cartesian -package:monoidal-functors

The Cartesian coordinate system. Coordinates are (x,y,z).

LPFP-core LPFPCore LPFPCore.CoordinateSystems

class (Category k, Monoid (UnitObject k), Object k (UnitObject k)) => Cartesian k

constrained-categories Control.Category.Constrained Control.Category.Constrained.Prelude

Quite a few categories (monoidal categories) will permit "products" of objects as objects again – in the Haskell sense those are tuples – allowing for "dyadic morphisms" (x,y) ~> r. Together with a unique UnitObject, this makes for a monoidal structure, with a few natural isomorphisms. Ordinary tuples may not always be powerful enough to express the product objects; we avoid making a dedicated associated type for the sake of simplicity, but allow for an extra constraint to be imposed on objects prior to consideration of pair-building. The name Cartesian is disputable: in category theory that would rather Imply cartesian closed category (which we represent with Curry). Monoidal would make sense, but we reserve that to Functors.

package Cartesian

Uses

Not on Stackage, so not searched. Coordinate systems

cartesianProduct :: Set a -> Set b -> Set (a, b)

containers Data.Set Data.Set.Internal

Calculate the Cartesian product of two sets.

cartesianProduct xs ys = fromList $ liftA2 (,) (toList xs) (toList ys)

Example:

cartesianProduct (fromList [1,2]) (fromList ['a','b']) =
fromList [(1,'a'), (1,'b'), (2,'a'), (2,'b')]

cartesianFromCube :: Cube sh -> (sh, sh, sh)

comfort-array Data.Array.Comfort.Shape

cartesianFromSquare :: Square sh -> (sh, sh)

comfort-array Data.Array.Comfort.Shape

cartesianProductWith :: Ord c => (a -> b -> c) -> Set a -> Set b -> Set c

algebraic-graphs Algebra.Graph.Internal

Compute the Cartesian product of two sets, applying a function to each resulting pair.

cartesianProduct :: (a -> b -> c) -> [a] -> [b] -> [c]

universe-base Data.Universe.Helpers

Slightly unfair 2-way Cartesian product: given two (possibly infinite) lists, produce a single list such that whenever v and w have finite indices in the input lists, (v,w) has finite index in the output list. Lower indices occur as the fst part of the tuple more frequently, but not exponentially so.

cartesianProduct :: NESet a -> NESet b -> NESet (a, b)

nonempty-containers Data.Set.NonEmpty

Calculate the Cartesian product of two sets.

cartesianProduct xs ys = fromList $ liftA2 (,) (toList xs) (toList ys)

Example:

cartesianProduct (fromList (1:|[2])) (fromList ('a':|['b'])) =
fromList ((1,'a') :| [(1,'b'), (2,'a'), (2,'b')])

cartesianFromSquare :: T (Square sh) -> T (sh, sh)

comfort-blas Numeric.BLAS.Slice

cartesianCoordinates :: Position -> (Double, Double, Double)

learn-physics Physics.Learn Physics.Learn.Position

Returns the three Cartesian coordinates as a triple from a position.

cartesianCoordinates :: Position -> (R, R, R)

LPFP-core LPFPCore LPFPCore.CoordinateSystems

cartesianProduct :: forall s t a b . (KnownSet s a, KnownSet t b) => SomeSetWith (ProductProof 'Regular s t) (a, b)

refined-containers Data.Set.Refined

Cartesian product of two sets. The elements are all pairs (x, y) for each x from s and for each y from t.

class (Morphism k, HasAgent k) => CartesianAgent k

constrained-categories Control.Arrow.Constrained

CartesianAttachUnit :: (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReCartesian k α (α, u)

constrained-categories Control.Category.Constrained.Reified

CartesianCompo :: Object k β => ReCartesian k α β -> ReCartesian k β γ -> ReCartesian k α γ

constrained-categories Control.Category.Constrained.Reified

CartesianDetachUnit :: (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReCartesian k (α, u) α

constrained-categories Control.Category.Constrained.Reified

CartesianId :: Object k α => ReCartesian k α α

constrained-categories Control.Category.Constrained.Reified

CartesianRegroup :: (ObjectPair k α β, ObjectPair k β γ, ObjectPair k α (β, γ), ObjectPair k (α, β) γ) => ReCartesian k (α, (β, γ)) ((α, β), γ)

constrained-categories Control.Category.Constrained.Reified

CartesianRegroup_ :: (ObjectPair k α β, ObjectPair k β γ, ObjectPair k α (β, γ), ObjectPair k (α, β) γ) => ReCartesian k ((α, β), γ) (α, (β, γ))

constrained-categories Control.Category.Constrained.Reified

CartesianSwap :: (ObjectPair k α β, ObjectPair k β α) => ReCartesian k (α, β) (β, α)

constrained-categories Control.Category.Constrained.Reified

unfairCartesianProduct :: (a -> b -> c) -> [a] -> [b] -> [c]

universe-base Data.Universe.Helpers

Very unfair 2-way Cartesian product: same guarantee as the slightly unfair one, except that lower indices may occur as the fst part of the tuple exponentially more frequently.