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feat: Void.get_mk #13894

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feat: Void.get_mk #13894

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32 changes: 27 additions & 5 deletions src/Init/System/ST.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -12,15 +12,37 @@ import Init.Classical

public section

opaque Void.nonemptyType (σ : Type) : NonemptyType.{0}
structure VoidSpec (σ : Type) (α : Type) where
private mk' ::
mk : σ → α
get : α → σ
get_mk {x} : get (mk x) = x

@[expose] def Void (σ : Type) : Type := Void.nonemptyType σ |>.type
opaque Void.nonemptyType (σ : Type) : Subtype (Nonempty <| VoidSpec σ ·) := ⟨σ, ⟨{
mk := id
get := id
get_mk := rfl
}⟩⟩

instance Void.instNonempty : Nonempty (Void σ) :=
by exact (Void.nonemptyType σ).property
@[expose] def Void (σ : Type) : Type := Void.nonemptyType σ |>.val

namespace Void

private noncomputable def spec (σ : Type) :=
Classical.choice (nonemptyType σ).property

instance instNonempty [Nonempty σ] : Nonempty (Void σ) :=
by exact .intro <| (spec σ).mk Classical.ofNonempty

@[extern "lean_void_mk", never_extract]
opaque Void.mk (x : σ) : Void σ
def mk (x : σ) : Void σ := (spec σ).mk x

noncomputable def get (x : Void σ) : σ := (spec σ).get x

@[simp, grind =] theorem get_mk {x : σ} : get (mk x) = x :=
(spec σ).get_mk

end Void

structure ST.Out (σ : Type) (α : Type) where
val : α
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