoT k represents a list of types which can be applied to a data type of kind k.

Constructors

LoT0 :: LoT *	Empty list of types.
(:&&:) :: k -> LoT ks -> LoT (k -> ks) infixr 5	Cons a type with a list of types.

type family (f :: k) :@@: (tys :: LoT k) :: * where ... Source #

Apply a list of types to a type constructor.

>>> :kind! Either :@@: (Int :&&: Bool :&&: LoT0)
Either Int Bool :: *

Equations

f :@@: _ = f
f :@@: as = f (HeadLoT as) :@@: TailLoT as

type LoT1 a = a :&&: LoT0 Source #

type LoT2 a b = a :&&: (b :&&: LoT0) Source #

type family HeadLoT (tys :: LoT (k -> k')) :: k where ... Source #

Head of a non-empty list of types.

>>> :kind! HeadLoT (Int :&&: LoT0)
Int :: *

Equations

HeadLoT (a :&&: _) = a

type family TailLoT (tys :: LoT (k -> k')) :: LoT k' where ... Source #

Tail of a non-empty list of types.

>>> :kind! TailLoT (Int :&&: Bool :&&: LoT0)
Bool :&&: LoT0 :: LoT (Type -> Type)

Equations

TailLoT (_ :&&: as) = as

type family SpineLoT (ts :: LoT k) :: LoT k where ... Source #

Construct the spine of a list of types whose length is known.

It can be useful to introduce unification variables for lists of types which will be fully instantiated during constraint resolution. A constraint p ~ SpineLoT p will thus instantiate the spine of p.

On concrete lists, this is the identity function.

Equations

SpineLoT (ts :: LoT (k -> k')) = HeadLoT ts :&&: SpineLoT (TailLoT ts)
SpineLoT (ts :: LoT *) = LoT0

Singleton for list of types

data SLoT (l :: LoT k) where Source #

Constructors

SLoT0 :: SLoT LoT0
SLoTA :: Proxy t -> SLoT ts -> SLoT (t :&&: ts)

class SForLoT (l :: LoT k) where Source #

Methods

slot :: SLoT l Source #

Instances

l ~ LoT0 => SForLoT (l :: LoT Type) Source #
Instance details Defined in Data.PolyKinded Methods slot :: SLoT l Source #
(l ~ (t :&&: ts), SForLoT ts) => SForLoT (l :: LoT (k -> k')) Source #
Instance details Defined in Data.PolyKinded Methods slot :: SLoT l Source #

data Proxy (t :: k) :: forall k. k -> Type #

Proxy is a type that holds no data, but has a phantom parameter of arbitrary type (or even kind). Its use is to provide type information, even though there is no value available of that type (or it may be too costly to create one).

Historically, Proxy :: Proxy a is a safer alternative to the 'undefined :: a' idiom.

>>> Proxy :: Proxy (Void, Int -> Int)
Proxy

Proxy can even hold types of higher kinds,

>>> Proxy :: Proxy Either
Proxy

>>> Proxy :: Proxy Functor
Proxy

>>> Proxy :: Proxy complicatedStructure
Proxy

Constructors

Proxy

Instances

Generic1 (Proxy :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 Proxy :: k -> Type # Methods from1 :: Proxy a -> Rep1 Proxy a # to1 :: Rep1 Proxy a -> Proxy a #
Monad (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b # (>>) :: Proxy a -> Proxy b -> Proxy b # return :: a -> Proxy a # fail :: String -> Proxy a #
Functor (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b # (<$) :: a -> Proxy b -> Proxy a #
Applicative (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a # (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # (>) :: Proxy a -> Proxy b -> Proxy b # (<*) :: Proxy a -> Proxy b -> Proxy a #
Foldable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # toList :: Proxy a -> [a] # null :: Proxy a -> Bool # length :: Proxy a -> Int # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # sum :: Num a => Proxy a -> a # product :: Num a => Proxy a -> a #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Alternative (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods empty :: Proxy a # (<\|>) :: Proxy a -> Proxy a -> Proxy a # some :: Proxy a -> Proxy [a] # many :: Proxy a -> Proxy [a] #
MonadPlus (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods mzero :: Proxy a # mplus :: Proxy a -> Proxy a -> Proxy a #
Bounded (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods minBound :: Proxy t # maxBound :: Proxy t #
Enum (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods succ :: Proxy s -> Proxy s # pred :: Proxy s -> Proxy s # toEnum :: Int -> Proxy s # fromEnum :: Proxy s -> Int # enumFrom :: Proxy s -> [Proxy s] # enumFromThen :: Proxy s -> Proxy s -> [Proxy s] # enumFromTo :: Proxy s -> Proxy s -> [Proxy s] # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] #
Eq (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (==) :: Proxy s -> Proxy s -> Bool # (/=) :: Proxy s -> Proxy s -> Bool #
Ord (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods compare :: Proxy s -> Proxy s -> Ordering # (<) :: Proxy s -> Proxy s -> Bool # (<=) :: Proxy s -> Proxy s -> Bool # (>) :: Proxy s -> Proxy s -> Bool # (>=) :: Proxy s -> Proxy s -> Bool # max :: Proxy s -> Proxy s -> Proxy s # min :: Proxy s -> Proxy s -> Proxy s #
Read (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods readsPrec :: Int -> ReadS (Proxy t) # readList :: ReadS [Proxy t] # readPrec :: ReadPrec (Proxy t) # readListPrec :: ReadPrec [Proxy t] #
Show (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods showsPrec :: Int -> Proxy s -> ShowS # show :: Proxy s -> String # showList :: [Proxy s] -> ShowS #
Ix (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods range :: (Proxy s, Proxy s) -> [Proxy s] # index :: (Proxy s, Proxy s) -> Proxy s -> Int # unsafeIndex :: (Proxy s, Proxy s) -> Proxy s -> Int inRange :: (Proxy s, Proxy s) -> Proxy s -> Bool # rangeSize :: (Proxy s, Proxy s) -> Int # unsafeRangeSize :: (Proxy s, Proxy s) -> Int
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 #
Semigroup (Proxy s)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
type Rep1 (Proxy :: k -> Type)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep1 (Proxy :: k -> Type) = D1 (MetaData "Proxy" "Data.Proxy" "base" False) (C1 (MetaCons "Proxy" PrefixI False) (U1 :: k -> Type))
type Rep (Proxy t)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep (Proxy t) = D1 (MetaData "Proxy" "Data.Proxy" "base" False) (C1 (MetaCons "Proxy" PrefixI False) (U1 :: Type -> Type))

Splitting types

type SplitF (t :: d) (f :: k) = SplitF' t f LoT0 Source #

Split a type t until the constructor f is found.

>>> :kind! SplitF (Either Int Bool) Either
Int :&&: Bool :&&: LoT0 :: LoT (* -> * -> *)
>>> :kind! SplitF (Either Int Bool) (Either Int)
Bool :&&: LoT0 :: LoT (* -> *)

data Nat Source #

Simple natural numbers.

Constructors

Z
S Nat

data TyEnv where Source #

A type constructor and a list of types that can be applied to it.

Constructors

TyEnv :: forall k. k -> LoT k -> TyEnv

type family SplitN (n :: Nat) t :: TyEnv where ... Source #

Split a type t until its list of types has length n.

>>> :kind! SplitN (Either Int Bool) (S (S Z))
TyEnv Either (Int :&&: Bool :&&: LoT0) :: TyEnv
>>> :kind! SplitF (Either Int Bool) (S Z)
TyEnv (Either Int) (Bool :&&: LoT0) :: TyEnv

Equations

SplitN n t = SplitN' n t LoT0