51 lines
1.5 KiB
Text
51 lines
1.5 KiB
Text
import Init.Control.Option
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universes u v
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def OptionT2 (m : Type u → Type v) (α : Type u) : Type v :=
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m (Option α)
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namespace OptionT2
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variable {m : Type u → Type v} [Monad m] {α β : Type u}
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@[inline] protected def bind (ma : OptionT2 m α) (f : α → OptionT2 m β) : OptionT2 m β :=
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(do {
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let a? ← ma;
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(match a? with
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| some a => f a
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| none => pure none)
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} : m (Option β))
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@[inline] protected def pure (a : α) : OptionT2 m α :=
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(Pure.pure (some a) : m (Option α))
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@[inline] protected def orelse (ma : OptionT2 m α) (mb : OptionT2 m α) : OptionT2 m α :=
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(do { let a? ← ma;
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(match a? with
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| some a => pure (some a)
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| _ => mb) } : m (Option α))
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@[inline] protected def fail : OptionT2 m α :=
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(pure none : m (Option α))
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end OptionT2
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instance optMonad1 {m} [Monad m] : Monad (OptionT2 m) :=
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{ pure := OptionT2.pure, bind := OptionT2.bind }
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def optMonad2 {m} [Monad m] : Monad (OptionT m) :=
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{ pure := OptionT.pure, bind := OptionT.bind }
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def optAlt1 {m} [Monad m] : Alternative (OptionT m) :=
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{ failure := OptionT.fail,
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orElse := OptionT.orElse,
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toApplicative := Monad.toApplicative }
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def optAlt2 {m} [Monad m] : Alternative (OptionT m) :=
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⟨OptionT.fail, OptionT.orElse⟩ -- it works because it treats `toApplicative` as an instance implicit argument
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def optAlt3 {m} [Monad m] : Alternative (OptionT2 m) :=
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{ failure := OptionT2.fail,
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orElse := OptionT2.orelse,
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toApplicative := Monad.toApplicative }
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