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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.

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

@[simp]

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

instance Option.instDecidableMemOptionInstMembershipOption {α : Type u_1} [DecidableEq α] (j : α) (o : Option α) : Decidable (j ∈ o)

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

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

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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.

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

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

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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.

@[inline]

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

guard p a returns some a if p a holds, otherwise 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.

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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.

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.

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

• 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)

  If a ~ b, then some a ~ some b

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

  none ~ none

Lifts a relation α → β → Prop to a relation Option α → Option β → 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 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.

@[inline]

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 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.

@[inline]

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

Flatten an Option of Option, a specialization of joinM.

@[inline]

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

Map a monadic function which returns Unit over an Option.

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

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

@[inline]

def Option.mapA {m : Type u_1 → Type u_2} [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.

@[inline]

def Option.sequence {m : Type u → Type u_1} [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.

@[inline]

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

A monadic analogue of Option.elim.

@[inline]

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

A monadic analogue of Option.getD.

instance Option.instLawfulBEqOptionInstBEqOption (α : Type u_1) [BEq α] [LawfulBEq α] : LawfulBEq (Option α)