Data.Vec.DataFamily.SpineStrict

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

Documentation

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

Vector, i.e. length-indexed list.

Instances

InlineInduction n => Monad (Vec n)

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

fail :: String -> Vec n a

InlineInduction n => Functor (Vec n)

Defined in Data.Vec.DataFamily.SpineStrict

Methods

fmap :: (a -> b) -> Vec n a -> Vec n b

(<$) :: a -> Vec n b -> Vec n a

InlineInduction n => Applicative (Vec n)

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

InlineInduction n => Foldable (Vec n)

Defined in Data.Vec.DataFamily.SpineStrict

Methods

fold :: Monoid m => Vec n m -> 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

InlineInduction n => Traversable (Vec n)

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)

InlineInduction n => Distributive (Vec n)

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)

InlineInduction n => Representable (Vec n)

Defined in Data.Vec.DataFamily.SpineStrict

Associated Types

type Rep (Vec n) :: Type

Methods

tabulate :: (Rep (Vec n) -> a) -> Vec n a

index :: Vec n a -> Rep (Vec n) -> a

InlineInduction n => Apply (Vec n)

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

(InlineInduction m, n ~ S m) => Traversable1 (Vec n)

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)

(InlineInduction m, n ~ S m) => Foldable1 (Vec n)

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

InlineInduction n => Bind (Vec n)

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

InlineInduction n => FunctorWithIndex (Fin n) (Vec n)

Defined in Data.Vec.DataFamily.SpineStrict

Methods

imap :: (Fin n -> a -> b) -> Vec n a -> Vec n b

imapped :: IndexedSetter (Fin n) (Vec n a) (Vec n b) a b

InlineInduction n => FoldableWithIndex (Fin n) (Vec n)

Defined in Data.Vec.DataFamily.SpineStrict

Methods

ifoldMap :: Monoid m => (Fin n -> a -> m) -> Vec n a -> m

ifolded :: IndexedFold (Fin n) (Vec n a) a

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

InlineInduction n => TraversableWithIndex (Fin n) (Vec n)

Defined in Data.Vec.DataFamily.SpineStrict

Methods

itraverse :: Applicative f => (Fin n -> a -> f b) -> Vec n a -> f (Vec n b)

itraversed :: IndexedTraversal (Fin n) (Vec n a) (Vec n b) a b

(Eq a, InlineInduction n) => Eq (Vec n a)

>>> 'a' ::: 'b' ::: VNil == 'a' ::: 'c' ::: VNil
False

Defined in Data.Vec.DataFamily.SpineStrict

Methods

(==) :: Vec n a -> Vec n a -> Bool

(/=) :: Vec n a -> Vec n a -> Bool

(Ord a, InlineInduction n) => Ord (Vec n a)

>>> compare ('a' ::: 'b' ::: VNil) ('a' ::: 'c' ::: VNil)
LT

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, InlineInduction n) => Show (Vec n a)

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, InlineInduction n) => Semigroup (Vec n a)

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, InlineInduction n) => Monoid (Vec n a)

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

(NFData a, InlineInduction n) => NFData (Vec n a)

Defined in Data.Vec.DataFamily.SpineStrict

Methods

rnf :: Vec n a -> ()

(Hashable a, InlineInduction n) => Hashable (Vec n a)

Defined in Data.Vec.DataFamily.SpineStrict

Methods

hashWithSalt :: Int -> Vec n a -> Int

hash :: Vec n a -> Int

Ixed (Vec n a)

Vec doesn't have At instance, as we cannot remove value from Vec. See ix in Data.Vec.DataFamily.SpineStrict module for an Lens (not Traversal).

Defined in Data.Vec.DataFamily.SpineStrict

Methods

ix :: Index (Vec n a) -> Traversal' (Vec n a) (IxValue (Vec n a))

InlineInduction n => Each (Vec n a) (Vec n b) a b

Defined in Data.Vec.DataFamily.SpineStrict

Methods

each :: Traversal (Vec n a) (Vec n b) a b

Field1 (Vec (S n) a) (Vec (S n) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_1 :: Lens (Vec (S n) a) (Vec (S n) a) a a

Field2 (Vec (S (S n)) a) (Vec (S (S n)) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_2 :: Lens (Vec (S (S n)) a) (Vec (S (S n)) a) a a

Field3 (Vec (S (S (S n))) a) (Vec (S (S (S n))) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_3 :: Lens (Vec (S (S (S n))) a) (Vec (S (S (S n))) a) a a

Field4 (Vec (S (S (S (S n)))) a) (Vec (S (S (S (S n)))) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_4 :: Lens (Vec (S (S (S (S n)))) a) (Vec (S (S (S (S n)))) a) a a

Field5 (Vec (S (S (S (S (S n))))) a) (Vec (S (S (S (S (S n))))) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_5 :: Lens (Vec (S (S (S (S (S n))))) a) (Vec (S (S (S (S (S n))))) a) a a

Field6 (Vec (S (S (S (S (S (S n)))))) a) (Vec (S (S (S (S (S (S n)))))) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_6 :: Lens (Vec (S (S (S (S (S (S n)))))) a) (Vec (S (S (S (S (S (S n)))))) a) a a

Field7 (Vec (S (S (S (S (S (S (S n))))))) a) (Vec (S (S (S (S (S (S (S n))))))) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_7 :: Lens (Vec (S (S (S (S (S (S (S n))))))) a) (Vec (S (S (S (S (S (S (S n))))))) a) a a

Field8 (Vec (S (S (S (S (S (S (S (S n)))))))) a) (Vec (S (S (S (S (S (S (S (S n)))))))) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_8 :: Lens (Vec (S (S (S (S (S (S (S (S n)))))))) a) (Vec (S (S (S (S (S (S (S (S n)))))))) a) a a

Field9 (Vec (S (S (S (S (S (S (S (S (S n))))))))) a) (Vec (S (S (S (S (S (S (S (S (S n))))))))) a) a a

Defined in Data.Vec.DataFamily.SpineStrict

Methods

_9 :: Lens (Vec (S (S (S (S (S (S (S (S (S n))))))))) a) (Vec (S (S (S (S (S (S (S (S (S n))))))))) a) a a

data Vec Z a

Defined in Data.Vec.DataFamily.SpineStrict

data Vec Z a = VNil

type Rep (Vec n)

Defined in Data.Vec.DataFamily.SpineStrict

type Rep (Vec n) = Fin n

data Vec (S n) a

Defined in Data.Vec.DataFamily.SpineStrict

data Vec (S n) a = a ::: !(Vec n a)

type Index (Vec n a)

Defined in Data.Vec.DataFamily.SpineStrict

type Index (Vec n a) = Fin n

type IxValue (Vec n a)

Defined in Data.Vec.DataFamily.SpineStrict

type IxValue (Vec n a) = a

Construction

empty :: Vec Z a

Empty Vec.

singleton :: a -> Vec (S Z) a

Vec with exactly one element.

>>> singleton True
True ::: VNil

Conversions

toPull :: forall n a. InlineInduction n => Vec n a -> Vec n a

Convert to pull Vec.

fromPull :: forall n a. InlineInduction n => Vec n a -> Vec n a

Convert from pull Vec.

_Pull :: InlineInduction n => Iso (Vec n a) (Vec n b) (Vec n a) (Vec n b)

An Iso from toPull and fromPull.

toList :: forall n a. InlineInduction n => Vec n a -> [a]

Convert Vec to list.

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

fromList :: InlineInduction n => [a] -> Maybe (Vec n a)

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

_Vec :: InlineInduction n => Prism' [a] (Vec n a)

Prism from list.

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

>>> "foo" ^? _Vec :: Maybe (Vec N.Nat2 Char)
Nothing

>>> _Vec # (True ::: False ::: VNil)
[True,False]

fromListPrefix :: InlineInduction n => [a] -> Maybe (Vec n a)

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. InlineInduction n => Vec n a -> r) -> r

Reify any list [a] to Vec n a.

>>> reifyList "foo" length
3

Indexing

(!) :: InlineInduction n => Vec n a -> Fin n -> a

Indexing.

>>> ('a' ::: 'b' ::: 'c' ::: VNil) ! F.S F.Z
'b'

ix :: Fin n -> Lens' (Vec n a) a

Index lens.

>>> ('a' ::: 'b' ::: 'c' ::: VNil) ^. ix (F.S F.Z)
'b'

>>> ('a' ::: 'b' ::: 'c' ::: VNil) & ix (F.S F.Z) .~ 'x'
'a' ::: 'x' ::: 'c' ::: VNil

_Cons :: Iso (Vec (S n) a) (Vec (S n) b) (a, Vec n a) (b, Vec n b)

Match on non-empty Vec.

Note: lens _Cons is a Prism. In fact, Vec n a cannot have an instance of Cons as types don't match.

_head :: Lens' (Vec (S n) a) a

Head lens. Note: lens _head is a Traversal'.

>>> ('a' ::: 'b' ::: 'c' ::: VNil) ^. _head
'a'

>>> ('a' ::: 'b' ::: 'c' ::: VNil) & _head .~ 'x'
'x' ::: 'b' ::: 'c' ::: VNil

_tail :: Lens' (Vec (S n) a) (Vec n a)

Head lens. Note: lens _head is a Traversal'.

cons :: a -> Vec n a -> Vec (S n) a

Cons an element in front of a Vec.

head :: Vec (S n) a -> a

The first element of a Vec.

tail :: Vec (S n) a -> Vec n a

The elements after the head of a Vec.

Concatenation and splitting

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

Append two Vec.

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

split :: InlineInduction n => Vec (Plus n m) a -> (Vec n a, Vec m a)

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. (InlineInduction m, InlineInduction n) => (a -> Vec m b) -> Vec n a -> Vec (Mult n m) b

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 :: (InlineInduction m, InlineInduction n) => Vec n (Vec m a) -> Vec (Mult n m) a

concatMap id

chunks :: (InlineInduction n, InlineInduction m) => Vec (Mult n m) a -> Vec n (Vec m a)

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, InlineInduction n) => (a -> m) -> Vec n a -> m

See Foldable.

foldMap1 :: forall s a n. (Semigroup s, InlineInduction n) => (a -> s) -> Vec (S n) a -> s

See Foldable1.

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

See FoldableWithIndex.

ifoldMap1 :: forall a n s. (Semigroup s, InlineInduction n) => (Fin (S n) -> a -> s) -> Vec (S n) a -> s

There is no type-class for this :(

foldr :: forall a b n. InlineInduction n => (a -> b -> b) -> b -> Vec n a -> b

Right fold.

ifoldr :: forall a b n. InlineInduction n => (Fin n -> a -> b -> b) -> b -> Vec n a -> b

Right fold with an index.

Special folds

length :: forall n a. InlineInduction n => Vec n a -> Int

Yield the length of a Vec. O(n)

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

Test whether a Vec is empty. O(1)

sum :: (Num a, InlineInduction n) => Vec n a -> a

Non-strict sum.

product :: (Num a, InlineInduction n) => Vec n a -> a

Non-strict product.

Mapping

map :: forall a b n. InlineInduction n => (a -> b) -> Vec n a -> Vec n b

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

imap :: InlineInduction n => (Fin n -> a -> b) -> Vec n a -> Vec n b

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

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

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

traverse1 :: forall n f a b. (Apply f, InlineInduction n) => (a -> f b) -> Vec (S n) a -> f (Vec (S n) b)

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

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

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, InlineInduction n) => (Fin n -> a -> f b) -> Vec n a -> f ()

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

Zipping

zipWith :: forall a b c n. InlineInduction n => (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c

Zip two Vecs with a function.

izipWith :: InlineInduction n => (Fin n -> a -> b -> c) -> Vec n a -> Vec n b -> Vec n c

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

Monadic

bind :: InlineInduction n => Vec n a -> (a -> Vec n b) -> Vec n b

Monadic bind.

join :: InlineInduction n => Vec n (Vec n a) -> Vec n a

Monadic join.

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

Universe

universe :: InlineInduction n => Vec n (Fin n)

Get all Fin n in a Vec n.

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

Extras

ensureSpine :: InlineInduction n => Vec n a -> Vec n a

Ensure spine.

>>> view (ix F.fin1) $ set (ix F.fin1) 'x' (error "err" :: Vec N.Nat2 Char)
*** Exception: err
...

>>> view (ix F.fin1) $ set (ix F.fin1) 'x' $ ensureSpine (error "err" :: Vec N.Nat2 Char)
'x'