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)

Defined in SizedGrid.Coord

Methods

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

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

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

Defined in SizedGrid.Coord

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)

Defined in SizedGrid.Coord

Methods

showsPrec :: Int -> Coord cs -> ShowS

show :: Coord cs -> String

showList :: [Coord cs] -> ShowS

Generic (Coord cs)

Defined in SizedGrid.Coord

Associated Types

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

Methods

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

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

All Semigroup cs => Semigroup (Coord cs)

Defined in SizedGrid.Coord

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)

Defined in SizedGrid.Coord

Methods

mempty :: Coord cs

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

mconcat :: [Coord cs] -> Coord cs

All ToJSON cs => ToJSON (Coord cs)

Defined in SizedGrid.Coord

Methods

toJSON :: Coord cs -> Value

toEncoding :: Coord cs -> Encoding

toJSONList :: [Coord cs] -> Value

toEncodingList :: [Coord cs] -> Encoding

All FromJSON cs => FromJSON (Coord cs)

Defined in SizedGrid.Coord

Methods

parseJSON :: Value -> Parser (Coord cs)

parseJSONList :: Value -> Parser [Coord cs]

All Random cs => Random (Coord cs)

Defined in SizedGrid.Coord

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)

Defined in SizedGrid.Coord

Associated Types

type Diff (Coord cs) :: Type

Methods

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

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

All AdditiveGroup cs => AdditiveGroup (Coord cs)

Defined in SizedGrid.Coord

Methods

zeroV :: Coord cs

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

negateV :: Coord cs -> Coord cs

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

(AllSizedKnown cs, All IsCoordLifted cs, All Monoid cs, All Semigroup cs, SListI cs) => ComonadStore (Coord cs) (FocusedGrid cs)

Defined in SizedGrid.Grid.Focused

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 IsCoordLifted cs => FunctorWithIndex (Coord cs) (Grid cs)

Defined in SizedGrid.Grid.Grid

Methods

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

imapped :: IndexedSetter (Coord cs) (Grid cs a) (Grid cs b) a b

All IsCoordLifted cs => FoldableWithIndex (Coord cs) (Grid cs)

Defined in SizedGrid.Grid.Grid

Methods

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

ifolded :: IndexedFold (Coord cs) (Grid cs a) 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 IsCoordLifted cs => TraversableWithIndex (Coord cs) (Grid cs)

Defined in SizedGrid.Grid.Grid

Methods

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

itraversed :: IndexedTraversal (Coord cs) (Grid cs a) (Grid cs b) a b

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

Defined in SizedGrid.Coord

Methods

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

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

Defined in SizedGrid.Coord

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'

Defined in SizedGrid.Coord

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'

Defined in SizedGrid.Coord

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'

Defined in SizedGrid.Coord

Methods

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

type Rep (Coord cs)

Defined in SizedGrid.Coord

type Rep (Coord cs) = D1 (MetaData "Coord" "SizedGrid.Coord" "sized-grid-0.2.0.1-13S2LxFyaLj8fVZ02bNPgR" True) (C1 (MetaCons "Coord" PrefixI True) (S1 (MetaSel (Just "unCoord") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (NP I cs))))

type Diff (Coord cs)

Defined in SizedGrid.Coord

type Diff (Coord cs) = CoordDiff cs

coordSplit :: Coord (c ': cs) -> (c, Coord cs)

pattern (:|) :: c -> Coord cs -> Coord (c ': cs) infixr 5

pattern EmptyCoord :: Coord '[]

_WrappedCoord :: Iso' (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])

Defined in SizedGrid.Coord

type CoordDiff ([] :: [k]) = ()

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

Defined in SizedGrid.Coord

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

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

Defined in SizedGrid.Coord

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

type CoordDiff (a ': (b ': (c ': (d ': ([] :: [Type])))) :: [Type])

Defined in SizedGrid.Coord

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

type CoordDiff (a ': (b ': (c ': ([] :: [Type]))) :: [Type])

Defined in SizedGrid.Coord

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

type CoordDiff (a ': (b ': ([] :: [Type])) :: [Type])

Defined in SizedGrid.Coord

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

type CoordDiff (a ': ([] :: [Type]) :: [Type])

Defined in SizedGrid.Coord

type CoordDiff (a ': ([] :: [Type]) :: [Type]) = 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 IsCoordLifted 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 n ': cs) = n * MaxCoordSize cs

coordPosition :: All IsCoordLifted 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

tranposeCoord :: Coord '[a, b] -> Coord '[b, a]

Swap x and y for a coord in 2D space

zeroCoord :: All IsCoordLifted cs => Coord cs

The zero position for a coord

class AllSizedKnown (cs :: [*]) where

Methods

sizeProof :: Dict (KnownNat (MaxCoordSize cs))

Instances

AllSizedKnown ([] :: [Type])

Defined in SizedGrid.Coord

Methods

sizeProof :: Dict (KnownNat (MaxCoordSize []))

(KnownNat n, AllSizedKnown as) => AllSizedKnown (c n ': as)

Defined in SizedGrid.Coord

Methods

sizeProof :: Dict (KnownNat (MaxCoordSize (c n ': as)))

class WeakenCoord as bs where

Methods

weakenCoord :: Coord as -> Maybe (Coord bs)

Instances

WeakenCoord ([] :: [Type]) ([] :: [Type])

Defined in SizedGrid.Coord

Methods

weakenCoord :: Coord [] -> Maybe (Coord [])

(WeakenCoord as bs, IsCoord c, KnownNat m) => WeakenCoord (c n ': as) (c m ': bs)

Defined in SizedGrid.Coord

Methods

weakenCoord :: Coord (c n ': as) -> Maybe (Coord (c m ': bs))

class StrengthenCoord as bs where

Methods

strengthenCoord :: Coord as -> Coord bs

Instances

StrengthenCoord ([] :: [Type]) ([] :: [Type])

Defined in SizedGrid.Coord

Methods

strengthenCoord :: Coord [] -> Coord []

(StrengthenCoord as bs, IsCoord c, n <= m, KnownNat m) => StrengthenCoord (c n ': as) (c m ': bs)

Defined in SizedGrid.Coord

Methods

strengthenCoord :: Coord (c n ': as) -> Coord (c m ': bs)