Dual

libretto.CoreLib.Dual

See theDual companion object

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 ┃
 ┗━━━━━┛                                     ┗━━━━━┛

Attributes

Companion:: object
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Supertypes: class Object
trait Matchable
class Any

Members list

Concise view

Value members

Concrete methods

Law stating that lInvert followed by rInvert is identity.

Attributes

Law stating that rInvert followed by lInvert is identity.

Attributes

Abstract 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   ┟─┘
 ┗━━━━━┛

Attributes

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 ┃
 ┗━━━━━━━┛

Attributes

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