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Language	Haskell2010

Data.Vec.DataFamily.SpineStrict

Contents

Construction
Conversions
Indexing
Reverse
Concatenation and splitting
Folds
Special folds
Mapping
Zipping
Monadic
Universe
Extras

Description

Spine-strict length-indexed list defined as data-family: Vec.

Data family variant allows lazy pattern matching. On the other hand, the Vec value doesn't "know" its length (i.e. there isn't withDict).

Agda

If you happen to familiar with Agda, then the difference between GADT and data-family version is maybe clearer:

module Vec where

open import Data.Nat
open import Relation.Binary.PropositionalEquality using (_≡_; refl)

-- "GADT"
data Vec (A : Set) : ℕ → Set where
  []  : Vec A 0
  _∷_ : ∀ {n} → A → Vec A n → Vec A (suc n)

infixr 50 _∷_

exVec : Vec ℕ 2
exVec = 13 ∷ 37 ∷ []

-- "data family"
data Unit : Set where
  [] : Unit

data _×_ (A B : Set) : Set where
  _∷_ : A → B → A × B

infixr 50 _×_

VecF : Set → ℕ → Set
VecF A zero    = Unit
VecF A (suc n) = A × VecF A n

exVecF : VecF ℕ 2
exVecF = 13 ∷ 37 ∷ []

reduction : VecF ℕ 2 ≡ ℕ × ℕ × Unit
reduction = refl

Synopsis

data family Vec (n :: Nat) a
empty :: Vec 'Z a
singleton :: a -> Vec ('S 'Z) a
toPull :: forall n a. SNatI n => Vec n a -> Vec n a
fromPull :: forall n a. SNatI n => Vec n a -> Vec n a
toList :: forall n a. SNatI n => Vec n a -> [a]
toNonEmpty :: forall n a. SNatI n => Vec ('S n) a -> NonEmpty a
fromList :: SNatI n => [a] -> Maybe (Vec n a)
fromListPrefix :: SNatI n => [a] -> Maybe (Vec n a)
reifyList :: [a] -> (forall n. SNatI n => Vec n a -> r) -> r
(!) :: SNatI n => Vec n a -> Fin n -> a
tabulate :: SNatI n => (Fin n -> a) -> Vec n a
cons :: a -> Vec n a -> Vec ('S n) a
snoc :: forall n a. SNatI n => Vec n a -> a -> Vec ('S n) a
head :: Vec ('S n) a -> a
last :: forall n a. SNatI n => Vec ('S n) a -> a
tail :: Vec ('S n) a -> Vec n a
init :: forall n a. SNatI n => Vec ('S n) a -> Vec n a
reverse :: forall n a. SNatI n => Vec n a -> Vec n a
(++) :: forall n m a. SNatI n => Vec n a -> Vec m a -> Vec (Plus n m) a
split :: SNatI n => Vec (Plus n m) a -> (Vec n a, Vec m a)
concatMap :: forall a b n m. (SNatI m, SNatI n) => (a -> Vec m b) -> Vec n a -> Vec (Mult n m) b
concat :: (SNatI m, SNatI n) => Vec n (Vec m a) -> Vec (Mult n m) a
chunks :: (SNatI n, SNatI m) => Vec (Mult n m) a -> Vec n (Vec m a)
foldMap :: (Monoid m, SNatI n) => (a -> m) -> Vec n a -> m
foldMap1 :: forall s a n. (Semigroup s, SNatI n) => (a -> s) -> Vec ('S n) a -> s
ifoldMap :: forall a n m. (Monoid m, SNatI n) => (Fin n -> a -> m) -> Vec n a -> m
ifoldMap1 :: forall a n s. (Semigroup s, SNatI n) => (Fin ('S n) -> a -> s) -> Vec ('S n) a -> s
foldr :: forall a b n. SNatI n => (a -> b -> b) -> b -> Vec n a -> b
ifoldr :: forall a b n. SNatI n => (Fin n -> a -> b -> b) -> b -> Vec n a -> b
length :: forall n a. SNatI n => Vec n a -> Int
null :: forall n a. SNatI n => Vec n a -> Bool
sum :: (Num a, SNatI n) => Vec n a -> a
product :: (Num a, SNatI n) => Vec n a -> a
map :: forall a b n. SNatI n => (a -> b) -> Vec n a -> Vec n b
imap :: SNatI n => (Fin n -> a -> b) -> Vec n a -> Vec n b
traverse :: forall n f a b. (Applicative f, SNatI n) => (a -> f b) -> Vec n a -> f (Vec n b)
traverse1 :: forall n f a b. (Apply f, SNatI n) => (a -> f b) -> Vec ('S n) a -> f (Vec ('S n) b)
itraverse :: forall n f a b. (Applicative f, SNatI n) => (Fin n -> a -> f b) -> Vec n a -> f (Vec n b)
itraverse_ :: forall n f a b. (Applicative f, SNatI n) => (Fin n -> a -> f b) -> Vec n a -> f ()
zipWith :: forall a b c n. SNatI n => (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c
izipWith :: SNatI n => (Fin n -> a -> b -> c) -> Vec n a -> Vec n b -> Vec n c
repeat :: SNatI n => x -> Vec n x
bind :: SNatI n => Vec n a -> (a -> Vec n b) -> Vec n b
join :: SNatI n => Vec n (Vec n a) -> Vec n a
universe :: SNatI n => Vec n (Fin n)
ensureSpine :: SNatI n => Vec n a -> Vec n a

Documentation

data family Vec (n :: Nat) a infixr 5 Source #

Vector, i.e. length-indexed list.

Instances

Instances details

SNatI n => Monad (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods (>>=) :: Vec n a -> (a -> Vec n b) -> Vec n b # (>>) :: Vec n a -> Vec n b -> Vec n b # return :: a -> Vec n a #
SNatI n => Functor (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods fmap :: (a -> b) -> Vec n a -> Vec n b # (<$) :: a -> Vec n b -> Vec n a #
SNatI n => Applicative (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods pure :: a -> Vec n a # (<>) :: Vec n (a -> b) -> Vec n a -> Vec n b # liftA2 :: (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c # (>) :: Vec n a -> Vec n b -> Vec n b # (<*) :: Vec n a -> Vec n b -> Vec n a #
SNatI n => Foldable (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods fold :: Monoid m => Vec n m -> m # foldMap :: Monoid m => (a -> m) -> Vec n a -> m # foldMap' :: Monoid m => (a -> m) -> Vec n a -> m # foldr :: (a -> b -> b) -> b -> Vec n a -> b # foldr' :: (a -> b -> b) -> b -> Vec n a -> b # foldl :: (b -> a -> b) -> b -> Vec n a -> b # foldl' :: (b -> a -> b) -> b -> Vec n a -> b # foldr1 :: (a -> a -> a) -> Vec n a -> a # foldl1 :: (a -> a -> a) -> Vec n a -> a # toList :: Vec n a -> [a] # null :: Vec n a -> Bool # length :: Vec n a -> Int # elem :: Eq a => a -> Vec n a -> Bool # maximum :: Ord a => Vec n a -> a # minimum :: Ord a => Vec n a -> a # sum :: Num a => Vec n a -> a # product :: Num a => Vec n a -> a #
SNatI n => Traversable (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods traverse :: Applicative f => (a -> f b) -> Vec n a -> f (Vec n b) # sequenceA :: Applicative f => Vec n (f a) -> f (Vec n a) # mapM :: Monad m => (a -> m b) -> Vec n a -> m (Vec n b) # sequence :: Monad m => Vec n (m a) -> m (Vec n a) #
SNatI n => Arbitrary1 (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods liftArbitrary :: Gen a -> Gen (Vec n a) # liftShrink :: (a -> [a]) -> Vec n a -> [Vec n a] #
SNatI n => Distributive (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods distribute :: Functor f => f (Vec n a) -> Vec n (f a) # collect :: Functor f => (a -> Vec n b) -> f a -> Vec n (f b) # distributeM :: Monad m => m (Vec n a) -> Vec n (m a) # collectM :: Monad m => (a -> Vec n b) -> m a -> Vec n (m b) #
SNatI n => Representable (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Associated Types type Rep (Vec n) # Methods tabulate :: (Rep (Vec n) -> a) -> Vec n a # index :: Vec n a -> Rep (Vec n) -> a #
SNatI n => Eq1 (Vec n) Source #	Since: 0.4
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods liftEq :: (a -> b -> Bool) -> Vec n a -> Vec n b -> Bool #
SNatI n => Ord1 (Vec n) Source #	Since: 0.4
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods liftCompare :: (a -> b -> Ordering) -> Vec n a -> Vec n b -> Ordering #
SNatI n => Show1 (Vec n) Source #	Since: 0.4
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Vec n a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Vec n a] -> ShowS #
(SNatI m, n ~ 'S m) => Traversable1 (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods traverse1 :: Apply f => (a -> f b) -> Vec n a -> f (Vec n b) # sequence1 :: Apply f => Vec n (f b) -> f (Vec n b) #
(SNatI m, n ~ 'S m) => Foldable1 (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods fold1 :: Semigroup m => Vec n m -> m # foldMap1 :: Semigroup m => (a -> m) -> Vec n a -> m # toNonEmpty :: Vec n a -> NonEmpty a #
SNatI n => Apply (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods (<.>) :: Vec n (a -> b) -> Vec n a -> Vec n b # (.>) :: Vec n a -> Vec n b -> Vec n b # (<.) :: Vec n a -> Vec n b -> Vec n a # liftF2 :: (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c #
SNatI n => Bind (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods (>>-) :: Vec n a -> (a -> Vec n b) -> Vec n b # join :: Vec n (Vec n a) -> Vec n a #
SNatI n => FunctorWithIndex (Fin n) (Vec n) Source #	Since: 0.4
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods imap :: (Fin n -> a -> b) -> Vec n a -> Vec n b #
SNatI n => FoldableWithIndex (Fin n) (Vec n) Source #	Since: 0.4
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods ifoldMap :: Monoid m => (Fin n -> a -> m) -> Vec n a -> m # ifoldMap' :: Monoid m => (Fin n -> a -> m) -> Vec n a -> m # ifoldr :: (Fin n -> a -> b -> b) -> b -> Vec n a -> b # ifoldl :: (Fin n -> b -> a -> b) -> b -> Vec n a -> b # ifoldr' :: (Fin n -> a -> b -> b) -> b -> Vec n a -> b # ifoldl' :: (Fin n -> b -> a -> b) -> b -> Vec n a -> b #
SNatI n => TraversableWithIndex (Fin n) (Vec n) Source #	Since: 0.4
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods itraverse :: Applicative f => (Fin n -> a -> f b) -> Vec n a -> f (Vec n b) #
(Eq a, SNatI n) => Eq (Vec n a) Source #	`>>>` `'a' ::: 'b' ::: VNil == 'a' ::: 'c' ::: VNil`False
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods (==) :: Vec n a -> Vec n a -> Bool # (/=) :: Vec n a -> Vec n a -> Bool #
(Ord a, SNatI n) => Ord (Vec n a) Source #	`>>>` `compare ('a' ::: 'b' ::: VNil) ('a' ::: 'c' ::: VNil)`LT
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods compare :: Vec n a -> Vec n a -> Ordering # (<) :: Vec n a -> Vec n a -> Bool # (<=) :: Vec n a -> Vec n a -> Bool # (>) :: Vec n a -> Vec n a -> Bool # (>=) :: Vec n a -> Vec n a -> Bool # max :: Vec n a -> Vec n a -> Vec n a # min :: Vec n a -> Vec n a -> Vec n a #
(Show a, SNatI n) => Show (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods showsPrec :: Int -> Vec n a -> ShowS # show :: Vec n a -> String # showList :: [Vec n a] -> ShowS #
(Semigroup a, SNatI n) => Semigroup (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods (<>) :: Vec n a -> Vec n a -> Vec n a # sconcat :: NonEmpty (Vec n a) -> Vec n a # stimes :: Integral b => b -> Vec n a -> Vec n a #
(Monoid a, SNatI n) => Monoid (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods mempty :: Vec n a # mappend :: Vec n a -> Vec n a -> Vec n a # mconcat :: [Vec n a] -> Vec n a #
(SNatI n, Function a) => Function (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods function :: (Vec n a -> b) -> Vec n a :-> b #
(SNatI n, Arbitrary a) => Arbitrary (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods arbitrary :: Gen (Vec n a) # shrink :: Vec n a -> [Vec n a] #
(SNatI n, CoArbitrary a) => CoArbitrary (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods coarbitrary :: Vec n a -> Gen b -> Gen b #
(NFData a, SNatI n) => NFData (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods rnf :: Vec n a -> () #
(Hashable a, SNatI n) => Hashable (Vec n a) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict Methods hashWithSalt :: Int -> Vec n a -> Int # hash :: Vec n a -> Int #
data Vec 'Z a Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict data Vec 'Z a = VNil
type Rep (Vec n) Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict type Rep (Vec n) = Fin n
data Vec ('S n) a Source #
Instance details Defined in Data.Vec.DataFamily.SpineStrict data Vec ('S n) a = a ::: !(Vec n a)

Construction

empty :: Vec 'Z a Source #

Empty Vec.

singleton :: a -> Vec ('S 'Z) a Source #

Vec with exactly one element.

>>> singleton True
True ::: VNil

Conversions

toPull :: forall n a. SNatI n => Vec n a -> Vec n a Source #

Convert to pull Vec.

fromPull :: forall n a. SNatI n => Vec n a -> Vec n a Source #

Convert from pull Vec.

toList :: forall n a. SNatI n => Vec n a -> [a] Source #

Convert Vec to list.

>>> toList $ 'f' ::: 'o' ::: 'o' ::: VNil
"foo"

toNonEmpty :: forall n a. SNatI n => Vec ('S n) a -> NonEmpty a Source #

>>> toNonEmpty $ 1 ::: 2 ::: 3 ::: VNil
1 :| [2,3]

Since: 0.4

fromList :: SNatI n => [a] -> Maybe (Vec n a) Source #

Convert list [a] to Vec n a. Returns Nothing if lengths don't match exactly.

>>> fromList "foo" :: Maybe (Vec N.Nat3 Char)
Just ('f' ::: 'o' ::: 'o' ::: VNil)

>>> fromList "quux" :: Maybe (Vec N.Nat3 Char)
Nothing

>>> fromList "xy" :: Maybe (Vec N.Nat3 Char)
Nothing

fromListPrefix :: SNatI n => [a] -> Maybe (Vec n a) Source #

Convert list [a] to Vec n a. Returns Nothing if input list is too short.

>>> fromListPrefix "foo" :: Maybe (Vec N.Nat3 Char)
Just ('f' ::: 'o' ::: 'o' ::: VNil)

>>> fromListPrefix "quux" :: Maybe (Vec N.Nat3 Char)
Just ('q' ::: 'u' ::: 'u' ::: VNil)

>>> fromListPrefix "xy" :: Maybe (Vec N.Nat3 Char)
Nothing

reifyList :: [a] -> (forall n. SNatI n => Vec n a -> r) -> r Source #

Reify any list [a] to Vec n a.

>>> reifyList "foo" length
3

Indexing

(!) :: SNatI n => Vec n a -> Fin n -> a Source #

Indexing.

>>> ('a' ::: 'b' ::: 'c' ::: VNil) ! FS FZ
'b'

tabulate :: SNatI n => (Fin n -> a) -> Vec n a Source #

Tabulating, inverse of !.

>>> tabulate id :: Vec N.Nat3 (Fin N.Nat3)
0 ::: 1 ::: 2 ::: VNil

cons :: a -> Vec n a -> Vec ('S n) a Source #

Cons an element in front of a Vec.

snoc :: forall n a. SNatI n => Vec n a -> a -> Vec ('S n) a Source #

Add a single element at the end of a Vec.

head :: Vec ('S n) a -> a Source #

The first element of a Vec.

last :: forall n a. SNatI n => Vec ('S n) a -> a Source #

The last element of a Vec.

Since: 0.4

tail :: Vec ('S n) a -> Vec n a Source #

The elements after the head of a Vec.

init :: forall n a. SNatI n => Vec ('S n) a -> Vec n a Source #

The elements before the last of a Vec.

Since: 0.4

Reverse

reverse :: forall n a. SNatI n => Vec n a -> Vec n a Source #

Reverse Vec.

>>> reverse ('a' ::: 'b' ::: 'c' ::: VNil)
'c' ::: 'b' ::: 'a' ::: VNil

Since: 0.2.1

Concatenation and splitting

(++) :: forall n m a. SNatI n => Vec n a -> Vec m a -> Vec (Plus n m) a infixr 5 Source #

Append two Vec.

>>> ('a' ::: 'b' ::: VNil) ++ ('c' ::: 'd' ::: VNil)
'a' ::: 'b' ::: 'c' ::: 'd' ::: VNil

split :: SNatI n => Vec (Plus n m) a -> (Vec n a, Vec m a) Source #

Split vector into two parts. Inverse of ++.

>>> split ('a' ::: 'b' ::: 'c' ::: VNil) :: (Vec N.Nat1 Char, Vec N.Nat2 Char)
('a' ::: VNil,'b' ::: 'c' ::: VNil)

>>> uncurry (++) (split ('a' ::: 'b' ::: 'c' ::: VNil) :: (Vec N.Nat1 Char, Vec N.Nat2 Char))
'a' ::: 'b' ::: 'c' ::: VNil

concatMap :: forall a b n m. (SNatI m, SNatI n) => (a -> Vec m b) -> Vec n a -> Vec (Mult n m) b Source #

Map over all the elements of a Vec and concatenate the resulting Vecs.

>>> concatMap (\x -> x ::: x ::: VNil) ('a' ::: 'b' ::: VNil)
'a' ::: 'a' ::: 'b' ::: 'b' ::: VNil

concat :: (SNatI m, SNatI n) => Vec n (Vec m a) -> Vec (Mult n m) a Source #

concatMap id

chunks :: (SNatI n, SNatI m) => Vec (Mult n m) a -> Vec n (Vec m a) Source #

Inverse of concat.

>>> chunks <$> fromListPrefix [1..] :: Maybe (Vec N.Nat2 (Vec N.Nat3 Int))
Just ((1 ::: 2 ::: 3 ::: VNil) ::: (4 ::: 5 ::: 6 ::: VNil) ::: VNil)

>>> let idVec x = x :: Vec N.Nat2 (Vec N.Nat3 Int)
>>> concat . idVec . chunks <$> fromListPrefix [1..]
Just (1 ::: 2 ::: 3 ::: 4 ::: 5 ::: 6 ::: VNil)

Folds

foldMap :: (Monoid m, SNatI n) => (a -> m) -> Vec n a -> m Source #

See Foldable.

foldMap1 :: forall s a n. (Semigroup s, SNatI n) => (a -> s) -> Vec ('S n) a -> s Source #

See Foldable1.

ifoldMap :: forall a n m. (Monoid m, SNatI n) => (Fin n -> a -> m) -> Vec n a -> m Source #

See FoldableWithIndex.

ifoldMap1 :: forall a n s. (Semigroup s, SNatI n) => (Fin ('S n) -> a -> s) -> Vec ('S n) a -> s Source #

There is no type-class for this :(

foldr :: forall a b n. SNatI n => (a -> b -> b) -> b -> Vec n a -> b Source #

Right fold.

ifoldr :: forall a b n. SNatI n => (Fin n -> a -> b -> b) -> b -> Vec n a -> b Source #

Right fold with an index.

Special folds

length :: forall n a. SNatI n => Vec n a -> Int Source #

Yield the length of a Vec. O(n)

null :: forall n a. SNatI n => Vec n a -> Bool Source #

Test whether a Vec is empty. O(1)

sum :: (Num a, SNatI n) => Vec n a -> a Source #

Non-strict sum.

product :: (Num a, SNatI n) => Vec n a -> a Source #

Non-strict product.

Mapping

map :: forall a b n. SNatI n => (a -> b) -> Vec n a -> Vec n b Source #

>>> map not $ True ::: False ::: VNil
False ::: True ::: VNil

imap :: SNatI n => (Fin n -> a -> b) -> Vec n a -> Vec n b Source #

>>> imap (,) $ 'a' ::: 'b' ::: 'c' ::: VNil
(0,'a') ::: (1,'b') ::: (2,'c') ::: VNil

traverse :: forall n f a b. (Applicative f, SNatI n) => (a -> f b) -> Vec n a -> f (Vec n b) Source #

Apply an action to every element of a Vec, yielding a Vec of results.

traverse1 :: forall n f a b. (Apply f, SNatI n) => (a -> f b) -> Vec ('S n) a -> f (Vec ('S n) b) Source #

Apply an action to non-empty Vec, yielding a Vec of results.

itraverse :: forall n f a b. (Applicative f, SNatI n) => (Fin n -> a -> f b) -> Vec n a -> f (Vec n b) Source #

Apply an action to every element of a Vec and its index, yielding a Vec of results.

itraverse_ :: forall n f a b. (Applicative f, SNatI n) => (Fin n -> a -> f b) -> Vec n a -> f () Source #

Apply an action to every element of a Vec and its index, ignoring the results.

Zipping

zipWith :: forall a b c n. SNatI n => (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c Source #

Zip two Vecs with a function.

izipWith :: SNatI n => (Fin n -> a -> b -> c) -> Vec n a -> Vec n b -> Vec n c Source #

Zip two Vecs. with a function that also takes the elements' indices.

repeat :: SNatI n => x -> Vec n x Source #

Repeat value

>>> repeat 'x' :: Vec N.Nat3 Char
'x' ::: 'x' ::: 'x' ::: VNil

Since: 0.2.1

Monadic

bind :: SNatI n => Vec n a -> (a -> Vec n b) -> Vec n b Source #

Monadic bind.

join :: SNatI n => Vec n (Vec n a) -> Vec n a Source #

Monadic join.

>>> join $ ('a' ::: 'b' ::: VNil) ::: ('c' ::: 'd' ::: VNil) ::: VNil
'a' ::: 'd' ::: VNil

Universe

universe :: SNatI n => Vec n (Fin n) Source #

Get all Fin n in a Vec n.

>>> universe :: Vec N.Nat3 (Fin N.Nat3)
0 ::: 1 ::: 2 ::: VNil

Extras

ensureSpine :: SNatI n => Vec n a -> Vec n a Source #

Ensure spine.

If we have an undefined Vec,

>>> let v = error "err" :: Vec N.Nat3 Char

And insert data into it later:

>>> let setHead :: a -> Vec ('S n) a -> Vec ('S n) a; setHead x (_ ::: xs) = x ::: xs

Then without a spine, it will fail:

>>> head $ setHead 'x' v
*** Exception: err
...

But with the spine, it won't:

>>> head $ setHead 'x' $ ensureSpine v
'x'