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authorAspen Smith <grfn@gws.fyi>2024-02-12T03·00-0500
committerclbot <clbot@tvl.fyi>2024-02-14T19·37+0000
commit82ecd61f5c699cf3af6c4eadf47a1c52b1d696c6 (patch)
tree429c5e078528000591742ec3211bc768ae913a78 /users/grfn/xanthous/src/Xanthous/Data.hs
parent0ba476a4266015f278f18d74094299de74a5a111 (diff)
chore(users): grfn -> aspen r/7511
Change-Id: I6c6847fac56f0a9a1a2209792e00a3aec5e672b9
Reviewed-on: https://cl.tvl.fyi/c/depot/+/10809
Autosubmit: aspen <root@gws.fyi>
Reviewed-by: sterni <sternenseemann@systemli.org>
Tested-by: BuildkiteCI
Reviewed-by: lukegb <lukegb@tvl.fyi>
Diffstat (limited to 'users/grfn/xanthous/src/Xanthous/Data.hs')
-rw-r--r--users/grfn/xanthous/src/Xanthous/Data.hs822
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diff --git a/users/grfn/xanthous/src/Xanthous/Data.hs b/users/grfn/xanthous/src/Xanthous/Data.hs
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--- a/users/grfn/xanthous/src/Xanthous/Data.hs
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@@ -1,822 +0,0 @@
-{-# LANGUAGE PartialTypeSignatures  #-}
-{-# LANGUAGE StandaloneDeriving     #-}
-{-# LANGUAGE RoleAnnotations        #-}
-{-# LANGUAGE RecordWildCards        #-}
-{-# LANGUAGE DeriveTraversable      #-}
-{-# LANGUAGE TemplateHaskell        #-}
-{-# LANGUAGE NoTypeSynonymInstances #-}
-{-# LANGUAGE DuplicateRecordFields  #-}
-{-# LANGUAGE QuantifiedConstraints  #-}
-{-# LANGUAGE UndecidableInstances   #-}
-{-# LANGUAGE AllowAmbiguousTypes    #-}
---------------------------------------------------------------------------------
--- | Common data types for Xanthous ------------------------------------------------------------------------------
-module Xanthous.Data
-  ( Opposite(..)
-
-    -- *
-  , Position'(..)
-  , Position
-  , x
-  , y
-
-    -- **
-  , Positioned(..)
-  , _Positioned
-  , position
-  , positioned
-  , loc
-  , _Position
-  , positionFromPair
-  , positionFromV2
-  , addPositions
-  , diffPositions
-  , stepTowards
-  , isUnit
-  , distance
-
-    -- * Boxes
-  , Box(..)
-  , topLeftCorner
-  , bottomRightCorner
-  , setBottomRightCorner
-  , dimensions
-  , inBox
-  , boxIntersects
-  , boxCenter
-  , boxEdge
-  , module Linear.V2
-
-    -- * Unit math
-  , Scalar(..)
-  , Per(..)
-  , invertRate
-  , invertedRate
-  , (|+|)
-  , (|*|)
-  , (|/|)
-  , (:+:)
-  , (:*:)
-  , (:/:)
-  , (:**:)(..)
-  , Ticks(..)
-  , Tiles(..)
-  , TicksPerTile
-  , TilesPerTick
-  , timesTiles
-  , Square(..)
-  , squared
-  , Cubic(..)
-  , Grams
-  , Meters
-  , Uno(..)
-  , Unit(..)
-  , UnitSymbol(..)
-
-    -- *
-  , Dimensions'(..)
-  , Dimensions
-  , HasWidth(..)
-  , HasHeight(..)
-
-    -- *
-  , Direction(..)
-  , move
-  , asPosition
-  , directionOf
-  , Cardinal(..)
-
-    -- *
-  , Corner(..)
-  , Edge(..)
-  , cornerEdges
-
-    -- *
-  , Neighbors(..)
-  , edges
-  , neighborDirections
-  , neighborPositions
-  , neighborCells
-  , arrayNeighbors
-  , rotations
-  , HasTopLeft(..)
-  , HasTop(..)
-  , HasTopRight(..)
-  , HasLeft(..)
-  , HasRight(..)
-  , HasBottomLeft(..)
-  , HasBottom(..)
-  , HasBottomRight(..)
-
-    -- *
-  , Hitpoints(..)
-  ) where
---------------------------------------------------------------------------------
-import           Xanthous.Prelude hiding (Left, Down, Right, (.=), elements)
---------------------------------------------------------------------------------
-import           Linear.V2 hiding (_x, _y)
-import qualified Linear.V2 as L
-import           Linear.V4 hiding (_x, _y)
-import           Test.QuickCheck (CoArbitrary, Function, elements)
-import           Test.QuickCheck.Arbitrary.Generic
-import           Data.Group
-import           Brick (Location(Location), Edges(..))
-import           Data.Monoid (Product(..), Sum(..))
-import           Data.Array.IArray
-import           Data.Aeson.Generic.DerivingVia
-import           Data.Aeson
-                 ( ToJSON(..), FromJSON(..), object, (.=), (.:), withObject)
-import           Data.Random (Distribution)
-import           Data.Coerce
-import           Data.Proxy (Proxy(Proxy))
---------------------------------------------------------------------------------
-import           Xanthous.Util (EqEqProp(..), EqProp, between)
-import           Xanthous.Orphans ()
-import           Xanthous.Util.Graphics
-import qualified Linear.Metric as Metric
---------------------------------------------------------------------------------
-
--- | opposite ∘ opposite ≡ id
-class Opposite x where
-  opposite :: x -> x
-
---------------------------------------------------------------------------------
-
--- fromScalar ∘ scalar ≡ id
-class Scalar a where
-  scalar :: a -> Double
-  fromScalar :: Double -> a
-
-instance Scalar Double where
-  scalar = id
-  fromScalar = id
-
-newtype ScalarIntegral a = ScalarIntegral a
-  deriving newtype (Eq, Ord, Num, Enum, Real, Integral)
-instance Integral a => Scalar (ScalarIntegral a) where
-  scalar = fromIntegral
-  fromScalar = floor
-
-deriving via (ScalarIntegral Integer) instance Scalar Integer
-deriving via (ScalarIntegral Word) instance Scalar Word
-
--- | Units of measure
-class Unit a where
-  unitSuffix :: Text
-type UnitSymbol :: Symbol -> Type -> Type
-newtype UnitSymbol suffix a = UnitSymbol a
-instance KnownSymbol suffix => Unit (UnitSymbol suffix a) where
-  unitSuffix = pack $ symbolVal @suffix Proxy
-
-newtype ShowUnitSuffix a b = ShowUnitSuffix a
-instance (Show b, Unit a, Coercible a b) => Show (ShowUnitSuffix a b) where
-  show a = show (coerce @_ @b a) <> " " <> unpack (unitSuffix @a)
-
---------------------------------------------------------------------------------
-
-data Position' a where
-  Position :: { _x :: a
-             , _y :: a
-             } -> (Position' a)
-  deriving stock (Show, Eq, Generic, Ord, Functor, Foldable, Traversable)
-  deriving anyclass (NFData, Hashable, CoArbitrary, Function)
-  deriving EqProp via EqEqProp (Position' a)
-  deriving (ToJSON, FromJSON)
-       via WithOptions '[ FieldLabelModifier '[Drop 1] ]
-                       (Position' a)
-
-x, y :: Lens' (Position' a) a
-x = lens (\(Position xx _) -> xx) (\(Position _ yy) xx -> Position xx yy)
-y = lens (\(Position _ yy) -> yy) (\(Position xx _) yy -> Position xx yy)
-
-type Position = Position' Int
-
-instance (Arbitrary a) => Arbitrary (Position' a) where
-  arbitrary = genericArbitrary
-  shrink (Position px py) = Position <$> shrink px <*> shrink py
-
-
-instance Num a => Semigroup (Position' a) where
-  (Position x₁ y₁) <> (Position x₂ y₂) = Position (x₁ + x₂) (y₁ + y₂)
-
-instance Num a => Monoid (Position' a) where
-  mempty = Position 0 0
-
-instance Num a => Group (Position' a) where
-  invert (Position px py) = Position (negate px) (negate py)
-
--- | Positions convert to scalars by discarding their orientation and just
--- measuring the length from the origin
-instance (Ord a, Num a, Scalar a) => Scalar (Position' a) where
-  scalar = fromIntegral . length . line 0 . view _Position
-  fromScalar n = Position (fromScalar n) (fromScalar n)
-
-data Positioned a where
-  Positioned :: Position -> a -> Positioned a
-  deriving stock (Show, Eq, Ord, Functor, Foldable, Traversable, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-type role Positioned representational
-
-_Positioned :: Iso (Position, a) (Position, b) (Positioned a) (Positioned b)
-_Positioned = iso hither yon
-  where
-    hither (pos, a) = Positioned pos a
-    yon (Positioned pos b) = (pos, b)
-
-instance Arbitrary a => Arbitrary (Positioned a) where
-  arbitrary = Positioned <$> arbitrary <*> arbitrary
-
-instance ToJSON a => ToJSON (Positioned a) where
-  toJSON (Positioned pos val) = object
-    [ "position" .= pos
-    , "data" .= val
-    ]
-
-instance FromJSON a => FromJSON (Positioned a) where
-  parseJSON = withObject "Positioned" $ \obj ->
-    Positioned <$> obj .: "position" <*> obj .: "data"
-
-position :: Lens' (Positioned a) Position
-position = lens
-  (\(Positioned pos _) -> pos)
-  (\(Positioned _ a) pos -> Positioned pos a)
-
-positioned :: Lens (Positioned a) (Positioned b) a b
-positioned = lens
-  (\(Positioned _ x') -> x')
-  (\(Positioned pos _) x' -> Positioned pos x')
-
-loc :: Iso' Position Location
-loc = iso hither yon
-  where
-    hither (Position px py) = Location (px, py)
-    yon (Location (lx, ly)) = Position lx ly
-
-_Position :: Iso' (Position' a) (V2 a)
-_Position = iso hither yon
-  where
-    hither (Position px py) = V2 px py
-    yon (V2 lx ly) = Position lx ly
-
-positionFromPair :: (Num a, Integral i, Integral j) => (i, j) -> Position' a
-positionFromPair (i, j) = Position (fromIntegral i) (fromIntegral j)
-
-positionFromV2 :: (Num a, Integral i) => V2 i -> Position' a
-positionFromV2 (V2 xx yy) = Position (fromIntegral xx) (fromIntegral yy)
-
--- | Add two positions
---
--- Operation for the additive group on positions
-addPositions :: Num a => Position' a -> Position' a -> Position' a
-addPositions = (<>)
-
--- | Subtract two positions.
---
--- diffPositions pos₁ pos₂ = pos₁ `addPositions` (invert pos₂)
-diffPositions :: Num a => Position' a -> Position' a -> Position' a
-diffPositions (Position x₁ y₁) (Position x₂ y₂) = Position (x₁ - x₂) (y₁ - y₂)
-
--- | Is this position a unit position? or: When taken as a difference, does this
--- position represent a step of one tile?
---
--- ∀ dir :: Direction. isUnit ('asPosition' dir)
-isUnit :: (Eq a, Num a) => Position' a -> Bool
-isUnit (Position px py) =
-  abs px `elem` [0,1] && abs py `elem` [0, 1] && (px, py) /= (0, 0)
-
---------------------------------------------------------------------------------
-
-data Dimensions' a = Dimensions
-  { _width :: a
-  , _height :: a
-  }
-  deriving stock (Show, Eq, Functor, Generic)
-  deriving anyclass (CoArbitrary, Function)
-makeFieldsNoPrefix ''Dimensions'
-
-instance Arbitrary a => Arbitrary (Dimensions' a) where
-  arbitrary = Dimensions <$> arbitrary <*> arbitrary
-
-type Dimensions = Dimensions' Word
-
---------------------------------------------------------------------------------
-
-data Direction where
-  Up        :: Direction
-  Down      :: Direction
-  Left      :: Direction
-  Right     :: Direction
-  UpLeft    :: Direction
-  UpRight   :: Direction
-  DownLeft  :: Direction
-  DownRight :: Direction
-  Here      :: Direction
-  deriving stock (Show, Eq, Ord, Generic)
-  deriving anyclass (CoArbitrary, Function, NFData, ToJSON, FromJSON, Hashable)
-
-deriving via (GenericArbitrary Direction) instance Arbitrary Direction
-
-instance Opposite Direction where
-  opposite Up        = Down
-  opposite Down      = Up
-  opposite Left      = Right
-  opposite Right     = Left
-  opposite UpLeft    = DownRight
-  opposite UpRight   = DownLeft
-  opposite DownLeft  = UpRight
-  opposite DownRight = UpLeft
-  opposite Here      = Here
-
-move :: Num a => Direction -> Position' a -> Position' a
-move Up        = y -~ 1
-move Down      = y +~ 1
-move Left      = x -~ 1
-move Right     = x +~ 1
-move UpLeft    = move Up . move Left
-move UpRight   = move Up . move Right
-move DownLeft  = move Down . move Left
-move DownRight = move Down . move Right
-move Here      = id
-
-asPosition :: Direction -> Position
-asPosition dir = move dir mempty
-
--- | Returns the direction that a given position is from a given source position
-directionOf
-  :: Position -- ^ Source
-  -> Position -- ^ Target
-  -> Direction
-directionOf (Position x₁ y₁) (Position x₂ y₂) =
-  case (x₁ `compare` x₂, y₁ `compare` y₂) of
-    (EQ, EQ) -> Here
-    (EQ, LT) -> Down
-    (EQ, GT) -> Up
-    (LT, EQ) -> Right
-    (GT, EQ) -> Left
-
-    (LT, LT) -> DownRight
-    (GT, LT) -> DownLeft
-
-    (LT, GT) -> UpRight
-    (GT, GT) -> UpLeft
-
--- | Take one (potentially diagonal) step towards the given position
---
--- ∀ src tgt. isUnit (src `diffPositions` (src `stepTowards tgt`))
-stepTowards
-  :: Position -- ^ Source
-  -> Position -- ^ Target
-  -> Position
-stepTowards (view _Position -> p₁) (view _Position -> p₂)
-  | p₁ == p₂ = _Position # p₁
-  | otherwise =
-    let (_:p:_) = line p₁ p₂
-    in _Position # p
-
--- | Newtype controlling arbitrary generation to only include cardinal
--- directions ('Up', 'Down', 'Left', 'Right')
-newtype Cardinal = Cardinal { getCardinal :: Direction }
-  deriving stock (Eq, Show, Ord, Generic)
-  deriving anyclass (NFData, Function, CoArbitrary)
-  deriving newtype (Opposite)
-
-instance Arbitrary Cardinal where
-  arbitrary = Cardinal <$> elements [Up, Down, Left, Right]
-
---------------------------------------------------------------------------------
-
-data Corner
-  = TopLeft
-  | TopRight
-  | BottomLeft
-  | BottomRight
-  deriving stock (Show, Eq, Ord, Enum, Bounded, Generic)
-  deriving Arbitrary via GenericArbitrary Corner
-
-instance Opposite Corner where
-  opposite TopLeft = BottomRight
-  opposite TopRight = BottomLeft
-  opposite BottomLeft = TopRight
-  opposite BottomRight = TopLeft
-
-data Edge
-  = TopEdge
-  | LeftEdge
-  | RightEdge
-  | BottomEdge
-  deriving stock (Show, Eq, Ord, Enum, Bounded, Generic)
-  deriving Arbitrary via GenericArbitrary Edge
-
-instance Opposite Edge where
-  opposite TopEdge = BottomEdge
-  opposite BottomEdge = TopEdge
-  opposite LeftEdge = RightEdge
-  opposite RightEdge = LeftEdge
-
-cornerEdges :: Corner -> (Edge, Edge)
-cornerEdges TopLeft = (TopEdge, LeftEdge)
-cornerEdges TopRight = (TopEdge, RightEdge)
-cornerEdges BottomLeft = (BottomEdge, LeftEdge)
-cornerEdges BottomRight = (BottomEdge, RightEdge)
-
---------------------------------------------------------------------------------
-
-data Neighbors a = Neighbors
-  { _topLeft
-  , _top
-  , _topRight
-  , _left
-  , _right
-  , _bottomLeft
-  , _bottom
-  , _bottomRight :: a
-  }
-  deriving stock (Show, Eq, Ord, Functor, Foldable, Traversable, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function, MonoFoldable)
-
-deriving via (GenericArbitrary (Neighbors a)) instance (Arbitrary a) => Arbitrary (Neighbors a)
-
-type instance Element (Neighbors a) = a
-
-makeFieldsNoPrefix ''Neighbors
-
-instance Applicative Neighbors where
-  pure α = Neighbors
-    { _topLeft     = α
-    , _top         = α
-    , _topRight    = α
-    , _left        = α
-    , _right       = α
-    , _bottomLeft  = α
-    , _bottom      = α
-    , _bottomRight = α
-    }
-  nf <*> nx = Neighbors
-    { _topLeft     = nf ^. topLeft     $ nx ^. topLeft
-    , _top         = nf ^. top         $ nx ^. top
-    , _topRight    = nf ^. topRight    $ nx ^. topRight
-    , _left        = nf ^. left        $ nx ^. left
-    , _right       = nf ^. right       $ nx ^. right
-    , _bottomLeft  = nf ^. bottomLeft  $ nx ^. bottomLeft
-    , _bottom      = nf ^. bottom      $ nx ^. bottom
-    , _bottomRight = nf ^. bottomRight $ nx ^. bottomRight
-    }
-
-edges :: Neighbors a -> Edges a
-edges neighs = Edges
-  { eTop = neighs ^. top
-  , eBottom = neighs ^. bottom
-  , eLeft = neighs ^. left
-  , eRight = neighs ^. right
-  }
-
-neighborDirections :: Neighbors Direction
-neighborDirections = Neighbors
-  { _topLeft     = UpLeft
-  , _top         = Up
-  , _topRight    = UpRight
-  , _left        = Left
-  , _right       = Right
-  , _bottomLeft  = DownLeft
-  , _bottom      = Down
-  , _bottomRight = DownRight
-  }
-
-neighborPositions :: Num a => Position' a -> Neighbors (Position' a)
-neighborPositions pos = (`move` pos) <$> neighborDirections
-
-neighborCells :: Num a => V2 a -> Neighbors (V2 a)
-neighborCells = map (view _Position) . neighborPositions . review _Position
-
-arrayNeighbors
-  :: (IArray a e, Ix i, Num i)
-  => a (V2 i) e
-  -> V2 i
-  -> Neighbors (Maybe e)
-arrayNeighbors arr center = arrLookup <$> neighborPositions (_Position # center)
-  where
-    arrLookup (view _Position -> pos)
-      | inRange (bounds arr) pos = Just $ arr ! pos
-      | otherwise                = Nothing
-
--- | Returns a list of all 4 90-degree rotations of the given neighbors
-rotations :: Neighbors a -> V4 (Neighbors a)
-rotations orig@(Neighbors tl t tr l r bl b br) = V4
-   orig                            -- tl t  tr
-                                   -- l     r
-                                   -- bl b  br
-
-   (Neighbors bl l tl b t br r tr) -- bl l tl
-                                   -- b    t
-                                   -- br r tr
-
-   (Neighbors br b bl r l tr t tl) -- br b bl
-                                   -- r    l
-                                   -- tr t tl
-
-   (Neighbors tr r br t b tl l bl) -- tr r br
-                                   -- t    b
-                                   -- tl l bl
-
---------------------------------------------------------------------------------
-
-newtype Per a b = Rate Double
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving (Arbitrary, Num, Ord, Enum, Real, Fractional, ToJSON, FromJSON)
-       via Double
-  deriving (Semigroup, Monoid) via Product Double
-  deriving Show via ShowUnitSuffix (Per a b) Double
-deriving via Double
-  instance ( Distribution d Double
-           , forall xx yy. Coercible xx yy => Coercible (d xx) (d yy)
-           )
-  => Distribution d (Per a b)
-
-instance (Unit a, Unit b) => Unit (a `Per` b) where
-  unitSuffix = unitSuffix @a <> "/" <> unitSuffix @b
-
-invertRate :: a `Per` b -> b `Per` a
-invertRate (Rate p) = Rate $ 1 / p
-
-invertedRate :: Iso (a `Per` b) (b' `Per` a') (b `Per` a) (a' `Per` b')
-invertedRate = iso invertRate invertRate
-
-type (:+:) :: Type -> Type -> Type
-type family (:+:) a b where
-  a :+: a       = a
-  a :+: (Uno b) = a
-
-infixl 6 |+|
-class AddUnit a b where
-  (|+|) :: a -> b -> a :+: b
-
-instance Scalar a => AddUnit a a where
-  x' |+| y' = fromScalar $ scalar x' + scalar y'
-
-instance (Scalar a, Scalar b) => AddUnit a (Uno b) where
-  x' |+| y' = fromScalar $ scalar x' + scalar y'
-
-type (:*:) :: Type -> Type -> Type
-type family (:*:) a b where
-  (a `Per` b) :*: b     = a
-  (Square a)  :*: a     = Cubic a
-  a           :*: a     = Square a
-  a           :*: Uno b = a
-  a           :*: b     = a :**: b
-
-infixl 7 |*|
-class MulUnit a b where
-  (|*|) :: a -> b -> a :*: b
-
-instance (Scalar a, Scalar b) => MulUnit (a `Per` b) b where
-  (Rate rate) |*| b = fromScalar $ rate * scalar b
-
-instance forall a. (Scalar a, a :*: a ~ Square a) => MulUnit a a where
-  x' |*| y' = Square @a . fromScalar $ scalar x' * scalar y'
-
-instance forall a. (Scalar a) => MulUnit (Square a) a where
-  x' |*| y' = Cubic @a . fromScalar $ scalar x' * scalar y'
-
-instance {-# INCOHERENT #-} forall a b.
-  (Scalar a, Scalar b, Scalar (a :*: Uno b))
-    => MulUnit a (Uno b) where
-  x' |*| y' = fromScalar $ scalar x' * scalar y'
-
-type (:/:) :: Type -> Type -> Type
-type family (:/:) a b where
-  (Square a) :/: a          = a
-  (Cubic a)  :/: a          = Square a
-  (Cubic a)  :/: (Square a) = a
-  (a :**: b) :/: b          = a
-  (a :**: b) :/: a          = b
-  a          :/: Uno b      = a
-  a          :/: b          = a `Per` b
-
-infixl 7 |/|
-class DivUnit a b where
-  (|/|) :: a -> b -> a :/: b
-
-instance Scalar a => DivUnit (Square a) a where
-  (Square a) |/| b = fromScalar $ scalar a / scalar b
-
-instance Scalar a => DivUnit (Cubic a) a where
-  (Cubic a) |/| b = fromScalar $ scalar a / scalar b
-
-instance (Scalar a, Cubic a :/: Square a ~ a)
-       => DivUnit (Cubic a) (Square a) where
-  (Cubic a) |/| (Square b) = fromScalar $ scalar a / scalar b
-
-instance (Scalar a, Scalar b) => DivUnit (a :**: b) b where
-  (Times a) |/| b = fromScalar $ scalar a / scalar b
-
-instance (Scalar a, Scalar b) => DivUnit (a :**: b) a where
-  (Times a) |/| b = fromScalar $ scalar a / scalar b
-
-instance {-# INCOHERENT #-} forall a b.
-  (Scalar a, Scalar b, Scalar (a :/: Uno b))
-    => DivUnit a (Uno b) where
-  x' |/| y' = fromScalar $ scalar x' / scalar y'
-
--- | Dimensionless quantitites (mass per unit mass, radians, etc)
---
--- see <https://en.wikipedia.org/wiki/Parts-per_notation#Uno>
-newtype Uno a = Uno a
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving ( Arbitrary, Num, Ord, Enum, Real, Fractional, ToJSON, FromJSON
-           , Scalar, Show
-           )
-       via a
-  deriving Unit via UnitSymbol "" (Uno a)
-
-newtype Square a = Square a
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving ( Arbitrary, Num, Ord, Enum, Real, Fractional, ToJSON, FromJSON
-           , Scalar
-           )
-       via a
-deriving via (a :: Type)
-  instance ( Distribution d a
-           , forall xx yy. Coercible xx yy => Coercible (d xx) (d yy)
-           )
-  => Distribution d (Square a)
-
-instance Unit a => Unit (Square a) where
-  unitSuffix = unitSuffix @a <> "²"
-
-instance Show a => Show (Square a) where
-  show (Square n) = show n <> "²"
-
-squared :: (Scalar a, a :*: a ~ Square a) => a -> Square a
-squared v = v |*| v
-
-newtype Cubic a = Cubic a
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving ( Arbitrary, Num, Ord, Enum, Real, Fractional, ToJSON, FromJSON
-           , Scalar
-           )
-       via a
-deriving via (a :: Type)
-  instance ( Distribution d a
-           , forall xx yy. Coercible xx yy => Coercible (d xx) (d yy)
-           )
-  => Distribution d (Cubic a)
-
-instance Unit a => Unit (Cubic a) where
-  unitSuffix = unitSuffix @a <> "³"
-
-instance Show a => Show (Cubic a) where
-  show (Cubic n) = show n <> "³"
-
-newtype (:**:) a b = Times Double
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving (Arbitrary, Num, Ord, Enum, Real, Fractional, ToJSON, FromJSON)
-       via Double
-  deriving (Semigroup, Monoid) via Sum Double
-  deriving Show via ShowUnitSuffix (a :**: b) Double
-deriving via Double
-  instance ( Distribution d Double
-           , forall xx yy. Coercible xx yy => Coercible (d xx) (d yy)
-           )
-  => Distribution d (a :**: b)
-
-instance (Unit a, Unit b) => Unit (a :**: b) where
-  unitSuffix = unitSuffix @a <> " " <> unitSuffix @b
-
---------------------------------------------------------------------------------
-
-newtype Ticks = Ticks Word
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving (Num, Ord, Bounded, Enum, Integral, Real, ToJSON, FromJSON) via Word
-  deriving (Semigroup, Monoid) via (Sum Word)
-  deriving Scalar via ScalarIntegral Ticks
-  deriving Arbitrary via GenericArbitrary Ticks
-  deriving Unit via UnitSymbol "ticks" Ticks
-  deriving Show via ShowUnitSuffix Ticks Word
-deriving via Word
-  instance ( Distribution d Word
-           , forall xx yy. Coercible xx yy => Coercible (d xx) (d yy)
-           )
-  => Distribution d Ticks
-
-newtype Tiles = Tiles Double
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving (Num, Ord, Enum, Real, ToJSON, FromJSON, Scalar) via Double
-  deriving (Semigroup, Monoid) via (Sum Double)
-  deriving Arbitrary via GenericArbitrary Tiles
-  deriving Unit via UnitSymbol "m" Tiles
-  deriving Show via ShowUnitSuffix Tiles Double
-deriving via Double
-  instance ( Distribution d Double
-           , forall xx yy. Coercible xx yy => Coercible (d xx) (d yy)
-           )
-  => Distribution d Tiles
-
-type TicksPerTile = Ticks `Per` Tiles
-type TilesPerTick = Tiles `Per` Ticks
-
-timesTiles :: TicksPerTile -> Tiles -> Ticks
-timesTiles = (|*|)
-
--- | Calculate the (cartesian) distance between two 'Position's, floored and
--- represented as a number of 'Tile's
---
--- Note that this is imprecise, and may be different than the length of a
--- bresenham's line between the points
-distance :: Position -> Position -> Tiles
-distance
-  = (fromScalar .) . (Metric.distance `on` (fmap fromIntegral . view _Position))
-
---------------------------------------------------------------------------------
-
-newtype Hitpoints = Hitpoints Word
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving ( Arbitrary, Num, Ord, Bounded, Enum, Integral, Real, Scalar
-           , ToJSON, FromJSON
-           )
-       via Word
-  deriving (Semigroup, Monoid) via Sum Word
-  deriving Unit via UnitSymbol "hp" Hitpoints
-  deriving Show via ShowUnitSuffix Hitpoints Word
-
---------------------------------------------------------------------------------
-
--- | Grams, the fundamental measure of weight in Xanthous.
-newtype Grams = Grams Double
-  deriving stock (Eq, Generic)
-  deriving anyclass (NFData, CoArbitrary, Function)
-  deriving ( Arbitrary, Num, Ord, Enum, Real, Floating, Fractional, RealFloat
-           , RealFrac, Scalar, ToJSON, FromJSON
-           )
-       via Double
-  deriving (Semigroup, Monoid) via Sum Double
-  deriving Unit via UnitSymbol "g" Grams
-  deriving Show via ShowUnitSuffix Grams Double
-
--- | Every tile is 1 meter
-type Meters = Tiles
-
---------------------------------------------------------------------------------
-
-data Box a = Box
-  { _topLeftCorner :: V2 a
-  , _dimensions    :: V2 a
-  }
-  deriving stock (Show, Eq, Ord, Functor, Generic)
-makeFieldsNoPrefix ''Box
-
--- It seems to be necessary to have an `Arg (V2 a) a` constraint, as a is passed
--- to V2 internally, in order to make GHC figure out this deriving via correctly.
-deriving via (GenericArbitrary (Box a)) instance (Arbitrary a) => Arbitrary (Box a)
-
-bottomRightCorner :: Num a => Box a -> V2 a
-bottomRightCorner box =
-  V2 (box ^. topLeftCorner . L._x + box ^. dimensions . L._x)
-     (box ^. topLeftCorner . L._y + box ^. dimensions . L._y)
-
-setBottomRightCorner :: (Num a, Ord a) => Box a -> V2 a -> Box a
-setBottomRightCorner box br@(V2 brx bry)
-  | brx < box ^. topLeftCorner . L._x || bry < box ^. topLeftCorner . L._y
-  = box & topLeftCorner .~ br
-        & dimensions . L._x .~ ((box ^. topLeftCorner . L._x) - brx)
-        & dimensions . L._y .~ ((box ^. topLeftCorner . L._y) - bry)
-  | otherwise
-  = box & dimensions . L._x .~ (brx - (box ^. topLeftCorner . L._x))
-        & dimensions . L._y .~ (bry - (box ^. topLeftCorner . L._y))
-
-inBox :: (Ord a, Num a) => Box a -> V2 a -> Bool
-inBox box pt = flip all [L._x, L._y] $ \component ->
-  between (box ^. topLeftCorner . component)
-          (box ^. to bottomRightCorner . component)
-          (pt ^. component)
-
-boxIntersects :: (Ord a, Num a) => Box a -> Box a -> Bool
-boxIntersects box₁ box₂
-  = any (inBox box₁) [box₂ ^. topLeftCorner, bottomRightCorner box₂]
-
-boxCenter :: (Fractional a) => Box a -> V2 a
-boxCenter box = V2 cx cy
- where
-   cx = box ^. topLeftCorner . L._x + (box ^. dimensions . L._x / 2)
-   cy = box ^. topLeftCorner . L._y + (box ^. dimensions . L._y / 2)
-
-boxEdge :: (Enum a, Num a) => Box a -> Edge -> [V2 a]
-boxEdge box LeftEdge =
-  V2 (box ^. topLeftCorner . L._x)
-  <$> [box ^. topLeftCorner . L._y .. box ^. to bottomRightCorner . L._y]
-boxEdge box RightEdge =
-  V2 (box ^. to bottomRightCorner . L._x)
-  <$> [box ^. to bottomRightCorner . L._y .. box ^. to bottomRightCorner . L._y]
-boxEdge box TopEdge =
-  flip V2 (box ^. topLeftCorner . L._y)
-  <$> [box ^. topLeftCorner . L._x .. box ^. to bottomRightCorner . L._x]
-boxEdge box BottomEdge =
-  flip V2 (box ^. to bottomRightCorner . L._y)
-  <$> [box ^. topLeftCorner . L._x .. box ^. to bottomRightCorner . L._x]