vec-0.1.1.1: Vec: length-indexed (sized) list

Safe HaskellNone
LanguageHaskell2010

Data.Vec.DataFamily.SpineStrict

Contents

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

Documentation

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

Vector, i.e. length-indexed list.

Instances
InlineInduction 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 #

fail :: String -> Vec n a #

InlineInduction 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 #

InlineInduction 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 #

InlineInduction 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 #

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) 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) #

InlineInduction 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) #

InlineInduction n => Representable (Vec n) Source # 
Instance details

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) 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 #

(InlineInduction 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) #

(InlineInduction 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 #

InlineInduction 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 #

InlineInduction n => FunctorWithIndex (Fin n) (Vec n) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) 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, InlineInduction 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, InlineInduction 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, InlineInduction 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, InlineInduction 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 #

(NFData a, InlineInduction n) => NFData (Vec n a) Source # 
Instance details

Defined in Data.Vec.DataFamily.SpineStrict

Methods

rnf :: Vec n a -> () #

(Hashable a, InlineInduction 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 #

Ixed (Vec n a) Source #

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).

Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

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 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)
type Index (Vec n a) Source # 
Instance details

Defined in Data.Vec.DataFamily.SpineStrict

type Index (Vec n a) = Fin n
type IxValue (Vec n a) Source # 
Instance details

Defined in Data.Vec.DataFamily.SpineStrict

type IxValue (Vec n a) = 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. InlineInduction n => Vec n a -> Vec n a Source #

Convert to pull Vec.

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

Convert from pull Vec.

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

An Iso from toPull and fromPull.

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

Convert Vec to list.

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

fromList :: InlineInduction 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

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

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

Reify any list [a] to Vec n a.

>>> reifyList "foo" length
3

Indexing

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

Indexing.

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

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

Index lens.

>>> ('a' ::: 'b' ::: 'c' ::: VNil) ^. ix (FS FZ)
'b'
>>> ('a' ::: 'b' ::: 'c' ::: VNil) & ix (FS FZ) .~ 'x'
'a' ::: 'x' ::: 'c' ::: VNil

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

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 Source #

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) Source #

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

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

Cons an element in front of a Vec.

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

The first element of a Vec.

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

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 Source #

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) 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. (InlineInduction m, InlineInduction 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

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

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

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

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

There is no type-class for this :(

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

Right fold.

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

Right fold with an index.

Special folds

length :: forall n a. InlineInduction 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, InlineInduction n) => Vec n a -> a Source #

Non-strict sum.

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

Non-strict product.

Mapping

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

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

imap :: InlineInduction 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, InlineInduction 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, InlineInduction 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, InlineInduction 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, InlineInduction 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. InlineInduction n => (a -> b -> c) -> Vec n a -> Vec n b -> Vec n c Source #

Zip two Vecs with a function.

izipWith :: InlineInduction 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.

Monadic

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

Monadic bind.

join :: InlineInduction 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 :: InlineInduction 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 :: InlineInduction n => Vec n a -> Vec n a Source #

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'