# Documentation

Std.Data.AssocList

inductive Std.AssocList (α : Type u) (β : Type v) :
Type (max u v)
• nil: {α : Type u} → {β : Type v} →

An empty list

• cons: {α : Type u} → {β : Type v} → αβ

Add a key, value pair to the list

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.

Instances For
instance Std.instInhabitedAssocList :
{a : Type u_1} → {a_1 : Type u_2} → Inhabited (Std.AssocList a a_1)
def Std.AssocList.toList {α : Type u_1} {β : Type u_2} :
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
Instances For
@[simp]
theorem Std.AssocList.empty_eq {α : Type u_1} {β : Type u_2} :
= Std.AssocList.nil
def Std.AssocList.isEmpty {α : Type u_1} {β : Type u_2} :
Bool

O(1). Is the list empty?

Instances For
@[simp]
theorem Std.AssocList.isEmpty_eq {α : Type u_1} {β : Type u_2} (l : ) :
@[specialize #[]]
def Std.AssocList.foldlM {m : Type u_1 → Type u_2} {δ : Type u_1} {α : Type u_3} {β : Type u_4} [] (f : δαβm δ) (init : δ) :
m δ

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

Equations
Instances For
@[simp]
theorem Std.AssocList.foldlM_eq {m : Type u_1 → Type u_2} {δ : Type u_1} {α : Type u_3} {β : Type u_4} [] (f : δαβm δ) (init : δ) (l : ) :
Std.AssocList.foldlM f init l = List.foldlM (fun d x => match x with | (a, b) => f d a b) init ()
@[inline]
def Std.AssocList.foldl {δ : Type u_1} {α : Type u_2} {β : Type u_3} (f : δαβδ) (init : δ) (as : ) :
δ

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

Instances For
@[simp]
theorem Std.AssocList.foldl_eq {δ : Type u_1} {α : Type u_2} {β : Type u_3} (f : δαβδ) (init : δ) (l : ) :
Std.AssocList.foldl f init l = List.foldl (fun d x => match x with | (a, b) => f d a b) init ()
def Std.AssocList.toListTR {α : Type u_1} {β : Type u_2} (as : ) :
List (α × β)

Optimized version of toList.

Instances For
@[specialize #[]]
def Std.AssocList.forM {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} [] (f : αβ) :

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

Equations
Instances For
@[simp]
theorem Std.AssocList.forM_eq {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} [] (f : αβ) (l : ) :
= List.forM () fun x => match x with | (a, b) => f a b
def Std.AssocList.mapKey {α : Type u_1} {δ : Type u_2} {β : Type u_3} (f : αδ) :

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

Equations
Instances For
@[simp]
theorem Std.AssocList.mapKey_toList {α : Type u_1} {δ : Type u_2} {β : Type u_3} (f : αδ) (l : ) :
= List.map (fun x => match x with | (a, b) => (f a, b)) ()
def Std.AssocList.mapVal {α : Type u_1} {β : Type u_2} {δ : Type u_3} (f : αβδ) :

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

Equations
Instances For
@[simp]
theorem Std.AssocList.mapVal_toList {α : Type u_1} {β : Type u_2} {δ : Type u_3} (f : αβδ) (l : ) :
= List.map (fun x => match x with | (a, b) => (a, f a b)) ()
@[specialize #[]]
def Std.AssocList.findEntryP? {α : Type u_1} {β : Type u_2} (p : αβBool) :
Option (α × β)

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

Equations
Instances For
@[simp]
theorem Std.AssocList.findEntryP?_eq {α : Type u_1} {β : Type u_2} (p : αβBool) (l : ) :
= List.find? (fun x => match x with | (a, b) => p a b) ()
@[inline]
def Std.AssocList.findEntry? {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :
Option (α × β)

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

Instances For
@[simp]
theorem Std.AssocList.findEntry?_eq {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :
= List.find? (fun x => x.fst == a) ()
def Std.AssocList.find? {α : Type u_1} {β : Type u_2} [BEq α] (a : α) :

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

Equations
Instances For
theorem Std.AssocList.find?_eq_findEntry? {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :
= Option.map (fun x => x.snd) ()
@[simp]
theorem Std.AssocList.find?_eq {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :
= Option.map (fun x => x.snd) (List.find? (fun x => x.fst == a) ())
@[specialize #[]]
def Std.AssocList.any {α : Type u_1} {β : Type u_2} (p : αβBool) :
Bool

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

Equations
Instances For
@[simp]
theorem Std.AssocList.any_eq {α : Type u_1} {β : Type u_2} (p : αβBool) (l : ) :
= List.any () fun x => match x with | (a, b) => p a b
@[specialize #[]]
def Std.AssocList.all {α : Type u_1} {β : Type u_2} (p : αβBool) :
Bool

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

Equations
Instances For
@[simp]
theorem Std.AssocList.all_eq {α : Type u_1} {β : Type u_2} (p : αβBool) (l : ) :
= List.all () fun x => match x with | (a, b) => p a b
def Std.AssocList.All {α : Type u_1} {β : Type u_2} (p : αβProp) (l : ) :

Returns true if every entry in the list satisfies p.

Instances For
@[inline]
def Std.AssocList.contains {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :

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

Instances For
@[simp]
theorem Std.AssocList.contains_eq {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :
= List.any () fun x => x.fst == a
def Std.AssocList.replace {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (b : β) :

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

Equations
Instances For
@[simp]
theorem Std.AssocList.replace_toList {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (b : β) (l : ) :
= List.replaceF (fun x => bif x.fst == a then some (a, b) else none) ()
@[specialize #[]]
def Std.AssocList.eraseP {α : Type u_1} {β : Type u_2} (p : αβBool) :

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

Equations
Instances For
@[simp]
theorem Std.AssocList.eraseP_toList {α : Type u_1} {β : Type u_2} (p : αβBool) (l : ) :
= List.eraseP (fun x => match x with | (a, b) => p a b) ()
@[inline]
def Std.AssocList.erase {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :

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

Instances For
@[simp]
theorem Std.AssocList.erase_toList {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (l : ) :
= List.eraseP (fun x => x.fst == a) ()
def Std.AssocList.modify {α : Type u_1} {β : Type u_2} [BEq α] (a : α) (f : αββ) :

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
Instances For
@[simp]
theorem Std.AssocList.modify_toList {α : Type u_1} {β : Type u_2} {f : αββ} [BEq α] (a : α) (l : ) :
= List.replaceF (fun x => match x with | (k, v) => bif k == a then some (a, f k v) else none) ()
@[specialize #[]]
def Std.AssocList.forIn {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} {δ : Type u_1} [] (as : ) (init : δ) (f : α × βδm ()) :
m δ

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

Equations
Instances For
instance Std.AssocList.instForInAssocListProd {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} :
ForIn m () (α × β)
@[simp]
theorem Std.AssocList.forIn_eq {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_4} {δ : Type u_1} [] (l : ) (init : δ) (f : α × βδm ()) :
forIn l init f = forIn () init f
def Std.AssocList.pop? {α : Type u_1} {β : Type u_2} :
Option ((α × β) × )

Split the list into head and tail, if possible.

Instances For
instance Std.AssocList.instToStreamAssocList {α : Type u_1} {β : Type u_2} :
ToStream () ()
instance Std.AssocList.instStreamAssocListProd {α : Type u_1} {β : Type u_2} :
Stream () (α × β)
def List.toAssocList {α : Type u_1} {β : Type u_2} :
List (α × β)

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

Equations
Instances For
@[simp]
theorem List.toAssocList_toList {α : Type u_1} {β : Type u_2} (l : List (α × β)) :
@[simp]
theorem Std.AssocList.toList_toAssocList {α : Type u_1} {β : Type u_2} (l : ) :