Goal.Geometry.Set

A module for describing Sets of Elements. Necessary in a few cases (such as discrete sets) that Manifolds don't handle well.

Sets

class (Eq s, Eq (Element s)) => Set s

Sets are collections of distinguishable Elements.

Associated Types

type Element s :: *

Instances

Set Continuum

Set Euclidean

Set Boolean

Set Integers

Set NaturalNumbers

Eq k => Set [k]

Set s => Set (Replicated s)

(Set s, Set r) => Set (s, r)

Manifold m => Set (Embedded m c)

class Set s => Discrete s where

A Discrete Set is one where we can list its elements. The returned list should satisfy the law

elements s = nub $ elements s

Methods

elements :: s -> [Element s]

Instances

Discrete Boolean

Discrete Integers

Discrete NaturalNumbers

Eq k => Discrete [k]

Discrete s => Discrete (Replicated s)

Instances

Discrete

data Boolean

True and False.

Constructors

Boolean

Instances

Eq Boolean

Read Boolean

Show Boolean

Discrete Boolean

Set Boolean

type Element Boolean = Bool

data NaturalNumbers

The set of natural numbers.

Constructors

NaturalNumbers

Instances

Eq NaturalNumbers

Read NaturalNumbers

Show NaturalNumbers

Discrete NaturalNumbers

Set NaturalNumbers

type Element NaturalNumbers = Int

data Integers

The set of integers.

Constructors

Integers

Instances

Eq Integers

Read Integers

Show Integers

Discrete Integers

Set Integers

type Element Integers = Int

Continuous

type Coordinates = Vector Double

Elements of Euclidean spaces are referred to as Coordinates.

newtype Euclidean

Euclidean space.

Constructors

Euclidean Int

Instances

Eq Euclidean

Read Euclidean

Show Euclidean

Set Euclidean

Manifold Euclidean

Riemannian Cartesian Euclidean

Transition Polar Cartesian Euclidean

Transition Cartesian Polar Euclidean

type Element Euclidean = Coordinates

data Continuum

One dimensional Euclidean space.

Constructors

Continuum

Instances

Eq Continuum

Read Continuum

Show Continuum

Set Continuum

Manifold Continuum

Riemannian Cartesian Continuum

type Element Continuum = Double

Combinators

Replicated

data Replicated m

A Replicated set is a single set multiplied a specified number of times via the Cartesian product.

Constructors

Replicated !m !Int

Instances

(Manifold m, Riemannian c m) => Riemannian c (Replicated m)

Legendre c m => Legendre c (Replicated m)

Eq m => Eq (Replicated m)

Read m => Read (Replicated m)

Show m => Show (Replicated m)

Discrete s => Discrete (Replicated s)

Set s => Set (Replicated s)

Manifold m => Manifold (Replicated m)

type Element (Replicated s) = [Element s]