tvl-depot/src/Xanthous/Data.hs

{-# LANGUAGE PartialTypeSignatures #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE ViewPatterns      #-}
{-# LANGUAGE RoleAnnotations   #-}
{-# LANGUAGE RecordWildCards   #-}
{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE DeriveFoldable    #-}
{-# LANGUAGE DeriveFunctor     #-}
{-# LANGUAGE TemplateHaskell   #-}
{-# LANGUAGE NoTypeSynonymInstances   #-}
--------------------------------------------------------------------------------
-- | Common data types for Xanthous
--------------------------------------------------------------------------------
module Xanthous.Data
  ( -- *
    Position'(..)
  , Position
  , x
  , y

  , Positioned(..)
  , _Positioned
  , position
  , positioned
  , loc
  , _Position
  , positionFromPair
  , addPositions
  , diffPositions
  , stepTowards
  , isUnit

    -- *
  , Per(..)
  , invertRate
  , invertedRate
  , (|*|)
  , Ticks(..)
  , Tiles(..)
  , TicksPerTile
  , TilesPerTick
  , timesTiles

    -- *
  , Dimensions'(..)
  , Dimensions
  , HasWidth(..)
  , HasHeight(..)

    -- *
  , Direction(..)
  , opposite
  , move
  , asPosition
  , directionOf

    -- *
  , Neighbors(..)
  , edges
  , neighborDirections
  , neighborPositions
  ) where
--------------------------------------------------------------------------------
import           Xanthous.Prelude hiding (Left, Down, Right)
import           Test.QuickCheck (Arbitrary, CoArbitrary, Function)
import           Test.QuickCheck.Arbitrary.Generic
import           Data.Group
import           Brick (Location(Location), Edges(..))
import           Data.Monoid (Product(..), Sum(..))
import           Data.Aeson.Generic.DerivingVia
import           Data.Aeson (ToJSON, FromJSON)
--------------------------------------------------------------------------------
import           Xanthous.Util (EqEqProp(..), EqProp)
import           Xanthous.Orphans ()
import           Xanthous.Util.Graphics
--------------------------------------------------------------------------------

-- 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

--------------------------------------------------------------------------------

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)
makeLenses ''Position'

type Position = Position' Int

instance Arbitrary a => Arbitrary (Position' a) where
  arbitrary = genericArbitrary
  shrink = genericShrink

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, 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 (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

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) (a, a)
_Position = iso hither yon
  where
    hither (Position px py) = (px, py)
    yon (lx, ly) = Position lx ly

positionFromPair :: (Num a, Integral i, Integral j) => (i, j) -> Position' a
positionFromPair (i, j) = Position (fromIntegral i) (fromIntegral j)

-- | 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, Generic)

instance Arbitrary Direction where
  arbitrary = genericArbitrary
  shrink = genericShrink

opposite :: Direction -> Direction
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 :: Direction -> Position -> Position
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

--------------------------------------------------------------------------------

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)
makeLenses ''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 :: Position -> Neighbors Position
neighborPositions pos = (`move` pos) <$> neighborDirections

--------------------------------------------------------------------------------

newtype Per a b = Rate Double
  deriving stock (Show, Eq, Generic)
  deriving anyclass (NFData, CoArbitrary, Function)
  deriving (Num, Ord, Enum, Real, ToJSON, FromJSON) via Double
  deriving (Semigroup, Monoid) via Product Double
instance Arbitrary (Per a b) where arbitrary = genericArbitrary

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

infixl 7 |*|
(|*|) :: (Scalar a, Scalar b) => a `Per` b -> b -> a
(|*|) (Rate rate) b = fromScalar $ rate * scalar b

newtype Ticks = Ticks Word
  deriving stock (Show, 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
instance Arbitrary Ticks where arbitrary = genericArbitrary

newtype Tiles = Tiles Double
  deriving stock (Show, Eq, Generic)
  deriving anyclass (NFData, CoArbitrary, Function)
  deriving (Num, Ord, Enum, Real, ToJSON, FromJSON, Scalar) via Double
  deriving (Semigroup, Monoid) via (Sum Double)
instance Arbitrary Tiles where arbitrary = genericArbitrary

type TicksPerTile = Ticks `Per` Tiles
type TilesPerTick = Tiles `Per` Ticks

timesTiles :: TicksPerTile -> Tiles -> Ticks
timesTiles = (|*|)