Data.Finite.Table

Provides Vec-backed tables indexed by Finite types.

Combined with Finite and its Generics-based derivation, this can effectively provide an array-backed container indexed by finite type. This is a low-syntactic-overhead way to create Representable functors of any desired shape: just define the index type, tack on the requisite deriving clauses, and start using Table MyType.

    data PrimaryColor = R | G | B
      deriving Generic
      deriving (Finite, Portray) via Wrapped Generic PrimaryColor

    newtype Color = Color { getComponents :: Table PrimaryColor Int8 }

    magenta :: Color
    magenta = Color (Table $ Vec.fromList [255, 0, 255])

    cyan :: Color
    cyan = Color $ tabulate (\case { R -> 0; G -> 255; B -> 255 })

    main = pp $ getComponents magenta
    -- "mkTable (\case { R -> 255; G -> 0; B -> 255 })"

Tables

newtype Table a b

A compact array of bs indexed by a, according to Finite a.

Constructors

Table (Vec (Cardinality a) b)

Instances

Finite a => FunctorWithIndex a (Table a)

Defined in Data.Finite.Table

Methods

imap :: (a -> a0 -> b) -> Table a a0 -> Table a b

Finite a => FoldableWithIndex a (Table a)

Defined in Data.Finite.Table

Methods

ifoldMap :: Monoid m => (a -> a0 -> m) -> Table a a0 -> m

ifoldMap' :: Monoid m => (a -> a0 -> m) -> Table a a0 -> m

ifoldr :: (a -> a0 -> b -> b) -> b -> Table a a0 -> b

ifoldl :: (a -> b -> a0 -> b) -> b -> Table a a0 -> b

ifoldr' :: (a -> a0 -> b -> b) -> b -> Table a a0 -> b

ifoldl' :: (a -> b -> a0 -> b) -> b -> Table a a0 -> b

Finite a => TraversableWithIndex a (Table a)

Defined in Data.Finite.Table

Methods

itraverse :: Applicative f => (a -> a0 -> f b) -> Table a a0 -> f (Table a b)

Functor (Table a)

Defined in Data.Finite.Table

Methods

fmap :: (a0 -> b) -> Table a a0 -> Table a b

(<$) :: a0 -> Table a b -> Table a a0

Finite a => Applicative (Table a)

Defined in Data.Finite.Table

Methods

pure :: a0 -> Table a a0

(<*>) :: Table a (a0 -> b) -> Table a a0 -> Table a b

liftA2 :: (a0 -> b -> c) -> Table a a0 -> Table a b -> Table a c

(*>) :: Table a a0 -> Table a b -> Table a b

(<*) :: Table a a0 -> Table a b -> Table a a0

Foldable (Table a)

Defined in Data.Finite.Table

Methods

fold :: Monoid m => Table a m -> m

foldMap :: Monoid m => (a0 -> m) -> Table a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Table a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Table a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Table a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Table a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Table a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Table a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Table a a0 -> a0

toList :: Table a a0 -> [a0]

null :: Table a a0 -> Bool

length :: Table a a0 -> Int

elem :: Eq a0 => a0 -> Table a a0 -> Bool

maximum :: Ord a0 => Table a a0 -> a0

minimum :: Ord a0 => Table a a0 -> a0

sum :: Num a0 => Table a a0 -> a0

product :: Num a0 => Table a a0 -> a0

Finite a => Traversable (Table a)

Defined in Data.Finite.Table

Methods

traverse :: Applicative f => (a0 -> f b) -> Table a a0 -> f (Table a b)

sequenceA :: Applicative f => Table a (f a0) -> f (Table a a0)

mapM :: Monad m => (a0 -> m b) -> Table a a0 -> m (Table a b)

sequence :: Monad m => Table a (m a0) -> m (Table a a0)

Finite a => Distributive (Table a)

Defined in Data.Finite.Table

Methods

distribute :: Functor f => f (Table a a0) -> Table a (f a0)

collect :: Functor f => (a0 -> Table a b) -> f a0 -> Table a (f b)

distributeM :: Monad m => m (Table a a0) -> Table a (m a0)

collectM :: Monad m => (a0 -> Table a b) -> m a0 -> Table a (m b)

Finite a => Representable (Table a)

Defined in Data.Finite.Table

Associated Types

type Rep (Table a)

Methods

tabulate :: (Rep (Table a) -> a0) -> Table a a0

index :: Table a a0 -> Rep (Table a) -> a0

Eq b => Eq (Table a b)

Defined in Data.Finite.Table

Methods

(==) :: Table a b -> Table a b -> Bool

(/=) :: Table a b -> Table a b -> Bool

Ord b => Ord (Table a b)

Defined in Data.Finite.Table

Methods

compare :: Table a b -> Table a b -> Ordering

(<) :: Table a b -> Table a b -> Bool

(<=) :: Table a b -> Table a b -> Bool

(>) :: Table a b -> Table a b -> Bool

(>=) :: Table a b -> Table a b -> Bool

max :: Table a b -> Table a b -> Table a b

min :: Table a b -> Table a b -> Table a b

Show b => Show (Table a b)

Defined in Data.Finite.Table

Methods

showsPrec :: Int -> Table a b -> ShowS

show :: Table a b -> String

showList :: [Table a b] -> ShowS

Generic (Table a b)

Defined in Data.Finite.Table

Associated Types

type Rep (Table a b) :: Type -> Type

Methods

from :: Table a b -> Rep (Table a b) x

to :: Rep (Table a b) x -> Table a b

(Finite k, Serialize a) => Serialize (Table k a)

Defined in Data.Finite.Table

Methods

put :: Putter (Table k a)

get :: Get (Table k a)

(Finite a, Default b) => Default (Table a b)

Defined in Data.Finite.Table

Methods

def :: Table a b

NFData a => NFData (Table k a)

Defined in Data.Finite.Table

Methods

rnf :: Table k a -> ()

(Finite a, Portray a, Portray b) => Portray (Table a b)

Pretty-print a Table as a mkTable expression.

    λ> pp $ (tabulate (even . finToInt) :: Table (Fin 3) Bool )
    mkTable (\case { 0 -> True; 1 -> False; 2 -> True })

Defined in Data.Finite.Table

Methods

portray :: Table a b -> Portrayal

portrayList :: [Table a b] -> Portrayal

(Finite a, Portray a, Diff b) => Diff (Table a b)

Defined in Data.Finite.Table

Methods

diff :: Table a b -> Table a b -> Maybe Portrayal

type Rep (Table a)

Defined in Data.Finite.Table

type Rep (Table a) = a

type Rep (Table a b)

Defined in Data.Finite.Table

type Rep (Table a b) = D1 ('MetaData "Table" "Data.Finite.Table" "finite-table-0.1.0.1-80KodpzxmlV375M2yGwzSk" 'True) (C1 ('MetaCons "Table" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vec (Cardinality a) b))))

(!) :: Finite a => Table a b -> a -> b

Infix index, monomorphized.

ix :: Finite a => a -> Lens' (Table a b) b

Lens on a single element.

idTable :: Finite a => Table a a

The identity morphism of a constrained category of Tables.

mkTable :: Finite a => (a -> b) -> Table a b

Monomorphized tabulate. Can be useful for type ambiguity reasons.

lmapTable :: (Finite b, Finite c) => (b -> c) -> Table c a -> Table b a

lmap for a constrained Profunctor.

composeTable :: (Finite a, Finite b) => Table b c -> Table a b -> Table a c

The composition of a constrained category of Tables.

Function Utilities

memoize :: Finite a => (a -> b) -> a -> b

Memoize a function by using a Vec as a lazy lookup table.

Given a function whose argument is a Finite type, return a new function that looks up the argument in a table constructed by applying the original function to every possible value. Since Vec stores its elements boxed, none of the applications of f in the table are forced until they're forced by calling the memoized function and forcing the result.

traverseRep :: forall x a b f. (Finite x, Applicative f) => (a -> f b) -> (x -> a) -> f (x -> b)

traverse a function whose argument is a finite enumerable type.

Representable Utilities

tabulateA :: (Traversable t, Representable t, Applicative f) => (Rep t -> f b) -> f (t b)

Convenience function for building any Representable as if by traverse.

tabulateA f = sequenceA (tabulate f) = traverse f (tabulate id)

retabulated :: (Representable f, Representable g, Rep f ~ Rep g) => Iso (f a) (f b) (g a) (g b)

An Iso between two Representable Functors with the same Rep type.