Safe Haskell	None
Language	Haskell2010

Data.Vector.Fixed.Cont

Contents

Type-level numbers
N-ary functions
- Combinators
Vector type class
Vector as continuation
Construction of ContVec
- Constructors
Transformations

Description

API for Church-encoded vectors. Implementation of function from Data.Vector.Fixed module uses these function internally in order to provide shortcut fusion.

Synopsis

data PeanoNum
- = Z
- | S PeanoNum
type family Peano (n :: Nat) :: PeanoNum where ...
type family Add (n :: PeanoNum) (m :: PeanoNum) :: PeanoNum where ...
type family Fn (n :: PeanoNum) a b where ...
newtype Fun (n :: PeanoNum) a b = Fun {
- unFun :: Fn n a b
}
type Arity (n :: Nat) = (ArityPeano (Peano n), KnownNat n, Peano (n + 1) ~ 'S (Peano n))
class ArityPeano (n :: PeanoNum) where
- accum :: (forall (k :: PeanoNum). t ('S k) -> a -> t k) -> (t 'Z -> b) -> t n -> Fun n a b
- applyFun :: (forall (k :: PeanoNum). t ('S k) -> (a, t k)) -> t n -> (CVecPeano n a, t 'Z)
- applyFunM :: Applicative f => (forall (k :: PeanoNum). t ('S k) -> (f a, t k)) -> t n -> (f (CVecPeano n a), t 'Z)
- reverseF :: Fun n a b -> Fun n a b
- gunfoldF :: Data a => (forall b x. Data b => c (b -> x) -> c x) -> T_gunfold c r a n -> c r
arity :: forall (n :: Nat) proxy. KnownNat n => proxy n -> Int
apply :: forall (n :: Nat) t a. Arity n => (forall (k :: PeanoNum). t ('S k) -> (a, t k)) -> t (Peano n) -> ContVec n a
applyM :: forall f (n :: Nat) t a. (Applicative f, Arity n) => (forall (k :: PeanoNum). t ('S k) -> (f a, t k)) -> t (Peano n) -> f (ContVec n a)
constFun :: forall (n :: PeanoNum) a b. Fun n a b -> Fun ('S n) a b
curryFirst :: forall (n :: PeanoNum) a b. Fun ('S n) a b -> a -> Fun n a b
uncurryFirst :: forall a (n :: PeanoNum) b. (a -> Fun n a b) -> Fun ('S n) a b
curryLast :: forall (n :: PeanoNum) a b. ArityPeano n => Fun ('S n) a b -> Fun n a (a -> b)
curryMany :: forall (n :: PeanoNum) (k :: PeanoNum) a b. ArityPeano n => Fun (Add n k) a b -> Fun n a (Fun k a b)
apLast :: forall (n :: PeanoNum) a b. ArityPeano n => Fun ('S n) a b -> a -> Fun n a b
shuffleFun :: forall (n :: PeanoNum) b a r. ArityPeano n => (b -> Fun n a r) -> Fun n a (b -> r)
withFun :: forall (n :: PeanoNum) a b. (Fun n a b -> Fun n a b) -> Fun ('S n) a b -> Fun ('S n) a b
type family Dim (v :: Type -> Type) :: Nat
class Arity (Dim v) => Vector (v :: Type -> Type) a where
- construct :: Fun (Peano (Dim v)) a (v a)
- inspect :: v a -> Fun (Peano (Dim v)) a b -> b
- basicIndex :: v a -> Int -> a
class (Vector (v n) a, Dim (v n) ~ n) => VectorN (v :: Nat -> Type -> Type) (n :: Nat) a
length :: KnownNat (Dim v) => v a -> Int
newtype ContVec (n :: Nat) a = ContVec (forall r. Fun (Peano n) a r -> r)
newtype CVecPeano (n :: PeanoNum) a = CVecPeano (forall r. Fun n a r -> r)
consPeano :: forall a (n :: PeanoNum). a -> CVecPeano n a -> CVecPeano ('S n) a
toContVec :: forall (n :: Nat) a. CVecPeano (Peano n) a -> ContVec n a
runContVec :: forall (n :: Nat) a r. Fun (Peano n) a r -> ContVec n a -> r
cvec :: forall v a (n :: Nat). (Vector v a, Dim v ~ n) => v a -> ContVec n a
fromList :: forall (n :: Nat) a. Arity n => [a] -> ContVec n a
fromList' :: forall (n :: Nat) a. Arity n => [a] -> ContVec n a
fromListM :: forall (n :: Nat) a. Arity n => [a] -> Maybe (ContVec n a)
toList :: forall (n :: Nat) a. Arity n => ContVec n a -> [a]
replicate :: forall (n :: Nat) a. Arity n => a -> ContVec n a
replicateM :: forall (n :: Nat) f a. (Arity n, Applicative f) => f a -> f (ContVec n a)
generate :: forall (n :: Nat) a. Arity n => (Int -> a) -> ContVec n a
generateM :: forall f (n :: Nat) a. (Applicative f, Arity n) => (Int -> f a) -> f (ContVec n a)
unfoldr :: forall (n :: Nat) b a. Arity n => (b -> (a, b)) -> b -> ContVec n a
basis :: forall a (n :: Nat). (Num a, Arity n) => Int -> ContVec n a
empty :: ContVec 0 a
cons :: forall (n :: Nat) a. Arity n => a -> ContVec n a -> ContVec (n + 1) a
consV :: forall (n :: Nat) a. Arity n => ContVec 1 a -> ContVec n a -> ContVec (n + 1) a
snoc :: forall (n :: Nat) a. Arity n => a -> ContVec n a -> ContVec (n + 1) a
concat :: forall (n :: Nat) (k :: Nat) a. (Arity n, Arity k, Arity (n + k), Peano (n + k) ~ Add (Peano n) (Peano k)) => ContVec n a -> ContVec k a -> ContVec (n + k) a
mk1 :: a -> ContVec 1 a
mk2 :: a -> a -> ContVec 2 a
mk3 :: a -> a -> a -> ContVec 3 a
mk4 :: a -> a -> a -> a -> ContVec 4 a
mk5 :: a -> a -> a -> a -> a -> ContVec 5 a
mk6 :: a -> a -> a -> a -> a -> a -> ContVec 6 a
mk7 :: a -> a -> a -> a -> a -> a -> a -> ContVec 7 a
mk8 :: a -> a -> a -> a -> a -> a -> a -> a -> ContVec 8 a
map :: forall (n :: Nat) a b. Arity n => (a -> b) -> ContVec n a -> ContVec n b
imap :: forall (n :: Nat) a b. Arity n => (Int -> a -> b) -> ContVec n a -> ContVec n b
mapM :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (a -> f b) -> ContVec n a -> f (ContVec n b)
imapM :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (Int -> a -> f b) -> ContVec n a -> f (ContVec n b)
mapM_ :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (a -> f b) -> ContVec n a -> f ()
imapM_ :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (Int -> a -> f b) -> ContVec n a -> f ()
scanl :: forall (n :: Nat) b a. Arity n => (b -> a -> b) -> b -> ContVec n a -> ContVec (n + 1) b
scanl1 :: forall (n :: Nat) a. Arity n => (a -> a -> a) -> ContVec n a -> ContVec n a
sequence :: forall (n :: Nat) f a. (Arity n, Applicative f) => ContVec n (f a) -> f (ContVec n a)
sequence_ :: forall (n :: Nat) f a. (Arity n, Applicative f) => ContVec n (f a) -> f ()
distribute :: forall f (n :: Nat) a. (Functor f, Arity n) => f (ContVec n a) -> ContVec n (f a)
collect :: forall f (n :: Nat) a b. (Functor f, Arity n) => (a -> ContVec n b) -> f a -> ContVec n (f b)
tail :: forall (n :: Nat) a. Arity n => ContVec (n + 1) a -> ContVec n a
reverse :: forall (n :: Nat) a. Arity n => ContVec n a -> ContVec n a
zipWith :: forall (n :: Nat) a b c. Arity n => (a -> b -> c) -> ContVec n a -> ContVec n b -> ContVec n c
zipWith3 :: forall (n :: Nat) a b c d. Arity n => (a -> b -> c -> d) -> ContVec n a -> ContVec n b -> ContVec n c -> ContVec n d
izipWith :: forall (n :: Nat) a b c. Arity n => (Int -> a -> b -> c) -> ContVec n a -> ContVec n b -> ContVec n c
izipWith3 :: forall (n :: Nat) a b c d. Arity n => (Int -> a -> b -> c -> d) -> ContVec n a -> ContVec n b -> ContVec n c -> ContVec n d
zipWithM :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (a -> b -> f c) -> ContVec n a -> ContVec n b -> f (ContVec n c)
zipWithM_ :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (a -> b -> f c) -> ContVec n a -> ContVec n b -> f ()
izipWithM :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (Int -> a -> b -> f c) -> ContVec n a -> ContVec n b -> f (ContVec n c)
izipWithM_ :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (Int -> a -> b -> f c) -> ContVec n a -> ContVec n b -> f ()
head :: forall (n :: Nat) a. (Arity n, 1 <= n) => ContVec n a -> a
index :: forall (n :: Nat) a. Arity n => Int -> ContVec n a -> a
element :: forall (n :: Nat) f a. (Arity n, Functor f) => Int -> (a -> f a) -> ContVec n a -> f (ContVec n a)
vector :: forall v a (n :: Nat). (Vector v a, Dim v ~ n) => ContVec n a -> v a
foldl :: forall (n :: Nat) b a. Arity n => (b -> a -> b) -> b -> ContVec n a -> b
foldl1 :: forall (n :: Nat) a. (Arity n, 1 <= n) => (a -> a -> a) -> ContVec n a -> a
foldr :: forall (n :: Nat) a b. Arity n => (a -> b -> b) -> b -> ContVec n a -> b
ifoldl :: forall (n :: Nat) b a. Arity n => (b -> Int -> a -> b) -> b -> ContVec n a -> b
ifoldr :: forall (n :: Nat) a b. Arity n => (Int -> a -> b -> b) -> b -> ContVec n a -> b
foldM :: forall (n :: Nat) m b a. (Arity n, Monad m) => (b -> a -> m b) -> b -> ContVec n a -> m b
ifoldM :: forall (n :: Nat) m b a. (Arity n, Monad m) => (b -> Int -> a -> m b) -> b -> ContVec n a -> m b
sum :: forall a (n :: Nat). (Num a, Arity n) => ContVec n a -> a
minimum :: forall a (n :: Nat). (Ord a, Arity n, 1 <= n) => ContVec n a -> a
maximum :: forall a (n :: Nat). (Ord a, Arity n, 1 <= n) => ContVec n a -> a
and :: forall (n :: Nat). Arity n => ContVec n Bool -> Bool
or :: forall (n :: Nat). Arity n => ContVec n Bool -> Bool
all :: forall (n :: Nat) a. Arity n => (a -> Bool) -> ContVec n a -> Bool
any :: forall (n :: Nat) a. Arity n => (a -> Bool) -> ContVec n a -> Bool
find :: forall (n :: Nat) a. Arity n => (a -> Bool) -> ContVec n a -> Maybe a
gfoldl :: forall c v a. (Vector v a, Data a) => (forall x y. Data x => c (x -> y) -> x -> c y) -> (forall x. x -> c x) -> v a -> c (v a)
gunfold :: forall con c v a. (Vector v a, Data a) => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> con -> c (v a)

Type-level numbers

data PeanoNum Source #

Peano numbers. Since type level naturals don't support induction we have to convert type nats to Peano representation first and work with it,

Constructors

Z
S PeanoNum

type family Peano (n :: Nat) :: PeanoNum where ... Source #

Convert type level natural to Peano representation

Equations

Peano 0 = 'Z
Peano n = 'S (Peano (n - 1))

type family Add (n :: PeanoNum) (m :: PeanoNum) :: PeanoNum where ... Source #

Type family for sum of unary natural numbers.

Equations

Add 'Z n = n
Add ('S n) k = 'S (Add n k)

N-ary functions

type family Fn (n :: PeanoNum) a b where ... Source #

Type family for n-ary functions. n is number of parameters of type a and b is result type.

Equations

Fn 'Z a b = b
Fn ('S n) a b = a -> Fn n a b

newtype Fun (n :: PeanoNum) a b Source #

Newtype wrapper which is used to make Fn injective. It's also a reader monad.

Constructors

Fun
Fields unFun :: Fn n a b

Instances

Instances details

ArityPeano n => Applicative (Fun n a) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods pure :: a0 -> Fun n a a0 # (<>) :: Fun n a (a0 -> b) -> Fun n a a0 -> Fun n a b # liftA2 :: (a0 -> b -> c) -> Fun n a a0 -> Fun n a b -> Fun n a c # (>) :: Fun n a a0 -> Fun n a b -> Fun n a b # (<*) :: Fun n a a0 -> Fun n a b -> Fun n a a0 #
ArityPeano n => Functor (Fun n a) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods fmap :: (a0 -> b) -> Fun n a a0 -> Fun n a b # (<$) :: a0 -> Fun n a b -> Fun n a a0 #
ArityPeano n => Monad (Fun n a) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods (>>=) :: Fun n a a0 -> (a0 -> Fun n a b) -> Fun n a b # (>>) :: Fun n a a0 -> Fun n a b -> Fun n a b # return :: a0 -> Fun n a a0 #

type Arity (n :: Nat) = (ArityPeano (Peano n), KnownNat n, Peano (n + 1) ~ 'S (Peano n)) Source #

Type class for type level number for which we can defined operations over N-ary functions.

class ArityPeano (n :: PeanoNum) where Source #

Type class for handling n-ary functions.

Methods

accum Source #

Arguments

:: (forall (k :: PeanoNum). t ('S k) -> a -> t k)	Fold function
-> (t 'Z -> b)	Extract result of fold
-> t n	Initial value
-> Fun n a b	Reduction function

Left fold over n elements exposed as n-ary function. These elements are supplied as arguments to the function.

applyFun Source #

Arguments

:: (forall (k :: PeanoNum). t ('S k) -> (a, t k))	Get value to apply to function
-> t n	Initial value
-> (CVecPeano n a, t 'Z)

Apply all parameters to the function.

applyFunM Source #

Arguments

:: Applicative f
=> (forall (k :: PeanoNum). t ('S k) -> (f a, t k))	Get value to apply to function
-> t n	Initial value
-> (f (CVecPeano n a), t 'Z)

Apply all parameters to the function using monadic actions. Note that for identity monad it's same as applyFun. Ignoring newtypes:

forall b. Fn n a b -> b  ~ ContVec n a

reverseF :: Fun n a b -> Fun n a b Source #

Reverse order of parameters. It's implemented directly in type class since expressing it in terms of accum will require putting ArityPeano constraint on step funcion

gunfoldF :: Data a => (forall b x. Data b => c (b -> x) -> c x) -> T_gunfold c r a n -> c r Source #

Worker function for gunfold

Instances

Instances details

ArityPeano 'Z Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods accum :: (forall (k :: PeanoNum). t ('S k) -> a -> t k) -> (t 'Z -> b) -> t 'Z -> Fun 'Z a b Source # applyFun :: (forall (k :: PeanoNum). t ('S k) -> (a, t k)) -> t 'Z -> (CVecPeano 'Z a, t 'Z) Source # applyFunM :: Applicative f => (forall (k :: PeanoNum). t ('S k) -> (f a, t k)) -> t 'Z -> (f (CVecPeano 'Z a), t 'Z) Source # reverseF :: Fun 'Z a b -> Fun 'Z a b Source # gunfoldF :: Data a => (forall b x. Data b => c (b -> x) -> c x) -> T_gunfold c r a 'Z -> c r Source #
ArityPeano n => ArityPeano ('S n) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods accum :: (forall (k :: PeanoNum). t ('S k) -> a -> t k) -> (t 'Z -> b) -> t ('S n) -> Fun ('S n) a b Source # applyFun :: (forall (k :: PeanoNum). t ('S k) -> (a, t k)) -> t ('S n) -> (CVecPeano ('S n) a, t 'Z) Source # applyFunM :: Applicative f => (forall (k :: PeanoNum). t ('S k) -> (f a, t k)) -> t ('S n) -> (f (CVecPeano ('S n) a), t 'Z) Source # reverseF :: Fun ('S n) a b -> Fun ('S n) a b Source # gunfoldF :: Data a => (forall b x. Data b => c (b -> x) -> c x) -> T_gunfold c r a ('S n) -> c r Source #

arity :: forall (n :: Nat) proxy. KnownNat n => proxy n -> Int Source #

Arity of function.

apply Source #

Arguments

:: forall (n :: Nat) t a. Arity n
=> (forall (k :: PeanoNum). t ('S k) -> (a, t k))	Get value to apply to function
-> t (Peano n)	Initial value
-> ContVec n a	N-ary function

Apply all parameters to the function.

applyM Source #

Arguments

:: forall f (n :: Nat) t a. (Applicative f, Arity n)
=> (forall (k :: PeanoNum). t ('S k) -> (f a, t k))	Get value to apply to function
-> t (Peano n)	Initial value
-> f (ContVec n a)

Apply all parameters to the function using applicative actions.

Combinators

constFun :: forall (n :: PeanoNum) a b. Fun n a b -> Fun ('S n) a b Source #

Prepend ignored parameter to function

curryFirst :: forall (n :: PeanoNum) a b. Fun ('S n) a b -> a -> Fun n a b Source #

Curry first parameter of n-ary function

uncurryFirst :: forall a (n :: PeanoNum) b. (a -> Fun n a b) -> Fun ('S n) a b Source #

Uncurry first parameter of n-ary function

curryLast :: forall (n :: PeanoNum) a b. ArityPeano n => Fun ('S n) a b -> Fun n a (a -> b) Source #

Curry last parameter of n-ary function

curryMany :: forall (n :: PeanoNum) (k :: PeanoNum) a b. ArityPeano n => Fun (Add n k) a b -> Fun n a (Fun k a b) Source #

Curry n first parameters of n-ary function

apLast :: forall (n :: PeanoNum) a b. ArityPeano n => Fun ('S n) a b -> a -> Fun n a b Source #

Apply last parameter to function. Unlike apFun we need to traverse all parameters but last hence Arity constraint.

shuffleFun :: forall (n :: PeanoNum) b a r. ArityPeano n => (b -> Fun n a r) -> Fun n a (b -> r) Source #

Move function parameter to the result of N-ary function.

withFun :: forall (n :: PeanoNum) a b. (Fun n a b -> Fun n a b) -> Fun ('S n) a b -> Fun ('S n) a b Source #

Recursive step for the function

Vector type class

type family Dim (v :: Type -> Type) :: Nat Source #

Size of vector expressed as type-level natural.

Instances

Instances details

type Dim Complex Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim Complex = 2
type Dim Only Source #
Instance details Defined in Data.Vector.Fixed type Dim Only = 1
type Dim Identity Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim Identity = 1
type Dim (Empty :: Type -> Type) Source #
Instance details Defined in Data.Vector.Fixed type Dim (Empty :: Type -> Type) = 0
type Dim (VecList n) Source #
Instance details Defined in Data.Vector.Fixed type Dim (VecList n) = n
type Dim (Vec n) Source #
Instance details Defined in Data.Vector.Fixed.Boxed type Dim (Vec n) = n
type Dim (ContVec n) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim (ContVec n) = n
type Dim (Vec n) Source #
Instance details Defined in Data.Vector.Fixed.Primitive type Dim (Vec n) = n
type Dim (Vec n) Source #
Instance details Defined in Data.Vector.Fixed.Storable type Dim (Vec n) = n
type Dim (Vec n) Source #
Instance details Defined in Data.Vector.Fixed.Unboxed type Dim (Vec n) = n
type Dim (Proxy :: Type -> Type) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim (Proxy :: Type -> Type) = 0
type Dim ((,) a) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim ((,) a) = 2
type Dim ((,,) a b) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim ((,,) a b) = 3
type Dim ((,,,) a b c) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim ((,,,) a b c) = 4
type Dim ((,,,,) a b c d) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim ((,,,,) a b c d) = 5
type Dim ((,,,,,) a b c d e) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim ((,,,,,) a b c d e) = 6
type Dim ((,,,,,,) a b c d e f) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim ((,,,,,,) a b c d e f) = 7

class Arity (Dim v) => Vector (v :: Type -> Type) a where Source #

Type class for vectors with fixed length. Instance should provide two functions: one to create vector and another for vector deconstruction. They must obey following law:

inspect v construct = v

For example instance for 2D vectors could be written as:

data V2 a = V2 a a

type instance V2 = 2
instance Vector V2 a where
  construct                = Fun V2
  inspect (V2 a b) (Fun f) = f a b

Minimal complete definition

construct, inspect

Methods

construct :: Fun (Peano (Dim v)) a (v a) Source #

N-ary function for creation of vectors.

inspect :: v a -> Fun (Peano (Dim v)) a b -> b Source #

Deconstruction of vector.

basicIndex :: v a -> Int -> a Source #

Optional more efficient implementation of indexing. Shouldn't be used directly, use ! instead.

Instances

Instances details

Vector Complex a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim Complex)) a (Complex a) Source # inspect :: Complex a -> Fun (Peano (Dim Complex)) a b -> b Source # basicIndex :: Complex a -> Int -> a Source #
Vector Only a Source #
Instance details Defined in Data.Vector.Fixed Methods construct :: Fun (Peano (Dim Only)) a (Only a) Source # inspect :: Only a -> Fun (Peano (Dim Only)) a b -> b Source # basicIndex :: Only a -> Int -> a Source #
Vector Identity a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim Identity)) a (Identity a) Source # inspect :: Identity a -> Fun (Peano (Dim Identity)) a b -> b Source # basicIndex :: Identity a -> Int -> a Source #
Vector (Empty :: Type -> Type) a Source #
Instance details Defined in Data.Vector.Fixed Methods construct :: Fun (Peano (Dim (Empty :: Type -> Type))) a (Empty a) Source # inspect :: Empty a -> Fun (Peano (Dim (Empty :: Type -> Type))) a b -> b Source # basicIndex :: Empty a -> Int -> a Source #
Arity n => Vector (VecList n) a Source #
Instance details Defined in Data.Vector.Fixed Methods construct :: Fun (Peano (Dim (VecList n))) a (VecList n a) Source # inspect :: VecList n a -> Fun (Peano (Dim (VecList n))) a b -> b Source # basicIndex :: VecList n a -> Int -> a Source #
Arity n => Vector (Vec n) a Source #
Instance details Defined in Data.Vector.Fixed.Boxed Methods construct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source # inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source # basicIndex :: Vec n a -> Int -> a Source #
Arity n => Vector (ContVec n) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim (ContVec n))) a (ContVec n a) Source # inspect :: ContVec n a -> Fun (Peano (Dim (ContVec n))) a b -> b Source # basicIndex :: ContVec n a -> Int -> a Source #
(Arity n, Prim a) => Vector (Vec n) a Source #
Instance details Defined in Data.Vector.Fixed.Primitive Methods construct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source # inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source # basicIndex :: Vec n a -> Int -> a Source #
(Arity n, Storable a) => Vector (Vec n) a Source #
Instance details Defined in Data.Vector.Fixed.Storable Methods construct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source # inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source # basicIndex :: Vec n a -> Int -> a Source #
Unbox n a => Vector (Vec n) a Source #
Instance details Defined in Data.Vector.Fixed.Unboxed Methods construct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source # inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source # basicIndex :: Vec n a -> Int -> a Source #
Vector (Proxy :: Type -> Type) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim (Proxy :: Type -> Type))) a (Proxy a) Source # inspect :: Proxy a -> Fun (Peano (Dim (Proxy :: Type -> Type))) a b -> b Source # basicIndex :: Proxy a -> Int -> a Source #
b ~ a => Vector ((,) b) a Source #	Note this instance (and other instances for tuples) is essentially monomorphic in element type. Vector type v of 2 element tuple `(Int,Int)` is `(,) Int` so it will only work with elements of type `Int`.
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim ((,) b))) a (b, a) Source # inspect :: (b, a) -> Fun (Peano (Dim ((,) b))) a b0 -> b0 Source # basicIndex :: (b, a) -> Int -> a Source #
(b ~ a, c ~ a) => Vector ((,,) b c) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim ((,,) b c))) a (b, c, a) Source # inspect :: (b, c, a) -> Fun (Peano (Dim ((,,) b c))) a b0 -> b0 Source # basicIndex :: (b, c, a) -> Int -> a Source #
(b ~ a, c ~ a, d ~ a) => Vector ((,,,) b c d) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim ((,,,) b c d))) a (b, c, d, a) Source # inspect :: (b, c, d, a) -> Fun (Peano (Dim ((,,,) b c d))) a b0 -> b0 Source # basicIndex :: (b, c, d, a) -> Int -> a Source #
(b ~ a, c ~ a, d ~ a, e ~ a) => Vector ((,,,,) b c d e) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim ((,,,,) b c d e))) a (b, c, d, e, a) Source # inspect :: (b, c, d, e, a) -> Fun (Peano (Dim ((,,,,) b c d e))) a b0 -> b0 Source # basicIndex :: (b, c, d, e, a) -> Int -> a Source #
(b ~ a, c ~ a, d ~ a, e ~ a, f ~ a) => Vector ((,,,,,) b c d e f) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim ((,,,,,) b c d e f))) a (b, c, d, e, f, a) Source # inspect :: (b, c, d, e, f, a) -> Fun (Peano (Dim ((,,,,,) b c d e f))) a b0 -> b0 Source # basicIndex :: (b, c, d, e, f, a) -> Int -> a Source #
(b ~ a, c ~ a, d ~ a, e ~ a, f ~ a, g ~ a) => Vector ((,,,,,,) b c d e f g) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim ((,,,,,,) b c d e f g))) a (b, c, d, e, f, g, a) Source # inspect :: (b, c, d, e, f, g, a) -> Fun (Peano (Dim ((,,,,,,) b c d e f g))) a b0 -> b0 Source # basicIndex :: (b, c, d, e, f, g, a) -> Int -> a Source #

class (Vector (v n) a, Dim (v n) ~ n) => VectorN (v :: Nat -> Type -> Type) (n :: Nat) a Source #

Vector parametrized by length. In ideal world it should be:

forall n. (Arity n, Vector (v n) a, Dim (v n) ~ n) => VectorN v a

Alas polymorphic constraints aren't allowed in haskell.

Instances

Instances details

Arity n => VectorN VecList n a Source #
Instance details Defined in Data.Vector.Fixed
Arity n => VectorN Vec n a Source #
Instance details Defined in Data.Vector.Fixed.Boxed
Arity n => VectorN ContVec n a Source #
Instance details Defined in Data.Vector.Fixed.Cont
(Arity n, Prim a) => VectorN Vec n a Source #
Instance details Defined in Data.Vector.Fixed.Primitive
(Arity n, Storable a) => VectorN Vec n a Source #
Instance details Defined in Data.Vector.Fixed.Storable
Unbox n a => VectorN Vec n a Source #
Instance details Defined in Data.Vector.Fixed.Unboxed

length :: KnownNat (Dim v) => v a -> Int Source #

Length of vector. Function doesn't evaluate its argument.

Vector as continuation

newtype ContVec (n :: Nat) a Source #

Vector represented as continuation. Alternative wording: it's Church encoded N-element vector.

Constructors

ContVec (forall r. Fun (Peano n) a r -> r)

Instances

Instances details

Arity n => VectorN ContVec n a Source #
Instance details Defined in Data.Vector.Fixed.Cont
Arity n => Applicative (ContVec n) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods pure :: a -> ContVec n a # (<>) :: ContVec n (a -> b) -> ContVec n a -> ContVec n b # liftA2 :: (a -> b -> c) -> ContVec n a -> ContVec n b -> ContVec n c # (>) :: ContVec n a -> ContVec n b -> ContVec n b # (<*) :: ContVec n a -> ContVec n b -> ContVec n a #
Arity n => Functor (ContVec n) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods fmap :: (a -> b) -> ContVec n a -> ContVec n b # (<$) :: a -> ContVec n b -> ContVec n a #
Arity n => Foldable (ContVec n) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods fold :: Monoid m => ContVec n m -> m # foldMap :: Monoid m => (a -> m) -> ContVec n a -> m # foldMap' :: Monoid m => (a -> m) -> ContVec n a -> m # foldr :: (a -> b -> b) -> b -> ContVec n a -> b # foldr' :: (a -> b -> b) -> b -> ContVec n a -> b # foldl :: (b -> a -> b) -> b -> ContVec n a -> b # foldl' :: (b -> a -> b) -> b -> ContVec n a -> b # foldr1 :: (a -> a -> a) -> ContVec n a -> a # foldl1 :: (a -> a -> a) -> ContVec n a -> a # toList :: ContVec n a -> [a] # null :: ContVec n a -> Bool # length :: ContVec n a -> Int # elem :: Eq a => a -> ContVec n a -> Bool # maximum :: Ord a => ContVec n a -> a # minimum :: Ord a => ContVec n a -> a # sum :: Num a => ContVec n a -> a # product :: Num a => ContVec n a -> a #
Arity n => Traversable (ContVec n) Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods traverse :: Applicative f => (a -> f b) -> ContVec n a -> f (ContVec n b) # sequenceA :: Applicative f => ContVec n (f a) -> f (ContVec n a) # mapM :: Monad m => (a -> m b) -> ContVec n a -> m (ContVec n b) # sequence :: Monad m => ContVec n (m a) -> m (ContVec n a) #
Arity n => Vector (ContVec n) a Source #
Instance details Defined in Data.Vector.Fixed.Cont Methods construct :: Fun (Peano (Dim (ContVec n))) a (ContVec n a) Source # inspect :: ContVec n a -> Fun (Peano (Dim (ContVec n))) a b -> b Source # basicIndex :: ContVec n a -> Int -> a Source #
type Dim (ContVec n) Source #
Instance details Defined in Data.Vector.Fixed.Cont type Dim (ContVec n) = n

newtype CVecPeano (n :: PeanoNum) a Source #

Same as ContVec but its length is expressed as Peano number.

Constructors

CVecPeano (forall r. Fun n a r -> r)

consPeano :: forall a (n :: PeanoNum). a -> CVecPeano n a -> CVecPeano ('S n) a Source #

Cons values to the CVecPeano.

toContVec :: forall (n :: Nat) a. CVecPeano (Peano n) a -> ContVec n a Source #

runContVec :: forall (n :: Nat) a r. Fun (Peano n) a r -> ContVec n a -> r Source #

Run continuation vector. It's same as inspect but with arguments flipped.

Construction of ContVec

cvec :: forall v a (n :: Nat). (Vector v a, Dim v ~ n) => v a -> ContVec n a Source #

Convert regular vector to continuation based one.

fromList :: forall (n :: Nat) a. Arity n => [a] -> ContVec n a Source #

Convert list to continuation-based vector. Will throw error if list is shorter than resulting vector.

fromList' :: forall (n :: Nat) a. Arity n => [a] -> ContVec n a Source #

Same as fromList bu throws error is list doesn't have same length as vector.

fromListM :: forall (n :: Nat) a. Arity n => [a] -> Maybe (ContVec n a) Source #

Convert list to continuation-based vector. Will fail with Nothing if list doesn't have right length.

toList :: forall (n :: Nat) a. Arity n => ContVec n a -> [a] Source #

Convert vector to the list

replicate :: forall (n :: Nat) a. Arity n => a -> ContVec n a Source #

Execute monadic action for every element of vector. Synonym for pure.

replicateM :: forall (n :: Nat) f a. (Arity n, Applicative f) => f a -> f (ContVec n a) Source #

Execute monadic action for every element of vector.

generate :: forall (n :: Nat) a. Arity n => (Int -> a) -> ContVec n a Source #

Generate vector from function which maps element's index to its value.

generateM :: forall f (n :: Nat) a. (Applicative f, Arity n) => (Int -> f a) -> f (ContVec n a) Source #

Generate vector from monadic function which maps element's index to its value.

unfoldr :: forall (n :: Nat) b a. Arity n => (b -> (a, b)) -> b -> ContVec n a Source #

Unfold vector.

basis :: forall a (n :: Nat). (Num a, Arity n) => Int -> ContVec n a Source #

Unit vector along Nth axis.

Constructors

empty :: ContVec 0 a Source #

Create empty vector.

cons :: forall (n :: Nat) a. Arity n => a -> ContVec n a -> ContVec (n + 1) a Source #

O(1) Prepend element to vector

consV :: forall (n :: Nat) a. Arity n => ContVec 1 a -> ContVec n a -> ContVec (n + 1) a Source #

Prepend single element vector to another vector.

snoc :: forall (n :: Nat) a. Arity n => a -> ContVec n a -> ContVec (n + 1) a Source #

O(1) Append element to vector

concat :: forall (n :: Nat) (k :: Nat) a. (Arity n, Arity k, Arity (n + k), Peano (n + k) ~ Add (Peano n) (Peano k)) => ContVec n a -> ContVec k a -> ContVec (n + k) a Source #

Concatenate vector

mk1 :: a -> ContVec 1 a Source #

mk2 :: a -> a -> ContVec 2 a Source #

mk3 :: a -> a -> a -> ContVec 3 a Source #

mk4 :: a -> a -> a -> a -> ContVec 4 a Source #

mk5 :: a -> a -> a -> a -> a -> ContVec 5 a Source #

mk6 :: a -> a -> a -> a -> a -> a -> ContVec 6 a Source #

mk7 :: a -> a -> a -> a -> a -> a -> a -> ContVec 7 a Source #

mk8 :: a -> a -> a -> a -> a -> a -> a -> a -> ContVec 8 a Source #

Transformations

map :: forall (n :: Nat) a b. Arity n => (a -> b) -> ContVec n a -> ContVec n b Source #

Map over vector. Synonym for fmap

imap :: forall (n :: Nat) a b. Arity n => (Int -> a -> b) -> ContVec n a -> ContVec n b Source #

Apply function to every element of the vector and its index.

mapM :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (a -> f b) -> ContVec n a -> f (ContVec n b) Source #

Effectful map over vector.

imapM :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (Int -> a -> f b) -> ContVec n a -> f (ContVec n b) Source #

Apply monadic function to every element of the vector and its index.

mapM_ :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (a -> f b) -> ContVec n a -> f () Source #

Apply monadic action to each element of vector and ignore result.

imapM_ :: forall (n :: Nat) f a b. (Arity n, Applicative f) => (Int -> a -> f b) -> ContVec n a -> f () Source #

Apply monadic action to each element of vector and its index and ignore result.

scanl :: forall (n :: Nat) b a. Arity n => (b -> a -> b) -> b -> ContVec n a -> ContVec (n + 1) b Source #

Left scan over vector

scanl1 :: forall (n :: Nat) a. Arity n => (a -> a -> a) -> ContVec n a -> ContVec n a Source #

Left scan over vector

sequence :: forall (n :: Nat) f a. (Arity n, Applicative f) => ContVec n (f a) -> f (ContVec n a) Source #

Evaluate every action in the vector from left to right.

sequence_ :: forall (n :: Nat) f a. (Arity n, Applicative f) => ContVec n (f a) -> f () Source #

Evaluate every action in the vector from left to right and ignore result.

distribute :: forall f (n :: Nat) a. (Functor f, Arity n) => f (ContVec n a) -> ContVec n (f a) Source #

The dual of sequenceA

collect :: forall f (n :: Nat) a b. (Functor f, Arity n) => (a -> ContVec n b) -> f a -> ContVec n (f b) Source #

tail :: forall (n :: Nat) a. Arity n => ContVec (n + 1) a -> ContVec n a Source #

O(1) Tail of vector.

reverse :: forall (n :: Nat) a. Arity n => ContVec n a -> ContVec n a Source #

Reverse order of elements in the vector

Zips

zipWith :: forall (n :: Nat) a b c. Arity n => (a -> b -> c) -> ContVec n a -> ContVec n b -> ContVec n c Source #

Zip two vector together using function.

zipWith3 :: forall (n :: Nat) a b c d. Arity n => (a -> b -> c -> d) -> ContVec n a -> ContVec n b -> ContVec n c -> ContVec n d Source #

Zip three vectors together

izipWith :: forall (n :: Nat) a b c. Arity n => (Int -> a -> b -> c) -> ContVec n a -> ContVec n b -> ContVec n c Source #

Zip two vector together using function which takes element index as well.

izipWith3 :: forall (n :: Nat) a b c d. Arity n => (Int -> a -> b -> c -> d) -> ContVec n a -> ContVec n b -> ContVec n c -> ContVec n d Source #

Zip three vectors together

zipWithM :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (a -> b -> f c) -> ContVec n a -> ContVec n b -> f (ContVec n c) Source #

Zip two vector together using monadic function.

zipWithM_ :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (a -> b -> f c) -> ContVec n a -> ContVec n b -> f () Source #

izipWithM :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (Int -> a -> b -> f c) -> ContVec n a -> ContVec n b -> f (ContVec n c) Source #

Zip two vector together using monadic function which takes element index as well..

izipWithM_ :: forall (n :: Nat) f a b c. (Arity n, Applicative f) => (Int -> a -> b -> f c) -> ContVec n a -> ContVec n b -> f () Source #

Getters

head :: forall (n :: Nat) a. (Arity n, 1 <= n) => ContVec n a -> a Source #

Finalizer function for getting head of the vector.

index :: forall (n :: Nat) a. Arity n => Int -> ContVec n a -> a Source #

O(n) Get value at specified index.

element :: forall (n :: Nat) f a. (Arity n, Functor f) => Int -> (a -> f a) -> ContVec n a -> f (ContVec n a) Source #

Twan van Laarhoven lens for continuation based vector

Vector construction

vector :: forall v a (n :: Nat). (Vector v a, Dim v ~ n) => ContVec n a -> v a Source #

Convert continuation to the vector.

Folds

foldl :: forall (n :: Nat) b a. Arity n => (b -> a -> b) -> b -> ContVec n a -> b Source #

Left fold over continuation vector.

foldl1 :: forall (n :: Nat) a. (Arity n, 1 <= n) => (a -> a -> a) -> ContVec n a -> a Source #

Left fold.

foldr :: forall (n :: Nat) a b. Arity n => (a -> b -> b) -> b -> ContVec n a -> b Source #

Right fold over continuation vector

ifoldl :: forall (n :: Nat) b a. Arity n => (b -> Int -> a -> b) -> b -> ContVec n a -> b Source #

Left fold over continuation vector.

ifoldr :: forall (n :: Nat) a b. Arity n => (Int -> a -> b -> b) -> b -> ContVec n a -> b Source #

Right fold over continuation vector

foldM :: forall (n :: Nat) m b a. (Arity n, Monad m) => (b -> a -> m b) -> b -> ContVec n a -> m b Source #

Monadic left fold over continuation vector.

ifoldM :: forall (n :: Nat) m b a. (Arity n, Monad m) => (b -> Int -> a -> m b) -> b -> ContVec n a -> m b Source #

Monadic left fold over continuation vector.

Special folds

sum :: forall a (n :: Nat). (Num a, Arity n) => ContVec n a -> a Source #

Sum all elements in the vector.

minimum :: forall a (n :: Nat). (Ord a, Arity n, 1 <= n) => ContVec n a -> a Source #

Minimal element of vector.

maximum :: forall a (n :: Nat). (Ord a, Arity n, 1 <= n) => ContVec n a -> a Source #

Maximal element of vector.

and :: forall (n :: Nat). Arity n => ContVec n Bool -> Bool Source #

Conjunction of elements of a vector.

or :: forall (n :: Nat). Arity n => ContVec n Bool -> Bool Source #

Disjunction of all elements of a vector.

all :: forall (n :: Nat) a. Arity n => (a -> Bool) -> ContVec n a -> Bool Source #

Determines whether all elements of vector satisfy predicate.

any :: forall (n :: Nat) a. Arity n => (a -> Bool) -> ContVec n a -> Bool Source #

Determines whether any of element of vector satisfy predicate.

find :: forall (n :: Nat) a. Arity n => (a -> Bool) -> ContVec n a -> Maybe a Source #

The find function takes a predicate and a vector and returns the leftmost element of the vector matching the predicate, or Nothing if there is no such element.

Data.Data.Data

gfoldl :: forall c v a. (Vector v a, Data a) => (forall x y. Data x => c (x -> y) -> x -> c y) -> (forall x. x -> c x) -> v a -> c (v a) Source #

Generic gfoldl which could work with any vector.

gunfold :: forall con c v a. (Vector v a, Data a) => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> con -> c (v a) Source #

Generic gunfoldl which could work with any vector. Since vector can only have one constructor argument for constructor is ignored.