instance Option.instDecidableEqOption : {α : Type u_1} → [inst : DecidableEq α] → DecidableEq (Option α)

Equations

• Option.instDecidableEqOption = Option.decEqOption✝

instance Option.instBEqOption : {α : Type u_1} → [inst : BEq α] → BEq (Option α)

Equations

• Option.instBEqOption = { beq := Option.beqOption✝ }

def Option.toMonad {m : Type u_1 → Type u_2} {α : Type u_1} [Monad m] [Alternative m] : Option α → m α

Equations

• Option.toMonad x = match x with | none => failure | some a => pure a

@[inline]

def Option.toBool {α : Type u_1} : Option α → Bool

Equations

• Option.toBool x = match x with | some val => true | none => false

@[inline]

def Option.isSome {α : Type u_1} : Option α → Bool

Equations

• Option.isSome x = match x with | some val => true | none => false

@[inline]

def Option.isNone {α : Type u_1} : Option α → Bool

Equations

• Option.isNone x = match x with | some val => false | none => true

@[inline]

def Option.isEqSome {α : Type u_1} [BEq α] : Option α → α → Bool

Equations

• Option.isEqSome x✝ x = match x✝, x with | some a, b => a == b | none, x => false

@[inline]

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

Equations

• Option.bind x✝ x = match x✝, x with | none, x => none | some a, b => b a

@[inline]

def Option.mapM {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} [Monad m] (f : α → m β) (o : Option α) : m (Option β)

Equations

• Option.mapM f o = match o with | some a => do let __do_lift ← f a pure (some __do_lift) | x => pure none

theorem Option.map_id {α : Type u_1} : Option.map id = id

@[inline]

def Option.filter {α : Type u_1} (p : α → Bool) : Option α → Option α

Equations

• Option.filter p x = match x with | some a => if p a = true then some a else none | none => none

@[inline]

def Option.all {α : Type u_1} (p : α → Bool) : Option α → Bool

Equations

• Option.all p x = match x with | some a => p a | none => true

@[inline]

def Option.any {α : Type u_1} (p : α → Bool) : Option α → Bool

Equations

• Option.any p x = match x with | some a => p a | none => false

@[macro_inline]

def Option.orElse {α : Type u_1} : Option α → (Unit → Option α) → Option α

Equations

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

instance Option.instOrElseOption {α : Type u_1} : OrElse (Option α)

Equations

• Option.instOrElseOption = { orElse := Option.orElse }

@[inline]

def Option.lt {α : Type u_1} (r : α → α → Prop) : Option α → Option α → Prop

Equations

• Option.lt r x✝ x = match x✝, x with | none, some val => True | some x, some y => r x y | x, x_1 => False

instance Option.instDecidableRelOptionLt {α : Type u_1} (r : α → α → Prop) [s : DecidableRel r] : DecidableRel (Option.lt r)

Equations

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

def Option.merge {α : Type u_1} (fn : α → α → α) : Option α → Option α → Option α

Take a pair of options and if they are both some, apply the given fn to produce an output. Otherwise act like orElse.

Equations

• Option.merge fn x✝ x = match x✝, x with | none, none => none | some x, none => some x | none, some y => some y | some x, some y => some (fn x y)

@[simp]

theorem Option.getD_none : ∀ {α : Type u_1} {a : α}, Option.getD none a = a

@[simp]

theorem Option.getD_some : ∀ {α : Type u_1} {a b : α}, Option.getD (some a) b = a

@[simp]

theorem Option.map_none' {α : Type u_1} {β : Type u_2} (f : α → β) : Option.map f none = none

@[simp]

theorem Option.map_some' {α : Type u_1} {β : Type u_2} (a : α) (f : α → β) : Option.map f (some a) = some (f a)

@[simp]

theorem Option.none_bind {α : Type u_1} {β : Type u_2} (f : α → Option β) : Option.bind none f = none

@[simp]

theorem Option.some_bind {α : Type u_1} {β : Type u_2} (a : α) (f : α → Option β) : Option.bind (some a) f = f a

@[inline]

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✝¹ x✝ x = match x✝¹, x✝, x with | some x, x_1, f => f x | none, y, x => y

@[inline]

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

@[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.

Equations

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

@[inline]

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]

@[inline]

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]

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)

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

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

• 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

@[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

@[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.

Equations

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

@[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.

Equations

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

@[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.

Equations

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

@[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.

Equations

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

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

Equations

• ⋯ = ⋯

@[simp]

theorem Option.all_none : ∀ {α : Type u_1} {p : α → Bool}, Option.all p none = true

@[simp]

theorem Option.all_some : ∀ {α : Type u_1} {p : α → Bool} {x : α}, Option.all p (some x) = p x

def Option.min {α : Type u_1} [Min α] : Option α → Option α → Option α

The minimum of two optional values.

Equations

• Option.min x✝ x = match x✝, x with | some x, some y => some (min x y) | some x, none => some x | none, some y => some y | none, none => none

instance Option.instMinOption {α : Type u_1} [Min α] : Min (Option α)

Equations

• Option.instMinOption = { min := Option.min }

@[simp]

theorem Option.min_some_some {α : Type u_1} [Min α] {a : α} {b : α} : min (some a) (some b) = some (min a b)

@[simp]

theorem Option.min_some_none {α : Type u_1} [Min α] {a : α} : min (some a) none = some a

@[simp]

theorem Option.min_none_some {α : Type u_1} [Min α] {b : α} : min none (some b) = some b

@[simp]

theorem Option.min_none_none {α : Type u_1} [Min α] : min none none = none

def Option.max {α : Type u_1} [Max α] : Option α → Option α → Option α

The maximum of two optional values.

Equations

• Option.max x✝ x = match x✝, x with | some x, some y => some (max x y) | some x, none => some x | none, some y => some y | none, none => none

instance Option.instMaxOption {α : Type u_1} [Max α] : Max (Option α)

Equations

• Option.instMaxOption = { max := Option.max }

@[simp]

theorem Option.max_some_some {α : Type u_1} [Max α] {a : α} {b : α} : max (some a) (some b) = some (max a b)

@[simp]

theorem Option.max_some_none {α : Type u_1} [Max α] {a : α} : max (some a) none = some a

@[simp]

theorem Option.max_none_some {α : Type u_1} [Max α] {b : α} : max none (some b) = some b

@[simp]

theorem Option.max_none_none {α : Type u_1} [Max α] : max none none = none

instance instLTOption {α : Type u_1} [LT α] : LT (Option α)

Equations

• instLTOption = { lt := Option.lt fun (x x_1 : α) => x < x_1 }

@[always_inline]

instance instFunctorOption : Functor Option

Equations

• instFunctorOption = { map := fun {α β : Type u_1} => Option.map, mapConst := fun {α β : Type u_1} => Option.map ∘ Function.const β }

@[always_inline]

instance instMonadOption : Monad Option

Equations

• instMonadOption = Monad.mk

@[always_inline]

instance instAlternativeOption : Alternative Option

Equations

• instAlternativeOption = Alternative.mk (fun {α : Type u_1} => none) fun {α : Type u_1} => Option.orElse

def liftOption {m : Type u_1 → Type u_2} {α : Type u_1} [Alternative m] : Option α → m α

Equations

• liftOption x = match x with | some a => pure a | none => failure

@[inline]

def Option.tryCatch {α : Type u_1} (x : Option α) (handle : Unit → Option α) : Option α

Equations

• Option.tryCatch x handle = match x with | some val => x | none => handle ()

instance instMonadExceptOfUnitOption : MonadExceptOf Unit Option

Equations

• instMonadExceptOfUnitOption = { throw := fun {α : Type u_1} (x : Unit) => none, tryCatch := fun {α : Type u_1} => Option.tryCatch }