inductive Batteries.AssocList (α : Type u) (β : Type v) : Type (max u v)

AssocList α β is "the same as" List (α × β), but flattening the structure leads to one fewer pointer indirection (in the current code generator). It is mainly intended as a component of HashMap, but it can also be used as a plain key-value map.

• nil: {α : Type u} → {β : Type v} → Batteries.AssocList α β

  An empty list

• cons: {α : Type u} → {β : Type v} → α → β → Batteries.AssocList α β → Batteries.AssocList α β

  Add a key, value pair to the list

instance Batteries.instInhabitedAssocList : {a : Type u_1} → {a_1 : Type u_2} → Inhabited (Batteries.AssocList a a_1)

Equations

• Batteries.instInhabitedAssocList = { default := Batteries.AssocList.nil }

def Batteries.AssocList.toList {α : Type u_1} {β : Type u_2} : Batteries.AssocList α β → List (α × β)

O(n). Convert an AssocList α β into the equivalent List (α × β). This is used to give specifications for all the AssocList functions in terms of corresponding list functions.

Equations

• Batteries.AssocList.nil.toList = []
• (Batteries.AssocList.cons a b es).toList = (a, b) :: es.toList

instance Batteries.AssocList.instEmptyCollection {α : Type u_1} {β : Type u_2} : EmptyCollection (Batteries.AssocList α β)

Equations

• Batteries.AssocList.instEmptyCollection = { emptyCollection := Batteries.AssocList.nil }

@[simp]

theorem Batteries.AssocList.empty_eq {α : Type u_1} {β : Type u_2} : ∅ = Batteries.AssocList.nil

def Batteries.AssocList.isEmpty {α : Type u_1} {β : Type u_2} : Batteries.AssocList α β → Bool

O(1). Is the list empty?

Equations

• Batteries.AssocList.nil.isEmpty = true
• x.isEmpty = false

@[simp]

theorem Batteries.AssocList.isEmpty_eq {α : Type u_1} {β : Type u_2} (l : Batteries.AssocList α β) : l.isEmpty = l.toList.isEmpty

def Batteries.AssocList.length {α : Type u_1} {β : Type u_2} (L : Batteries.AssocList α β) : Nat

The number of entries in an AssocList.

Equations

• Batteries.AssocList.nil.length = 0
• (Batteries.AssocList.cons a b es).length = es.length + 1

@[simp]

theorem Batteries.AssocList.length_nil {α : Type u_1} {β : Type u_2} : Batteries.AssocList.nil.length = 0

@[simp]

theorem Batteries.AssocList.length_cons : ∀ {α : Type u_1} {a : α} {β : Type u_2} {b : β} {t : Batteries.AssocList α β}, (Batteries.AssocList.cons a b t).length = t.length + 1

theorem Batteries.AssocList.length_toList {α : Type u_1} {β : Type u_2} (l : Batteries.AssocList α β) : l.toList.length = l.length

@[specialize #[]]

def Batteries.AssocList.foldlM {m : Type u_1 → Type u_2} {δ : Type u_1} {α : Type u_3} {β : Type u_4} [Monad m] (f : δ → α → β → m δ) (init : δ) : Batteries.AssocList α β → m δ

O(n). Fold a monadic function over the list, from head to tail.

Equations

• Batteries.AssocList.foldlM f x Batteries.AssocList.nil = pure x
• Batteries.AssocList.foldlM f x (Batteries.AssocList.cons a b es) = do let __do_lift ← f x a b Batteries.AssocList.foldlM f __do_lift es

@[simp]

theorem Batteries.AssocList.foldlM_eq {m : Type u_1 → Type u_2} {δ : Type u_1} {α : Type u_3} {β : Type u_4} [Monad m] (f : δ → α → β → m δ) (init : δ) (l : Batteries.AssocList α β) : Batteries.AssocList.foldlM f init l = List.foldlM (fun (d : δ) (x : α × β) => match x with | (a, b) => f d a b) init l.toList

@[inline]

def Batteries.AssocList.foldl {δ : Type u_1} {α : Type u_2} {β : Type u_3} (f : δ → α → β → δ) (init : δ) (as : Batteries.AssocList α β) : δ

O(n). Fold a function over the list, from head to tail.

Equations

• Batteries.AssocList.foldl f init as = (Batteries.AssocList.foldlM f init as).run

@[simp]

theorem Batteries.AssocList.foldl_eq {δ : Type u_1} {α : Type u_2} {β : Type u_3} (f : δ → α → β → δ) (init : δ) (l : Batteries.AssocList α β) : Batteries.AssocList.foldl f init l = List.foldl (fun (d : δ) (x : α × β) => match x with | (a, b) => f d a b) init l.toList

def Batteries.AssocList.toListTR {α : Type u_1} {β : Type u_2} (as : Batteries.AssocList α β) : List (α × β)

Optimized version of toList.

Equations

• as.toListTR = (Batteries.AssocList.foldl (fun (r : Array (α × β)) (a : α) (b : β) => r.push (a, b)) #[] as).toList

@[csimp]

theorem Batteries.AssocList.toList_eq_toListTR : @Batteries.AssocList.toList = @Batteries.AssocList.toListTR

@[specialize #[]]

def Batteries.AssocList.forM {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} [Monad m] (f : α → β → m PUnit) : Batteries.AssocList α β → m PUnit

O(n). Run monadic function f on all elements in the list, from head to tail.

Equations

• Batteries.AssocList.forM f Batteries.AssocList.nil = pure PUnit.unit
• Batteries.AssocList.forM f (Batteries.AssocList.cons a b es) = do f a b Batteries.AssocList.forM f es

@[simp]

theorem Batteries.AssocList.forM_eq {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} [Monad m] (f : α → β → m PUnit) (l : Batteries.AssocList α β) : Batteries.AssocList.forM f l = l.toList.forM fun (x : α × β) => match x with | (a, b) => f a b

def Batteries.AssocList.mapKey {α : Type u_1} {δ : Type u_2} {β : Type u_3} (f : α → δ) : Batteries.AssocList α β → Batteries.AssocList δ β

O(n). Map a function f over the keys of the list.

Equations

• Batteries.AssocList.mapKey f Batteries.AssocList.nil = Batteries.AssocList.nil
• Batteries.AssocList.mapKey f (Batteries.AssocList.cons a b es) = Batteries.AssocList.cons (f a) b (Batteries.AssocList.mapKey f es)

@[simp]

theorem Batteries.AssocList.toList_mapKey {α : Type u_1} {δ : Type u_2} {β : Type u_3} (f : α → δ) (l : Batteries.AssocList α β) : (Batteries.AssocList.mapKey f l).toList = List.map (fun (x : α × β) => match x with | (a, b) => (f a, b)) l.toList

@[simp]

theorem Batteries.AssocList.length_mapKey : ∀ {α : Type u_1} {α_1 : Type u_2} {f : α → α_1} {β : Type u_3} {l : Batteries.AssocList α β}, (Batteries.AssocList.mapKey f l).length = l.length

def Batteries.AssocList.mapVal {α : Type u_1} {β : Type u_2} {δ : Type u_3} (f : α → β → δ) : Batteries.AssocList α β → Batteries.AssocList α δ

O(n). Map a function f over the values of the list.

Equations

• Batteries.AssocList.mapVal f Batteries.AssocList.nil = Batteries.AssocList.nil
• Batteries.AssocList.mapVal f (Batteries.AssocList.cons a b es) = Batteries.AssocList.cons a (f a b) (Batteries.AssocList.mapVal f es)

@[simp]

theorem Batteries.AssocList.toList_mapVal {α : Type u_1} {β : Type u_2} {δ : Type u_3} (f : α → β → δ) (l : Batteries.AssocList α β) : (Batteries.AssocList.mapVal f l).toList = List.map (fun (x : α × β) => match x with | (a, b) => (a, f a b)) l.toList

@[simp]

theorem Batteries.AssocList.length_mapVal : ∀ {α : Type u_1} {β : Type u_2} {β_1 : Type u_3} {f : α → β → β_1} {l : Batteries.AssocList α β}, (Batteries.AssocList.mapVal f l).length = l.length

@[specialize #[]]

def Batteries.AssocList.findEntryP? {α : Type u_1} {β : Type u_2} (p : α → β → Bool) : Batteries.AssocList α β → Option (α × β)

O(n). Returns the first entry in the list whose entry satisfies p.

Equations

• Batteries.AssocList.findEntryP? p Batteries.AssocList.nil = none
• Batteries.AssocList.findEntryP? p (Batteries.AssocList.cons a b es) = bif p a b then some (a, b) else Batteries.AssocList.findEntryP? p es

@[simp]

theorem Batteries.AssocList.findEntryP?_eq {α : Type u_1} {β : Type u_2} (p : α → β → Bool) (l : Batteries.AssocList α β) : Batteries.AssocList.findEntryP? p l = List.find? (fun (x : α × β) => match x with | (a, b) => p a b) l.toList

@[inline]

def Batteries.AssocList.findEntry? {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : Option (α × β)

O(n). Returns the first entry in the list whose key is equal to a.

Equations

• Batteries.AssocList.findEntry? a l = Batteries.AssocList.findEntryP? (fun (k : α) (x : β) => k == a) l

@[simp]

theorem Batteries.AssocList.findEntry?_eq {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : Batteries.AssocList.findEntry? a l = List.find? (fun (x : α × β) => x.fst == a) l.toList

def Batteries.AssocList.find? {α : Type u_1} {β : Type u_2} [BEq α] (a : α) : Batteries.AssocList α β → Option β

O(n). Returns the first value in the list whose key is equal to a.

Equations

• Batteries.AssocList.find? a Batteries.AssocList.nil = none
• Batteries.AssocList.find? a (Batteries.AssocList.cons a_1 b es) = match a_1 == a with | true => some b | false => Batteries.AssocList.find? a es

theorem Batteries.AssocList.find?_eq_findEntry? {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : Batteries.AssocList.find? a l = Option.map (fun (x : α × β) => x.snd) (Batteries.AssocList.findEntry? a l)

@[simp]

theorem Batteries.AssocList.find?_eq {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : Batteries.AssocList.find? a l = Option.map (fun (x : α × β) => x.snd) (List.find? (fun (x : α × β) => x.fst == a) l.toList)

@[specialize #[]]

def Batteries.AssocList.any {α : Type u_1} {β : Type u_2} (p : α → β → Bool) : Batteries.AssocList α β → Bool

O(n). Returns true if any entry in the list satisfies p.

Equations

• Batteries.AssocList.any p Batteries.AssocList.nil = false
• Batteries.AssocList.any p (Batteries.AssocList.cons a b es) = (p a b || Batteries.AssocList.any p es)

@[simp]

theorem Batteries.AssocList.any_eq {α : Type u_1} {β : Type u_2} (p : α → β → Bool) (l : Batteries.AssocList α β) : Batteries.AssocList.any p l = l.toList.any fun (x : α × β) => match x with | (a, b) => p a b

@[specialize #[]]

def Batteries.AssocList.all {α : Type u_1} {β : Type u_2} (p : α → β → Bool) : Batteries.AssocList α β → Bool

O(n). Returns true if every entry in the list satisfies p.

Equations

• Batteries.AssocList.all p Batteries.AssocList.nil = true
• Batteries.AssocList.all p (Batteries.AssocList.cons a b es) = (p a b && Batteries.AssocList.all p es)

@[simp]

theorem Batteries.AssocList.all_eq {α : Type u_1} {β : Type u_2} (p : α → β → Bool) (l : Batteries.AssocList α β) : Batteries.AssocList.all p l = l.toList.all fun (x : α × β) => match x with | (a, b) => p a b

def Batteries.AssocList.All {α : Type u_1} {β : Type u_2} (p : α → β → Prop) (l : Batteries.AssocList α β) : Prop

Returns true if every entry in the list satisfies p.

Equations

• Batteries.AssocList.All p l = ∀ (a : α × β), a ∈ l.toList → p a.fst a.snd

@[inline]

def Batteries.AssocList.contains {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : Bool

O(n). Returns true if there is an element in the list whose key is equal to a.

Equations

• Batteries.AssocList.contains a l = Batteries.AssocList.any (fun (k : α) (x : β) => k == a) l

@[simp]

theorem Batteries.AssocList.contains_eq {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : Batteries.AssocList.contains a l = l.toList.any fun (x : α × β) => x.fst == a

def Batteries.AssocList.replace {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (b : β) : Batteries.AssocList α β → Batteries.AssocList α β

O(n). Replace the first entry in the list with key equal to a to have key a and value b.

Equations

• One or more equations did not get rendered due to their size.
• Batteries.AssocList.replace a b Batteries.AssocList.nil = Batteries.AssocList.nil

@[simp]

theorem Batteries.AssocList.toList_replace {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (b : β) (l : Batteries.AssocList α β) : (Batteries.AssocList.replace a b l).toList = List.replaceF (fun (x : α × β) => bif x.fst == a then some (a, b) else none) l.toList

@[simp]

theorem Batteries.AssocList.length_replace {α : Type u_1} : ∀ {β : Type u_2} {b : β} {l : Batteries.AssocList α β} [inst : BEq α] {a : α}, (Batteries.AssocList.replace a b l).length = l.length

@[specialize #[]]

def Batteries.AssocList.eraseP {α : Type u_1} {β : Type u_2} (p : α → β → Bool) : Batteries.AssocList α β → Batteries.AssocList α β

O(n). Remove the first entry in the list with key equal to a.

Equations

• Batteries.AssocList.eraseP p Batteries.AssocList.nil = Batteries.AssocList.nil
• Batteries.AssocList.eraseP p (Batteries.AssocList.cons a b es) = bif p a b then es else Batteries.AssocList.cons a b (Batteries.AssocList.eraseP p es)

@[simp]

theorem Batteries.AssocList.toList_eraseP {α : Type u_1} {β : Type u_2} (p : α → β → Bool) (l : Batteries.AssocList α β) : (Batteries.AssocList.eraseP p l).toList = List.eraseP (fun (x : α × β) => match x with | (a, b) => p a b) l.toList

@[inline]

def Batteries.AssocList.erase {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : Batteries.AssocList α β

O(n). Remove the first entry in the list with key equal to a.

Equations

• Batteries.AssocList.erase a l = Batteries.AssocList.eraseP (fun (k : α) (x : β) => k == a) l

@[simp]

theorem Batteries.AssocList.toList_erase {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : Batteries.AssocList α β) : (Batteries.AssocList.erase a l).toList = List.eraseP (fun (x : α × β) => x.fst == a) l.toList

def Batteries.AssocList.modify {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (f : α → β → β) : Batteries.AssocList α β → Batteries.AssocList α β

O(n). Replace the first entry a', b in the list with key equal to a to have key a and value f a' b.

Equations

• One or more equations did not get rendered due to their size.
• Batteries.AssocList.modify a f Batteries.AssocList.nil = Batteries.AssocList.nil

@[simp]

theorem Batteries.AssocList.toList_modify {α : Type u_1} {β : Type u_2} {f : α → β → β} [BEq α] (a : α) (l : Batteries.AssocList α β) : (Batteries.AssocList.modify a f l).toList = List.replaceF (fun (x : α × β) => match x with | (k, v) => bif k == a then some (a, f k v) else none) l.toList

@[simp]

theorem Batteries.AssocList.length_modify {α : Type u_1} : ∀ {β : Type u_2} {f : α → β → β} {l : Batteries.AssocList α β} [inst : BEq α] {a : α}, (Batteries.AssocList.modify a f l).length = l.length

@[specialize #[]]

def Batteries.AssocList.forIn {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} {δ : Type u_1} [Monad m] (as : Batteries.AssocList α β) (init : δ) (f : α × β → δ → m (ForInStep δ)) : m δ

The implementation of ForIn, which enables for (k, v) in aList do ... notation.

Equations

• Batteries.AssocList.nil.forIn init f = pure init
• (Batteries.AssocList.cons a b es).forIn init f = do let __do_lift ← f (a, b) init match __do_lift with | ForInStep.done d => pure d | ForInStep.yield d => es.forIn d f

instance Batteries.AssocList.instForInProd {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} : ForIn m (Batteries.AssocList α β) (α × β)

Equations

• Batteries.AssocList.instForInProd = { forIn := fun {β_1 : Type ?u.28} [Monad m] => Batteries.AssocList.forIn }

@[simp]

theorem Batteries.AssocList.forIn_eq {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} {δ : Type u_1} [Monad m] (l : Batteries.AssocList α β) (init : δ) (f : α × β → δ → m (ForInStep δ)) : forIn l init f = forIn l.toList init f

def Batteries.AssocList.pop? {α : Type u_1} {β : Type u_2} : Batteries.AssocList α β → Option ((α × β) × Batteries.AssocList α β)

Split the list into head and tail, if possible.

Equations

• Batteries.AssocList.nil.pop? = none
• (Batteries.AssocList.cons a b es).pop? = some ((a, b), es)

instance Batteries.AssocList.instToStream {α : Type u_1} {β : Type u_2} : ToStream (Batteries.AssocList α β) (Batteries.AssocList α β)

Equations

• Batteries.AssocList.instToStream = { toStream := fun (x : Batteries.AssocList α β) => x }

instance Batteries.AssocList.instStreamProd {α : Type u_1} {β : Type u_2} : Stream (Batteries.AssocList α β) (α × β)

Equations

• Batteries.AssocList.instStreamProd = { next? := Batteries.AssocList.pop? }

def List.toAssocList {α : Type u_1} {β : Type u_2} : List (α × β) → Batteries.AssocList α β

Converts a list into an AssocList. This is the inverse function to AssocList.toList.

Equations

• [].toAssocList = Batteries.AssocList.nil
• ((a, b) :: es).toAssocList = Batteries.AssocList.cons a b es.toAssocList

@[simp]

theorem List.toList_toAssocList {α : Type u_1} {β : Type u_2} (l : List (α × β)) : l.toAssocList.toList = l

@[simp]

theorem Batteries.AssocList.toList_toAssocList {α : Type u_1} {β : Type u_2} (l : Batteries.AssocList α β) : l.toList.toAssocList = l

@[simp]

theorem List.length_toAssocList {α : Type u_1} {β : Type u_2} (l : List (α × β)) : l.toAssocList.length = l.length

def Batteries.AssocList.beq {α : Type u_1} {β : Type u_2} [BEq α] [BEq β] : Batteries.AssocList α β → Batteries.AssocList α β → Bool

Implementation of == on AssocList.

Equations

• Batteries.AssocList.nil.beq Batteries.AssocList.nil = true
• (Batteries.AssocList.cons key value tail).beq Batteries.AssocList.nil = false
• Batteries.AssocList.nil.beq (Batteries.AssocList.cons key value tail) = false
• (Batteries.AssocList.cons a b t).beq (Batteries.AssocList.cons a' b' t') = (a == a' && b == b' && t.beq t')

instance Batteries.AssocList.instBEq {α : Type u_1} {β : Type u_2} [BEq α] [BEq β] : BEq (Batteries.AssocList α β)

Boolean equality for AssocList. (This relation cares about the ordering of the key-value pairs.)

Equations

• Batteries.AssocList.instBEq = { beq := Batteries.AssocList.beq }

@[simp]

theorem Batteries.AssocList.beq_nil₂ {α : Type u_1} {β : Type u_2} [BEq α] [BEq β] : (Batteries.AssocList.nil == Batteries.AssocList.nil) = true

@[simp]

theorem Batteries.AssocList.beq_nil_cons {α : Type u_1} {β : Type u_2} {a : α} {b : β} {t : Batteries.AssocList α β} [BEq α] [BEq β] : (Batteries.AssocList.nil == Batteries.AssocList.cons a b t) = false

@[simp]

theorem Batteries.AssocList.beq_cons_nil {α : Type u_1} {β : Type u_2} {a : α} {b : β} {t : Batteries.AssocList α β} [BEq α] [BEq β] : (Batteries.AssocList.cons a b t == Batteries.AssocList.nil) = false

@[simp]

theorem Batteries.AssocList.beq_cons₂ {α : Type u_1} {β : Type u_2} {a : α} {b : β} {t : Batteries.AssocList α β} {a' : α} {b' : β} {t' : Batteries.AssocList α β} [BEq α] [BEq β] : (Batteries.AssocList.cons a b t == Batteries.AssocList.cons a' b' t') = (a == a' && b == b' && t == t')

instance Batteries.AssocList.instLawfulBEq {α : Type u_1} {β : Type u_2} [BEq α] [LawfulBEq α] [BEq β] [LawfulBEq β] : LawfulBEq (Batteries.AssocList α β)

Equations

• ⋯ = ⋯

theorem Batteries.AssocList.beq_eq {α : Type u_1} {β : Type u_2} [BEq α] [BEq β] {l : Batteries.AssocList α β} {m : Batteries.AssocList α β} : (l == m) = (l.toList == m.toList)