SizedGrid.Coord

Documentation

type family Length cs where ...

Length of a type level list

Equations

Length '[] = 0

Length (c ': cs) = (+) 1 (Length cs)

newtype Coord cs

A multideminsion coordinate

Constructors

Coord

Fields

• unCoord :: NP I cs

Instances

All * Eq cs => Eq (Coord cs)

Methods

(==) :: Coord cs -> Coord cs -> Bool

(/=) :: Coord cs -> Coord cs -> Bool

(All * Eq cs, All * Ord cs) => Ord (Coord cs)

Methods

compare :: Coord cs -> Coord cs -> Ordering

(<) :: Coord cs -> Coord cs -> Bool

(<=) :: Coord cs -> Coord cs -> Bool

(>) :: Coord cs -> Coord cs -> Bool

(>=) :: Coord cs -> Coord cs -> Bool

max :: Coord cs -> Coord cs -> Coord cs

min :: Coord cs -> Coord cs -> Coord cs

All * Show cs => Show (Coord cs)

Methods

showsPrec :: Int -> Coord cs -> ShowS

show :: Coord cs -> String

showList :: [Coord cs] -> ShowS

Generic (Coord cs)

Associated Types

type Rep (Coord cs) :: * -> *

Methods

from :: Coord cs -> Rep (Coord cs) x

to :: Rep (Coord cs) x -> Coord cs

All * Semigroup cs => Semigroup (Coord cs)

Methods

(<>) :: Coord cs -> Coord cs -> Coord cs

sconcat :: NonEmpty (Coord cs) -> Coord cs

stimes :: Integral b => b -> Coord cs -> Coord cs

(All * Semigroup cs, All * Monoid cs) => Monoid (Coord cs)

Methods

mempty :: Coord cs

mappend :: Coord cs -> Coord cs -> Coord cs

mconcat :: [Coord cs] -> Coord cs

All * ToJSON cs => ToJSON (Coord cs)

Methods

toJSON :: Coord cs -> Value

toEncoding :: Coord cs -> Encoding

toJSONList :: [Coord cs] -> Value

toEncodingList :: [Coord cs] -> Encoding

All * FromJSON cs => FromJSON (Coord cs)

Methods

parseJSON :: Value -> Parser (Coord cs)

parseJSONList :: Value -> Parser [Coord cs]

All * Random cs => Random (Coord cs)

Methods

randomR :: RandomGen g => (Coord cs, Coord cs) -> g -> (Coord cs, g)

random :: RandomGen g => g -> (Coord cs, g)

randomRs :: RandomGen g => (Coord cs, Coord cs) -> g -> [Coord cs]

randoms :: RandomGen g => g -> [Coord cs]

randomRIO :: (Coord cs, Coord cs) -> IO (Coord cs)

randomIO :: IO (Coord cs)

(All * AffineSpace cs, AdditiveGroup (CoordDiff * cs), IsProductType (CoordDiff * cs) (MapDiff cs)) => AffineSpace (Coord cs)

Associated Types

type Diff (Coord cs) :: *

Methods

(.-.) :: Coord cs -> Coord cs -> Diff (Coord cs)

(.+^) :: Coord cs -> Diff (Coord cs) -> Coord cs

All * AdditiveGroup cs => AdditiveGroup (Coord cs)

Methods

zeroV :: Coord cs

(^+^) :: Coord cs -> Coord cs -> Coord cs

negateV :: Coord cs -> Coord cs

(^-^) :: Coord cs -> Coord cs -> Coord cs

(KnownNat (MaxCoordSize * cs), All * IsCoord cs, All * Monoid cs, All * Semigroup cs, SListI * cs) => ComonadStore (Coord cs) (FocusedGrid cs)

Methods

pos :: FocusedGrid cs a -> Coord cs

peek :: Coord cs -> FocusedGrid cs a -> a

peeks :: (Coord cs -> Coord cs) -> FocusedGrid cs a -> a

seek :: Coord cs -> FocusedGrid cs a -> FocusedGrid cs a

seeks :: (Coord cs -> Coord cs) -> FocusedGrid cs a -> FocusedGrid cs a

experiment :: Functor f => (Coord cs -> f (Coord cs)) -> FocusedGrid cs a -> f a

All * IsCoord cs => FunctorWithIndex (Coord cs) (Grid cs)

Methods

imap :: (Coord cs -> a -> b) -> Grid cs a -> Grid cs b

imapped :: (Indexable (Coord cs) p, Settable f) => p a (f b) -> Grid cs a -> f (Grid cs b)

All * IsCoord cs => FoldableWithIndex (Coord cs) (Grid cs)

Methods

ifoldMap :: Monoid m => (Coord cs -> a -> m) -> Grid cs a -> m

ifolded :: (Indexable (Coord cs) p, Contravariant f, Applicative f) => p a (f a) -> Grid cs a -> f (Grid cs a)

ifoldr :: (Coord cs -> a -> b -> b) -> b -> Grid cs a -> b

ifoldl :: (Coord cs -> b -> a -> b) -> b -> Grid cs a -> b

ifoldr' :: (Coord cs -> a -> b -> b) -> b -> Grid cs a -> b

ifoldl' :: (Coord cs -> b -> a -> b) -> b -> Grid cs a -> b

All * IsCoord cs => TraversableWithIndex (Coord cs) (Grid cs)

Methods

itraverse :: Applicative f => (Coord cs -> a -> f b) -> Grid cs a -> f (Grid cs b)

itraversed :: (Indexable (Coord cs) p, Applicative f) => p a (f b) -> Grid cs a -> f (Grid cs b)

Field1 (Coord ((:) * a cs)) (Coord ((:) * a' cs)) a a'

Methods

_1 :: Lens (Coord ((* ': a) cs)) (Coord ((* ': a') cs)) a a'

Field2 (Coord ((:) * a ((:) * b cs))) (Coord ((:) * a ((:) * b' cs))) b b'

Methods

_2 :: Lens (Coord ((* ': a) ((* ': b) cs))) (Coord ((* ': a) ((* ': b') cs))) b b'

Field3 (Coord ((:) * a ((:) * b ((:) * c cs)))) (Coord ((:) * a ((:) * b ((:) * c' cs)))) c c'

Methods

_3 :: Lens (Coord ((* ': a) ((* ': b) ((* ': c) cs)))) (Coord ((* ': a) ((* ': b) ((* ': c') cs)))) c c'

Field4 (Coord ((:) * a ((:) * b ((:) * c ((:) * d cs))))) (Coord ((:) * a ((:) * b ((:) * c ((:) * d' cs))))) d d'

Methods

_4 :: Lens (Coord ((* ': a) ((* ': b) ((* ': c) ((* ': d) cs))))) (Coord ((* ': a) ((* ': b) ((* ': c) ((* ': d') cs))))) d d'

Field5 (Coord ((:) * a ((:) * b ((:) * c ((:) * d ((:) * e cs)))))) (Coord ((:) * a ((:) * b ((:) * c ((:) * d ((:) * e' cs)))))) e e'

Methods

_5 :: Lens (Coord ((* ': a) ((* ': b) ((* ': c) ((* ': d) ((* ': e) cs)))))) (Coord ((* ': a) ((* ': b) ((* ': c) ((* ': d) ((* ': e') cs)))))) e e'

type Rep (Coord cs)

type Rep (Coord cs) = D1 * (MetaData "Coord" "SizedGrid.Coord" "sized-grid-0.1.1.0-L0M4rnLtRA7L2yFvGQ8gsz" True) (C1 * (MetaCons "Coord" PrefixI True) (S1 * (MetaSel (Just Symbol "unCoord") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (NP * I cs))))

type Diff (Coord cs)

type Diff (Coord cs) = CoordDiff * cs

_WrappedCoord :: Lens' (Coord cs) (NP I cs)

coordHead :: Lens (Coord (a ': as)) (Coord (a' ': as)) a a'

Get the first element of a coord. Thanks to type level information, we can write this as a total Lens

coordTail :: Lens (Coord (a ': as)) (Coord (a ': as')) (Coord as) (Coord as')

A Lens into the the tail of Coord

singleCoord :: a -> Coord '[a]

Turn a single element into a one dimensional Coord

appendCoord :: a -> Coord as -> Coord (a ': as)

Add a new element to a Coord. This increases the dimensionality

type family CoordDiff (cs :: [k]) :: *

The type of difference between two coords. A n-dimensional coord should have a Diff of an n-tuple of Integers. We use Identity and our 1-tuple. Unfortuantly, each instance is manual at the moment.

Instances

type CoordDiff k ([] k)

type CoordDiff k ([] k) = ()

type CoordDiff * ((:) * a ((:) * b ((:) * c ((:) * d ((:) * e ((:) * f ([] *)))))))

type CoordDiff * ((:) * a ((:) * b ((:) * c ((:) * d ((:) * e ((:) * f ([] *))))))) = (Diff a, Diff b, Diff c, Diff d, Diff e, Diff f)

type CoordDiff * ((:) * a ((:) * b ((:) * c ((:) * d ((:) * e ([] *))))))

type CoordDiff * ((:) * a ((:) * b ((:) * c ((:) * d ((:) * e ([] *)))))) = (Diff a, Diff b, Diff c, Diff d, Diff e)

type CoordDiff * ((:) * a ((:) * b ((:) * c ((:) * d ([] *)))))

type CoordDiff * ((:) * a ((:) * b ((:) * c ((:) * d ([] *))))) = (Diff a, Diff b, Diff c, Diff d)

type CoordDiff * ((:) * a ((:) * b ((:) * c ([] *))))

type CoordDiff * ((:) * a ((:) * b ((:) * c ([] *)))) = (Diff a, Diff b, Diff c)

type CoordDiff * ((:) * a ((:) * b ([] *)))

type CoordDiff * ((:) * a ((:) * b ([] *))) = (Diff a, Diff b)

type CoordDiff * ((:) * a ([] *))

type CoordDiff * ((:) * a ([] *)) = Identity (Diff a)

type family MapDiff xs where ...

Apply Diff to each element of a type level list. This is required as type families can't be partially applied.

Equations

MapDiff '[] = '[]

MapDiff (x ': xs) = Diff x ': MapDiff xs

allCoord :: forall cs. All IsCoord cs => [Coord cs]

Generate all possible coords in order

type family MaxCoordSize (cs :: [k]) :: Nat where ...

The number of elements a coord can have. This is equal to the product of the CoordSized of each element

Equations

MaxCoordSize '[] = 1

MaxCoordSize (c ': cs) = CoordSized c * MaxCoordSize cs

coordPosition :: All IsCoord cs => Coord cs -> Int

Convert a Coord to its position in a vector

type family AllDiffSame a xs :: Constraint where ...

All Diffs of the members of the list must be equal

Equations

AllDiffSame _ '[] = ()

AllDiffSame a (x ': xs) = (Diff x ~ a, AllDiffSame a xs)

moorePoints :: forall a cs. (Enum a, Num a, AllDiffSame a cs, All AffineSpace cs) => a -> Coord cs -> [Coord cs]

Calculate the Moore neighbourhood around a point. Includes the center

vonNeumanPoints :: forall a cs. (Enum a, Num a, Ord a, All Integral (MapDiff cs), AllDiffSame a cs, All AffineSpace cs, Ord (CoordDiff cs), IsProductType (CoordDiff cs) (MapDiff cs), AdditiveGroup (CoordDiff cs)) => a -> Coord cs -> [Coord cs]

Calculate the von Neuman neighbourhood around a point. Includes the center