Safe Haskell	Safe
Language	Haskell2010

Math.Combinat.TypeLevel

Contents

Proxy
Type-level naturals as type arguments
Hiding the type parameter

Description

Type-level hackery.

This module is used for groups whose parameters are encoded as type-level natural numbers, for example finite cyclic groups, free groups, symmetric groups and braid groups.

Synopsis

Proxy

data Proxy k t :: forall k. k -> * #

A concrete, poly-kinded proxy type

Constructors

Proxy

Instances

Monad (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 *)
Methods fmap :: (a -> b) -> Proxy * a -> Proxy * b # (<$) :: a -> Proxy * b -> Proxy * a #
Applicative (Proxy *)
Methods pure :: a -> Proxy * a # (<>) :: Proxy (a -> b) -> Proxy * a -> Proxy * b # (>) :: Proxy a -> Proxy * b -> Proxy * b # (<) :: Proxy a -> Proxy * b -> Proxy * a #
Foldable (Proxy *)
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 *)
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) #
Generic1 (Proxy *)
Associated Types type Rep1 (Proxy * :: * -> ) :: -> * # Methods from1 :: Proxy * a -> Rep1 (Proxy ) a # to1 :: Rep1 (Proxy ) a -> Proxy * a #
Alternative (Proxy *)
Methods empty :: Proxy * a # (<\|>) :: Proxy * a -> Proxy * a -> Proxy * a # some :: Proxy * a -> Proxy * [a] # many :: Proxy * a -> Proxy * [a] #
MonadPlus (Proxy *)
Methods mzero :: Proxy * a # mplus :: Proxy * a -> Proxy * a -> Proxy * a #
Bounded (Proxy k s)
Methods minBound :: Proxy k s # maxBound :: Proxy k s #
Enum (Proxy k s)
Methods succ :: Proxy k s -> Proxy k s # pred :: Proxy k s -> Proxy k s # toEnum :: Int -> Proxy k s # fromEnum :: Proxy k s -> Int # enumFrom :: Proxy k s -> [Proxy k s] # enumFromThen :: Proxy k s -> Proxy k s -> [Proxy k s] # enumFromTo :: Proxy k s -> Proxy k s -> [Proxy k s] # enumFromThenTo :: Proxy k s -> Proxy k s -> Proxy k s -> [Proxy k s] #
Eq (Proxy k s)
Methods (==) :: Proxy k s -> Proxy k s -> Bool # (/=) :: Proxy k s -> Proxy k s -> Bool #
Ord (Proxy k s)
Methods compare :: Proxy k s -> Proxy k s -> Ordering # (<) :: Proxy k s -> Proxy k s -> Bool # (<=) :: Proxy k s -> Proxy k s -> Bool # (>) :: Proxy k s -> Proxy k s -> Bool # (>=) :: Proxy k s -> Proxy k s -> Bool # max :: Proxy k s -> Proxy k s -> Proxy k s # min :: Proxy k s -> Proxy k s -> Proxy k s #
Read (Proxy k s)
Methods readsPrec :: Int -> ReadS (Proxy k s) # readList :: ReadS [Proxy k s] # readPrec :: ReadPrec (Proxy k s) # readListPrec :: ReadPrec [Proxy k s] #
Show (Proxy k s)
Methods showsPrec :: Int -> Proxy k s -> ShowS # show :: Proxy k s -> String # showList :: [Proxy k s] -> ShowS #
Ix (Proxy k s)
Methods range :: (Proxy k s, Proxy k s) -> [Proxy k s] # index :: (Proxy k s, Proxy k s) -> Proxy k s -> Int # unsafeIndex :: (Proxy k s, Proxy k s) -> Proxy k s -> Int inRange :: (Proxy k s, Proxy k s) -> Proxy k s -> Bool # rangeSize :: (Proxy k s, Proxy k s) -> Int # unsafeRangeSize :: (Proxy k s, Proxy k s) -> Int
Generic (Proxy k t)
Associated Types type Rep (Proxy k t) :: * -> * # Methods from :: Proxy k t -> Rep (Proxy k t) x # to :: Rep (Proxy k t) x -> Proxy k t #
Monoid (Proxy k s)
Methods mempty :: Proxy k s # mappend :: Proxy k s -> Proxy k s -> Proxy k s # mconcat :: [Proxy k s] -> Proxy k s #
type Rep1 (Proxy *)
type Rep1 (Proxy *) = D1 (MetaData "Proxy" "Data.Proxy" "base" False) (C1 (MetaCons "Proxy" PrefixI False) U1)
type Rep (Proxy k t)
type Rep (Proxy k t) = D1 (MetaData "Proxy" "Data.Proxy" "base" False) (C1 (MetaCons "Proxy" PrefixI False) U1)

proxyUndef :: Proxy a -> a Source #

proxyOf :: a -> Proxy a Source #

proxyOf1 :: f a -> Proxy a Source #

proxyOf2 :: g (f a) -> Proxy a Source #

asProxyTypeOf :: a -> Proxy * a -> a #

asProxyTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the tag of the second.

asProxyTypeOf1 :: f a -> Proxy a -> f a Source #

Type-level naturals as type arguments

typeArg :: KnownNat n => f (n :: Nat) -> Integer Source #

iTypeArg :: KnownNat n => f (n :: Nat) -> Int Source #

Hiding the type parameter

data Some f Source #

Hide the type parameter of a functor. Example: Some Braid

Constructors

KnownNat n => Some (f n)

withSome :: Some f -> (forall n. KnownNat n => f n -> a) -> a Source #

Uses the value inside a Some

withSomeM :: Monad m => Some f -> (forall n. KnownNat n => f n -> m a) -> m a Source #

Monadic version of withSome

selectSome :: Integral int => (forall n. KnownNat n => f n) -> int -> Some f Source #

Given a polymorphic value, we select at run time the one specified by the second argument

selectSomeM :: forall m f int. (Integral int, Monad m) => (forall n. KnownNat n => m (f n)) -> int -> m (Some f) Source #

Monadic version of selectSome

withSelected :: Integral int => (forall n. KnownNat n => f n -> a) -> (forall n. KnownNat n => f n) -> int -> a Source #

Combination of selectSome and withSome: we make a temporary structure of the given size, but we immediately consume it.

withSelectedM :: forall m f int a. (Integral int, Monad m) => (forall n. KnownNat n => f n -> a) -> (forall n. KnownNat n => m (f n)) -> int -> m a Source #

(Half-)monadic version of withSelected