SizedGrid.Ordinal

Documentation

data Ordinal m where

An Ordinal can only hold m different values, ususally corresponding to 0 .. m - 1. We store it here using a Proxy of a type level number and use constraints to keep the required invariants.

Desprite represeting a number, Ordinal is not an instance of Num and many functions (such as negate) would only be partial

Constructors

Ordinal :: (KnownNat n, KnownNat m, ((n + 1) <=? m) ~ True) => Proxy n -> Ordinal m

Instances

((<=) 1 m, KnownNat m) => Bounded (Ordinal m)

Methods

minBound :: Ordinal m

maxBound :: Ordinal m

((<=) 1 m, KnownNat m) => Enum (Ordinal m)

Methods

succ :: Ordinal m -> Ordinal m

pred :: Ordinal m -> Ordinal m

toEnum :: Int -> Ordinal m

fromEnum :: Ordinal m -> Int

enumFrom :: Ordinal m -> [Ordinal m]

enumFromThen :: Ordinal m -> Ordinal m -> [Ordinal m]

enumFromTo :: Ordinal m -> Ordinal m -> [Ordinal m]

enumFromThenTo :: Ordinal m -> Ordinal m -> Ordinal m -> [Ordinal m]

Eq (Ordinal m)

Methods

(==) :: Ordinal m -> Ordinal m -> Bool

(/=) :: Ordinal m -> Ordinal m -> Bool

Ord (Ordinal m)

Methods

compare :: Ordinal m -> Ordinal m -> Ordering

(<) :: Ordinal m -> Ordinal m -> Bool

(<=) :: Ordinal m -> Ordinal m -> Bool

(>) :: Ordinal m -> Ordinal m -> Bool

(>=) :: Ordinal m -> Ordinal m -> Bool

max :: Ordinal m -> Ordinal m -> Ordinal m

min :: Ordinal m -> Ordinal m -> Ordinal m

Show (Ordinal m)

Methods

showsPrec :: Int -> Ordinal m -> ShowS

show :: Ordinal m -> String

showList :: [Ordinal m] -> ShowS

((<=) 1 m, KnownNat m) => Random (Ordinal m)

Methods

randomR :: RandomGen g => (Ordinal m, Ordinal m) -> g -> (Ordinal m, g)

random :: RandomGen g => g -> (Ordinal m, g)

randomRs :: RandomGen g => (Ordinal m, Ordinal m) -> g -> [Ordinal m]

randoms :: RandomGen g => g -> [Ordinal m]

randomRIO :: (Ordinal m, Ordinal m) -> IO (Ordinal m)

randomIO :: IO (Ordinal m)

KnownNat m => ToJSONKey (Ordinal m)

Methods

toJSONKey :: ToJSONKeyFunction (Ordinal m)

toJSONKeyList :: ToJSONKeyFunction [Ordinal m]

KnownNat m => ToJSON (Ordinal m)

Methods

toJSON :: Ordinal m -> Value

toEncoding :: Ordinal m -> Encoding

toJSONList :: [Ordinal m] -> Value

toEncodingList :: [Ordinal m] -> Encoding

KnownNat m => FromJSONKey (Ordinal m)

Methods

fromJSONKey :: FromJSONKeyFunction (Ordinal m)

fromJSONKeyList :: FromJSONKeyFunction [Ordinal m]

KnownNat m => FromJSON (Ordinal m)

Methods

parseJSON :: Value -> Parser (Ordinal m)

parseJSONList :: Value -> Parser [Ordinal m]

((<=) 1 n, KnownNat n) => IsCoord (Ordinal n)

Associated Types

type CoordSized (Ordinal n) :: Nat

Methods

asOrdinal :: Iso' (Ordinal n) (Ordinal (CoordSized (Ordinal n)))

zeroPosition :: Ordinal n

sCoordSized :: proxy (Ordinal n) -> Proxy Nat (CoordSized (Ordinal n))

maxCoordSize :: proxy (Ordinal n) -> Integer

type CoordSized (Ordinal n)

type CoordSized (Ordinal n) = n

numToOrdinal :: forall a m. (KnownNat m, Integral a) => a -> Maybe (Ordinal m)

Convert a normal integral to an ordinal. If it is outside the range (or= m), Nothing is returned.

ordinalToNum :: Num a => Ordinal m -> a

Transform an ordinal to a given number