/Я language (β)/Behaviour/First/

> First : forall t e . t `C'AR__` t `L` Stops e `T` _

Interpretation: this label point to a first item that does exist.

Demonstration: Arrow component relating to a First item in a List:

> derive `ha` First `har___` Null `ho'vt` Unit `ryo` Enter = Empty `har` Unit
> derive `ha` First `har___` Only `ho'ut'st` A `_ryo` Enter = Exist `har'st` A

Demonstration: Scope components relating to a First item in a List:

> this `ha` within `ha` First `har___` Null `ho'vt` Unit `ryo` Enter = Empty `har` Unit
> this `ha` within `ha` First `har___` Only `ho'ut'st` B `_ryo` Enter = Exist `har'st` A
> that `ha` within `ha` First `har___` Null `ho'vt` Unit `ryo` Enter `har___` Empty `har` Unit = Null `ho'vt` Unit `ryo` Enter
> that `ha` within `ha` First `har___` Null `ho'vt` Unit `ryo` Enter `har___` Exist `har'st` A = Null `ho'vt` Unit `ryo` Enter
> that `ha` within `ha` First `har___` Only `ho'ut'st` B `_ryo` Enter `har___` Empty `har` Unit = Null `ho'vt` Unit `ryo` Enter
> that `ha` within `ha` First `har___` Only `ho'ut'st` B `_ryo` Enter `har___` Exist `har'st` A = Only `ho'ut'st` A `_ryo` Enter

Demonstration: converting a Product of Maybe items into Maybe of Sum of these items:

> Exist `har'st` A `hjd__'dcps` First `ha` Exist `har'st` B = Exist `ha` This `har'st` A
> Empty `har` Unit `hjd_'dcps` First `ha` Exist `har'st` B = Exist `ha` That `har'st` B
> Empty `har` Unit `hjd_'dcps` First `ha` Empty `har` Unit = Empty `har` Unit
> Exist `har'st` A `hjd__'dcps` First `ha` Empty `har` Unit = Exist `ha` This `har'st` A

Demonstration: converting a Product of Stops items into Stops of Sum of these items:

> Valid `har'st` A `hjd_'dcps` First `ha` Valid `har'st` B = Valid `ha` This `har'st` A
> Error `har'st` A `hjd_'dcps` First `ha` Valid `har'st` B = Valid `ha` That `har'st` B
> Error `har'st` A `hjd_'dcps` First `ha` Error `har'st` B = Error `har'st` A
> Valid `har'st` A `hjd_'dcps` First `ha` Error `har'st` B = Valid `ha` This `har'st` A

Counterpart: label that points to an item that does not exist yet is Fresh.