Dual

trait Dual[A, B]

Evidence that A flowing in one direction is equivalent to to B flowing in the opposite direction. It must hold that

       ┏━━━━━┓                         ┏━━━━━┓
       ┞─┐ r ┃                         ┃  l  ┞─┐
       ╎A│ I ┃                         ┃  I  ╎B│
       ┟─┘ n ┃                         ┃  n  ┟─┘
 ┏━━━━━┫   v ┃     ┏━━━━━━━━━┓         ┃  v  ┣━━━━━┓     ┏━━━━━━━━━┓
 ┃  l  ┞─┐ e ┃     ┞─┐       ┞─┐       ┃  e  ┞─┐ r ┃     ┞─┐       ┞─┐
 ┃  I  ╎B│ r ┃  =  ╎A│ id[A] ╎A│       ┃  r  ╎A│ I ┃  =  ╎B│ id[B] ╎B│
 ┃  n  ┟─┘ t ┃     ┟─┘       ┟─┘       ┃  t  ┟─┘ n ┃     ┟─┘       ┟─┘
 ┃  v  ┣━━━━━┛     ┗━━━━━━━━━┛         ┗━━━━━┫   v ┃     ┗━━━━━━━━━┛
 ┃  e  ┞─┐                                   ┞─┐ e ┃
 ┃  r  ╎A│                                   ╎B│ r ┃
 ┃  t  ┟─┘                                   ┟─┘ t ┃
 ┗━━━━━┛                                     ┗━━━━━┛

Companion: object

class Object

trait Matchable

class Any

Value members

Methods

Law stating that lInvert followed by rInvert is identity.

Law stating that rInvert followed by lInvert is identity.

Fields

Reverses the output that flows against the -⚬ arrow (say it is the B output) to its dual (A) flowing in the direction of the arrow.

 ┏━━━━━┓
 ┃ l   ┞─┐
 ┃ I ┌─╎B│
 ┃ n ┆ ┟─┘
 ┃ v ┆ ┃
 ┃ e ┆ ┞─┐
 ┃ r └→╎A│
 ┃ t   ┟─┘
 ┗━━━━━┛

Reverses the input that flows along the -⚬ arrow (say it is the A input) to its dual (B) flowing against the direction of the arrow.

 ┏━━━━━━━┓
 ┞─┐   r ┃
 ╎A│─┐ I ┃
 ┟─┘ ┆ n ┃
 ┃   ┆ v ┃
 ┞─┐ ┆ e ┃
 ╎B│←┘ r ┃
 ┟─┘   t ┃
 ┗━━━━━━━┛