Idris2/libs/contrib/Data/Void.idr

module Data.Void

export
absurdity : Uninhabited t => (0 _ : t) -> s
absurdity x = void (uninhabited x)

export
contradiction : (Uninhabited t) => (0 _ : x -> t) -> (x -> s)
contradiction since x = absurdity (since x)
[contrib] Add misc libraries to contrib (#667) * [contrib] Add misc libraries to contrib Expose some `private` function in libs/base that I needed, and seem like their visibility was forgotten I'd appreciate a code review, especially to tell me I'm re-implementing something that's already elsewhere in the library Mostly extending existing functionality: * `Data/Void.idr`: add some utility functions for manipulating absurdity. * `Decidable/Decidable/Extra.idr`: add support for double negation elimination in decidable relations * `Data/Fun/Extra.idr`: + add `application` (total and partil) for n-ary functions + add (slightly) dependent versions of these operations * `Decidable/Order/Strict.idr`: a strict preorder is what you get when you remove the diagonal from a pre-order. For example, `<` is the associated preorder for `<=` over `Nat`. Analogous to `Decidable.Order`. The proof search mechanism struggled a bit, so I had to hack it --- sorry. Eventually we should move `Data.Fun.Extra.Pointwise` to `Data.Vect.Quantifiers` in base but we don't have any interesting uses for it at the moment so it's not urgent. Co-authored by @gallais 2020-09-14 18:22:46 +03:00			`module Data.Void`

			`export`
			`absurdity : Uninhabited t => (0 _ : t) -> s`
			`absurdity x = void (uninhabited x)`

			`export`
			`contradiction : (Uninhabited t) => (0 _ : x -> t) -> (x -> s)`
			`contradiction since x = absurdity (since x)`