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def Option.elim {α : Type u_1} {β : Sort u_2} : Option α → β → (α → β) → β

An elimination principle for Option. It is a nondependent version of Option.recOn.

Equations

• Option.elim x x x = match x, x, x with | some x, x_1, f => f x | none, y, x => y

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instance Option.instMembershipOption {α : Type u_1} : Membership α (Option α)

Equations

• Option.instMembershipOption = { mem := fun a b => b = some a }

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@[simp]

theorem Option.mem_def {α : Type u_1} {a : α} {b : Option α} : a ∈ b ↔ b = some a

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theorem Option.isNone_iff_eq_none {α : Type u_1} {o : Option α} : Option.isNone o = true ↔ o = none

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theorem Option.some_inj {α : Type u_1} {a : α} {b : α} : some a = some b ↔ a = b

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@[inline]

def Option.decidable_eq_none {α : Type u_1} {o : Option α} : Decidable (o = none)

o = none is decidable even if the wrapped type does not have decidable equality. This is not an instance because it is not definitionally equal to instance : DecidableEq Option. Try to use o.isNone or o.isSome instead.

Equations

• Option.decidable_eq_none = decidable_of_decidable_of_iff (_ : Option.isNone o = true ↔ o = none)

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instance Option.instForAllOptionDecidableForAllMemInstMembershipOption {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] (o : Option α) : Decidable ((a : α) → a ∈ o → p a)

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• One or more equations did not get rendered due to their size.

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instance Option.instForAllOptionDecidableExistsAndMemInstMembershipOption {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] (o : Option α) : Decidable (∃ a, a ∈ o ∧ p a)

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• One or more equations did not get rendered due to their size.

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def Option.get {α : Type u} (o : Option α) : Option.isSome o = true → α

Extracts the value a from an option that is known to be some a for some a.

Equations

• Option.get x x = match x, x with | some x, x_1 => x

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def Option.guard {α : Type u_1} (p : α → Prop) [inst : DecidablePred p] (a : α) : Option α

guard p a returns some a if p a holds, otherwise none.

Equations

• Option.guard p a = if p a then some a else none

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def Option.toList {α : Type u_1} : Option α → List α

Cast of Option to List. Returns [a] if the input is some a, and [] if it is none.

Equations

• Option.toList x = match x with | none => [] | some a => [a]

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def Option.toArray {α : Type u_1} : Option α → Array α

Cast of Option to Array. Returns [a] if the input is some a, and [] if it is none.

Equations

• Option.toArray x = match x with | none => #[] | some a => #[a]

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def Option.liftOrGet {α : Type u_1} (f : α → α → α) : Option α → Option α → Option α

Two arguments failsafe function. Returns f a b if the inputs are some a and some b, and "does nothing" otherwise.

Equations

• Option.liftOrGet f x x = match x, x with | none, none => none | some a, none => some a | none, some b => some b | some a, some b => some (f a b)

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inductive Option.Rel {α : Type u_1} {β : Type u_2} (r : α → β → Prop) : Option α → Option β → Prop

• If a ~ b, then some a ~ some b

  some: ∀ {α : Type u_1} {β : Type u_2} {r : α → β → Prop} {a : α} {b : β}, r a b → Option.Rel r (some a) (some b)

• none ~ none

  none: ∀ {α : Type u_1} {β : Type u_2} {r : α → β → Prop}, Option.Rel r none none

Lifts a relation α → β → Prop→ β → Prop→ Prop to a relation Option α → Option β → Prop→ Option β → Prop→ Prop by just adding none ~ none.

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def Option.pbind {α : Type u_1} {β : Type u_2} (x : Option α) : ((a : α) → a ∈ x → Option β) → Option β

Partial bind. If for some x : Option α, f : Π (a : α), a ∈ x → Option β∈ x → Option β→ Option β is a partial function defined on a : α giving an Option β, where some a = x, then pbind x f h is essentially the same as bind x f but is defined only when all x = some a, using the proof to apply f.

Equations

• Option.pbind x x = match x, x with | none, x => none | some a, f => f a (_ : some a = some a)

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def Option.pmap {α : Type u_1} {β : Type u_2} {p : α → Prop} (f : (a : α) → p a → β) (x : Option α) : ((a : α) → a ∈ x → p a) → Option β

Partial map. If f : Π a, p a → β→ β is a partial function defined on a : α satisfying p, then pmap f x h is essentially the same as map f x but is defined only when all members of x satisfy p, using the proof to apply f.

Equations

• Option.pmap f x x = match x, x with | none, x => none | some a, H => some (f a (Option.pmap.proof_1 a H))

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@[inline]

def Option.join {α : Type u_1} (x : Option (Option α)) : Option α

Flatten an Option of Option, a specialization of joinM.

Equations

• Option.join x = Option.bind x id

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def Option.forM {m : Type → Type u_1} {α : Type u_2} [inst : Pure m] : Option α → (α → m PUnit) → m PUnit

Map a monadic function which returns Unit over an Option.

Equations

• Option.forM x x = match x, x with | none, x => pure () | some a, f => f a

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instance Option.instForMOption {m : Type → Type u_1} {α : Type u_2} : ForM m (Option α) α

Equations

• Option.instForMOption = { forM := fun [Monad m] => Option.forM }

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instance Option.instForIn'OptionInferInstanceMembershipInstMembershipOption {m : Type u_1 → Type u_2} {α : Type u_3} : ForIn' m (Option α) α inferInstance

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• One or more equations did not get rendered due to their size.

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def Option.mapA {m : Type u_1 → Type u_2} [inst : Applicative m] {α : Type u_3} {β : Type u_1} (f : α → m β) : Option α → m (Option β)

Like Option.mapM but for applicative functors.

Equations

• Option.mapA f x = match x with | none => pure none | some x => some <$> f x

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def Option.sequence {m : Type u → Type u_1} [inst : Monad m] {α : Type u} : Option (m α) → m (Option α)

If you maybe have a monadic computation in a [Monad m] which produces a term of type α, then there is a naturally associated way to always perform a computation in m which maybe produces a result.

Equations

• Option.sequence x = match x with | none => pure none | some fn => some <$> fn

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def Option.elimM {m : Type u_1 → Type u_2} {α : Type u_1} {β : Type u_1} [inst : Monad m] (x : m (Option α)) (y : m β) (z : α → m β) : m β

A monadic analogue of Option.elim.

Equations

• Option.elimM x y z = do let __do_lift ← x Option.elim __do_lift y z

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def Option.getDM {m : Type u_1 → Type u_2} {α : Type u_1} [inst : Monad m] (x : Option α) (y : m α) : m α

A monadic analogue of Option.getD.

Equations

• Option.getDM x y = match x with | some a => pure a | none => y