Decidable and Monad instances for List not (yet) in Std

theorem List.bind_singleton {α : Type u} {β : Type v} (f : α → List β) (x : α) : List.bind [x] f = f x

@[simp]

theorem List.bind_singleton' {α : Type u} (l : List α) : (List.bind l fun (x : α) => [x]) = l

theorem List.map_eq_bind {α : Type u_1} {β : Type u_2} (f : α → β) (l : List α) : List.map f l = List.bind l fun (x : α) => [f x]

theorem List.bind_assoc {γ : Type w} {α : Type u_1} {β : Type u_2} (l : List α) (f : α → List β) (g : β → List γ) : List.bind (List.bind l f) g = List.bind l fun (x : α) => List.bind (f x) g

instance List.instMonad : Monad List

Equations

• List.instMonad = Monad.mk

@[simp]

theorem List.pure_def {α : Type u} (a : α) : pure a = [a]

instance List.instLawfulMonad : LawfulMonad List

Equations

• List.instLawfulMonad = ⋯

instance List.instAlternative : Alternative List

Equations

• List.instAlternative = Alternative.mk @List.nil fun {α : Type u} (l : List α) (l' : Unit → List α) => List.append l (l' ())

instance List.decidableBex {α : Type u} {p : α → Prop} [DecidablePred p] (l : List α) : Decidable (∃ (x : α), x ∈ l ∧ p x)

Equations

• One or more equations did not get rendered due to their size.
• List.decidableBex [] = isFalse ⋯

instance List.decidableBall {α : Type u} {p : α → Prop} [DecidablePred p] (l : List α) : Decidable (∀ (x : α), x ∈ l → p x)

Equations

• List.decidableBall l = match inferInstance with | isFalse h => isTrue ⋯ | isTrue h => isFalse ⋯