9e4f9d317b
This PR adds BEq instance for `DTreeMap`/`TreeMap`/`TreeSet` and their extensional variants and proves lemmas relating it to the equivalence of hashmaps/equality of extensional variants. Stacked on top of #11266
565 lines
23 KiB
Text
565 lines
23 KiB
Text
/-
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Copyright (c) 2025 Robin Arnez. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Robin Arnez, Markus Himmel, Paul Reichert
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-/
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module
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prelude
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public import Std.Data.ExtDTreeMap.Basic
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@[expose] public section
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/-!
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# Extensional tree maps
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This file develops the type `Std.ExtTreeMap` of tree maps.
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Lemmas about the operations on `Std.ExtTreeMap` will be available in the
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module `Std.Data.ExtTreeMap.Lemmas`.
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See the module `Std.Data.TreeMap.Raw.Basic` for a variant of this type which is safe to use in
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nested inductive types.
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-/
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set_option autoImplicit false
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set_option linter.missingDocs true
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universe u v w w₂
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variable {α : Type u} {β : Type v} {γ : Type w} {cmp : α → α → Ordering}
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namespace Std
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/--
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Extensional tree maps.
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A tree map stores an assignment of keys to values. It depends on a comparator function that
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defines an ordering on the keys and provides efficient order-dependent queries, such as retrieval
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of the minimum or maximum.
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To ensure that the operations behave as expected, the comparator function `cmp` should satisfy
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certain laws that ensure a consistent ordering:
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* If `a` is less than (or equal) to `b`, then `b` is greater than (or equal) to `a`
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and vice versa (see the `OrientedCmp` typeclass).
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* If `a` is less than or equal to `b` and `b` is, in turn, less than or equal to `c`, then `a`
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is less than or equal to `c` (see the `TransCmp` typeclass).
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Keys for which `cmp a b = Ordering.eq` are considered the same, i.e., there can be only one entry
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with key either `a` or `b` in a tree map. Looking up either `a` or `b` always yields the same entry,
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if any is present.
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To avoid expensive copies, users should make sure that the tree map is used linearly.
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Internally, the tree maps are represented as size-bounded trees, a type of self-balancing binary
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search tree with efficient order statistic lookups.
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In contrast to regular tree maps, `Std.ExtTreeMap` offers several extensionality lemmas
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and therefore has more lemmas about equality of tree maps. This doesn't affect the amount of
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supported functions though: `Std.ExtTreeMap` supports all operations from `Std.TreeMap`.
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In order to use most functions, a `TransCmp` instance is required. This is necessary to make sure
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that the functions are congruent, i.e. equivalent tree maps as parameters produce equivalent return
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values.
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These tree maps contain a bundled well-formedness invariant, which means that they cannot
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be used in nested inductive types. For these use cases, `Std.TreeMap.Raw` and
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`Std.TreeMap.Raw.WF` unbundle the invariant from the tree map. When in doubt, prefer
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`ExtTreeMap` over `TreeMap.Raw`.
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-/
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structure ExtTreeMap (α : Type u) (β : Type v) (cmp : α → α → Ordering := by exact compare) where
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/-- Internal implementation detail of the tree map. -/
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inner : ExtDTreeMap α (fun _ => β) cmp
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namespace ExtTreeMap
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@[inline, inherit_doc ExtDTreeMap.empty]
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def empty : ExtTreeMap α β cmp :=
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⟨ExtDTreeMap.empty⟩
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instance : EmptyCollection (ExtTreeMap α β cmp) where
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emptyCollection := empty
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instance : Inhabited (ExtTreeMap α β cmp) := ⟨∅⟩
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@[simp, grind =]
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theorem empty_eq_emptyc : (empty : ExtTreeMap α β cmp) = ∅ :=
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rfl
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@[inline, inherit_doc ExtDTreeMap.insert]
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def insert [TransCmp cmp] (l : ExtTreeMap α β cmp) (a : α) (b : β) : ExtTreeMap α β cmp :=
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⟨l.inner.insert a b⟩
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instance [TransCmp cmp] : Singleton (α × β) (ExtTreeMap α β cmp) where
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singleton e := (∅ : ExtTreeMap α β cmp).insert e.1 e.2
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instance [TransCmp cmp] : Insert (α × β) (ExtTreeMap α β cmp) where
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insert e s := s.insert e.1 e.2
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instance [TransCmp cmp] : LawfulSingleton (α × β) (ExtTreeMap α β cmp) where
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insert_empty_eq _ := rfl
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@[inline, inherit_doc ExtDTreeMap.insertIfNew]
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def insertIfNew [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (b : β) : ExtTreeMap α β cmp :=
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⟨t.inner.insertIfNew a b⟩
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@[inline, inherit_doc ExtDTreeMap.containsThenInsert]
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def containsThenInsert [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (b : β) : Bool × ExtTreeMap α β cmp :=
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let p := t.inner.containsThenInsert a b
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(p.1, ⟨p.2⟩)
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@[inline, inherit_doc ExtDTreeMap.containsThenInsertIfNew]
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def containsThenInsertIfNew [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (b : β) :
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Bool × ExtTreeMap α β cmp :=
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let p := t.inner.containsThenInsertIfNew a b
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(p.1, ⟨p.2⟩)
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@[inline, inherit_doc ExtDTreeMap.getThenInsertIfNew?]
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def getThenInsertIfNew? [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (b : β) : Option β × ExtTreeMap α β cmp :=
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letI : Ord α := ⟨cmp⟩
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let p := ExtDTreeMap.Const.getThenInsertIfNew? t.inner a b
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(p.1, ⟨p.2⟩)
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@[inline, inherit_doc ExtDTreeMap.contains]
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def contains [TransCmp cmp] (l : ExtTreeMap α β cmp) (a : α) : Bool :=
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l.inner.contains a
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instance [TransCmp cmp] : Membership α (ExtTreeMap α β cmp) where
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mem m a := m.contains a
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instance [TransCmp cmp] {m : ExtTreeMap α β cmp} {a : α} : Decidable (a ∈ m) :=
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inferInstanceAs <| Decidable (m.contains a)
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@[inline, inherit_doc ExtDTreeMap.size]
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def size (t : ExtTreeMap α β cmp) : Nat :=
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t.inner.size
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@[inline, inherit_doc ExtDTreeMap.isEmpty]
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def isEmpty (t : ExtTreeMap α β cmp) : Bool :=
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t.inner.isEmpty
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@[inline, inherit_doc ExtDTreeMap.erase]
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def erase [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) : ExtTreeMap α β cmp :=
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⟨t.inner.erase a⟩
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@[inline, inherit_doc ExtDTreeMap.Const.get?]
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def get? [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) : Option β :=
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ExtDTreeMap.Const.get? t.inner a
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@[inline, inherit_doc ExtDTreeMap.Const.get]
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def get [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (h : a ∈ t) : β :=
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ExtDTreeMap.Const.get t.inner a h
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@[inline, inherit_doc ExtDTreeMap.Const.get!]
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def get! [TransCmp cmp] [Inhabited β] (t : ExtTreeMap α β cmp) (a : α) : β :=
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ExtDTreeMap.Const.get! t.inner a
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@[inline, inherit_doc ExtDTreeMap.Const.getD]
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def getD [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (fallback : β) : β :=
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ExtDTreeMap.Const.getD t.inner a fallback
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instance [TransCmp cmp] : GetElem? (ExtTreeMap α β cmp) α β (fun m a => a ∈ m) where
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getElem m a h := m.get a h
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getElem? m a := m.get? a
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getElem! m a := m.get! a
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@[inline, inherit_doc ExtDTreeMap.getKey?]
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def getKey? [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) : Option α :=
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t.inner.getKey? a
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@[inline, inherit_doc ExtDTreeMap.getKey]
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def getKey [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (h : a ∈ t) : α :=
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t.inner.getKey a h
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@[inline, inherit_doc ExtDTreeMap.getKey!]
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def getKey! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) (a : α) : α :=
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t.inner.getKey! a
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@[inline, inherit_doc ExtDTreeMap.getKeyD]
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def getKeyD [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (fallback : α) : α :=
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t.inner.getKeyD a fallback
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@[inline, inherit_doc ExtDTreeMap.Const.minEntry?]
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def minEntry? [TransCmp cmp] (t : ExtTreeMap α β cmp) : Option (α × β) :=
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ExtDTreeMap.Const.minEntry? t.inner
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@[inline, inherit_doc ExtDTreeMap.Const.minEntry]
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def minEntry [TransCmp cmp] (t : ExtTreeMap α β cmp) (h : t ≠ ∅) : α × β :=
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ExtDTreeMap.Const.minEntry t.inner (fun _ => nomatch t)
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@[inline, inherit_doc ExtDTreeMap.Const.minEntry!]
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def minEntry! [TransCmp cmp] [Inhabited (α × β)] (t : ExtTreeMap α β cmp) : α × β :=
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ExtDTreeMap.Const.minEntry! t.inner
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@[inline, inherit_doc ExtDTreeMap.Const.minEntryD]
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def minEntryD [TransCmp cmp] (t : ExtTreeMap α β cmp) (fallback : α × β) : α × β :=
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ExtDTreeMap.Const.minEntryD t.inner fallback
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@[inline, inherit_doc ExtDTreeMap.Const.maxEntry?]
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def maxEntry? [TransCmp cmp] (t : ExtTreeMap α β cmp) : Option (α × β) :=
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ExtDTreeMap.Const.maxEntry? t.inner
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@[inline, inherit_doc ExtDTreeMap.Const.maxEntry]
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def maxEntry [TransCmp cmp] (t : ExtTreeMap α β cmp) (h : t ≠ ∅) : α × β :=
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ExtDTreeMap.Const.maxEntry t.inner (fun _ => nomatch t)
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@[inline, inherit_doc ExtDTreeMap.Const.maxEntry!]
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def maxEntry! [TransCmp cmp] [Inhabited (α × β)] (t : ExtTreeMap α β cmp) : α × β :=
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ExtDTreeMap.Const.maxEntry! t.inner
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@[inline, inherit_doc ExtDTreeMap.Const.maxEntryD]
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def maxEntryD [TransCmp cmp] (t : ExtTreeMap α β cmp) (fallback : α × β) : α × β :=
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ExtDTreeMap.Const.maxEntryD t.inner fallback
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@[inline, inherit_doc ExtDTreeMap.minKey?]
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def minKey? [TransCmp cmp] (t : ExtTreeMap α β cmp) : Option α :=
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ExtDTreeMap.minKey? t.inner
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@[inline, inherit_doc ExtDTreeMap.minKey]
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def minKey [TransCmp cmp] (t : ExtTreeMap α β cmp) (h : t ≠ ∅) : α :=
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ExtDTreeMap.minKey t.inner (fun _ => nomatch t)
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@[inline, inherit_doc ExtDTreeMap.minKey!]
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def minKey! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) : α :=
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ExtDTreeMap.minKey! t.inner
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@[inline, inherit_doc ExtDTreeMap.minKeyD]
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def minKeyD [TransCmp cmp] (t : ExtTreeMap α β cmp) (fallback : α) : α :=
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ExtDTreeMap.minKeyD t.inner fallback
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@[inline, inherit_doc ExtDTreeMap.maxKey?]
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def maxKey? [TransCmp cmp] (t : ExtTreeMap α β cmp) : Option α :=
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ExtDTreeMap.maxKey? t.inner
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@[inline, inherit_doc ExtDTreeMap.maxKey]
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def maxKey [TransCmp cmp] (t : ExtTreeMap α β cmp) (h : t ≠ ∅) : α :=
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ExtDTreeMap.maxKey t.inner (fun _ => nomatch t)
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@[inline, inherit_doc ExtDTreeMap.maxKey!]
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def maxKey! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) : α :=
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ExtDTreeMap.maxKey! t.inner
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@[inline, inherit_doc ExtDTreeMap.maxKeyD]
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def maxKeyD [TransCmp cmp] (t : ExtTreeMap α β cmp) (fallback : α) : α :=
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ExtDTreeMap.maxKeyD t.inner fallback
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@[inline, inherit_doc ExtDTreeMap.Const.entryAtIdx?]
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def entryAtIdx? [TransCmp cmp] (t : ExtTreeMap α β cmp) (n : Nat) : Option (α × β) :=
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ExtDTreeMap.Const.entryAtIdx? t.inner n
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@[inline, inherit_doc ExtDTreeMap.Const.entryAtIdx]
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def entryAtIdx [TransCmp cmp] (t : ExtTreeMap α β cmp) (n : Nat) (h : n < t.size) : α × β :=
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ExtDTreeMap.Const.entryAtIdx t.inner n h
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@[inline, inherit_doc ExtDTreeMap.Const.entryAtIdx!]
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def entryAtIdx! [TransCmp cmp] [Inhabited (α × β)] (t : ExtTreeMap α β cmp) (n : Nat) : α × β :=
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ExtDTreeMap.Const.entryAtIdx! t.inner n
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@[inline, inherit_doc ExtDTreeMap.Const.entryAtIdxD]
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def entryAtIdxD [TransCmp cmp] (t : ExtTreeMap α β cmp) (n : Nat) (fallback : α × β) : α × β :=
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ExtDTreeMap.Const.entryAtIdxD t.inner n fallback
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@[inline, inherit_doc ExtDTreeMap.keyAtIdx?]
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def keyAtIdx? [TransCmp cmp] (t : ExtTreeMap α β cmp) (n : Nat) : Option α :=
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ExtDTreeMap.keyAtIdx? t.inner n
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@[inline, inherit_doc ExtDTreeMap.keyAtIdx]
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def keyAtIdx [TransCmp cmp] (t : ExtTreeMap α β cmp) (n : Nat) (h : n < t.size) : α :=
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ExtDTreeMap.keyAtIdx t.inner n h
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@[inline, inherit_doc ExtDTreeMap.keyAtIdx!]
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def keyAtIdx! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) (n : Nat) : α :=
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ExtDTreeMap.keyAtIdx! t.inner n
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@[inline, inherit_doc ExtDTreeMap.keyAtIdxD]
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def keyAtIdxD [TransCmp cmp] (t : ExtTreeMap α β cmp) (n : Nat) (fallback : α) : α :=
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ExtDTreeMap.keyAtIdxD t.inner n fallback
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryGE?]
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def getEntryGE? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option (α × β) :=
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ExtDTreeMap.Const.getEntryGE? t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryGT?]
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def getEntryGT? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option (α × β) :=
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ExtDTreeMap.Const.getEntryGT? t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryLE?]
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def getEntryLE? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option (α × β) :=
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ExtDTreeMap.Const.getEntryLE? t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryLT?]
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def getEntryLT? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option (α × β) :=
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ExtDTreeMap.Const.getEntryLT? t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryGE]
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def getEntryGE [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, (cmp a k).isGE) :
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α × β :=
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ExtDTreeMap.Const.getEntryGE t.inner k h
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@[inline, inherit_doc DTreeMap.Const.getEntryGT]
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def getEntryGT [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, cmp a k = .gt) :
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α × β :=
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ExtDTreeMap.Const.getEntryGT t.inner k h
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@[inline, inherit_doc DTreeMap.Const.getEntryLE]
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def getEntryLE [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, (cmp a k).isLE) :
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α × β :=
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ExtDTreeMap.Const.getEntryLE t.inner k h
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@[inline, inherit_doc DTreeMap.Const.getEntryLT]
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def getEntryLT [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, cmp a k = .lt) :
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α × β :=
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ExtDTreeMap.Const.getEntryLT t.inner k h
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryGE!]
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def getEntryGE! [TransCmp cmp] [Inhabited (α × β)] (t : ExtTreeMap α β cmp) (k : α) : (α × β) :=
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ExtDTreeMap.Const.getEntryGE! t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryGT!]
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def getEntryGT! [TransCmp cmp] [Inhabited (α × β)] (t : ExtTreeMap α β cmp) (k : α) : (α × β) :=
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ExtDTreeMap.Const.getEntryGT! t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryLE!]
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def getEntryLE! [TransCmp cmp] [Inhabited (α × β)] (t : ExtTreeMap α β cmp) (k : α) : (α × β) :=
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ExtDTreeMap.Const.getEntryLE! t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryLT!]
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def getEntryLT! [TransCmp cmp] [Inhabited (α × β)] (t : ExtTreeMap α β cmp) (k : α) : (α × β) :=
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ExtDTreeMap.Const.getEntryLT! t.inner k
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryGED]
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def getEntryGED [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α × β) : (α × β) :=
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ExtDTreeMap.Const.getEntryGED t.inner k fallback
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryGTD]
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def getEntryGTD [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α × β) : (α × β) :=
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ExtDTreeMap.Const.getEntryGTD t.inner k fallback
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryLED]
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def getEntryLED [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α × β) : (α × β) :=
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ExtDTreeMap.Const.getEntryLED t.inner k fallback
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@[inline, inherit_doc ExtDTreeMap.Const.getEntryLTD]
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def getEntryLTD [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α × β) : (α × β) :=
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ExtDTreeMap.Const.getEntryLTD t.inner k fallback
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@[inline, inherit_doc ExtDTreeMap.getKeyGE?]
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def getKeyGE? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option α :=
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ExtDTreeMap.getKeyGE? t.inner k
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@[inline, inherit_doc ExtDTreeMap.getKeyGT?]
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def getKeyGT? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option α :=
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ExtDTreeMap.getKeyGT? t.inner k
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@[inline, inherit_doc ExtDTreeMap.getKeyLE?]
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def getKeyLE? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option α :=
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ExtDTreeMap.getKeyLE? t.inner k
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@[inline, inherit_doc ExtDTreeMap.getKeyLT?]
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def getKeyLT? [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) : Option α :=
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ExtDTreeMap.getKeyLT? t.inner k
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@[inline, inherit_doc ExtDTreeMap.getKeyGE]
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def getKeyGE [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, (cmp a k).isGE) : α :=
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ExtDTreeMap.getKeyGE t.inner k h
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|
||
@[inline, inherit_doc ExtDTreeMap.getKeyGT]
|
||
def getKeyGT [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, cmp a k = .gt) : α :=
|
||
ExtDTreeMap.getKeyGT t.inner k h
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyLE]
|
||
def getKeyLE [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, (cmp a k).isLE) : α :=
|
||
ExtDTreeMap.getKeyLE t.inner k h
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyLT]
|
||
def getKeyLT [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (h : ∃ a ∈ t, cmp a k = .lt) : α :=
|
||
ExtDTreeMap.getKeyLT t.inner k h
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyGE!]
|
||
def getKeyGE! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) (k : α) : α :=
|
||
ExtDTreeMap.getKeyGE! t.inner k
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyGT!]
|
||
def getKeyGT! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) (k : α) : α :=
|
||
ExtDTreeMap.getKeyGT! t.inner k
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyLE!]
|
||
def getKeyLE! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) (k : α) : α :=
|
||
ExtDTreeMap.getKeyLE! t.inner k
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyLT!]
|
||
def getKeyLT! [TransCmp cmp] [Inhabited α] (t : ExtTreeMap α β cmp) (k : α) : α :=
|
||
ExtDTreeMap.getKeyLT! t.inner k
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyGED]
|
||
def getKeyGED [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α) : α :=
|
||
ExtDTreeMap.getKeyGED t.inner k fallback
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyGTD]
|
||
def getKeyGTD [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α) : α :=
|
||
ExtDTreeMap.getKeyGTD t.inner k fallback
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyLED]
|
||
def getKeyLED [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α) : α :=
|
||
ExtDTreeMap.getKeyLED t.inner k fallback
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.getKeyLTD]
|
||
def getKeyLTD [TransCmp cmp] (t : ExtTreeMap α β cmp) (k : α) (fallback : α) : α :=
|
||
ExtDTreeMap.getKeyLTD t.inner k fallback
|
||
|
||
variable {δ : Type w} {m : Type w → Type w₂} [Monad m] [LawfulMonad m]
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.filter]
|
||
def filter (f : α → β → Bool) (m : ExtTreeMap α β cmp) : ExtTreeMap α β cmp :=
|
||
⟨m.inner.filter f⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.filterMap]
|
||
def filterMap (f : (a : α) → β → Option γ) (m : ExtTreeMap α β cmp) : ExtTreeMap α γ cmp :=
|
||
⟨m.inner.filterMap f⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.map]
|
||
def map (f : α → β → γ) (t : ExtTreeMap α β cmp) : ExtTreeMap α γ cmp :=
|
||
⟨t.inner.map f⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.foldlM]
|
||
def foldlM [TransCmp cmp] (f : δ → (a : α) → β → m δ) (init : δ) (t : ExtTreeMap α β cmp) : m δ :=
|
||
t.inner.foldlM f init
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.foldl]
|
||
def foldl [TransCmp cmp] (f : δ → (a : α) → β → δ) (init : δ) (t : ExtTreeMap α β cmp) : δ :=
|
||
t.inner.foldl f init
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.foldrM]
|
||
def foldrM [TransCmp cmp] (f : (a : α) → β → δ → m δ) (init : δ) (t : ExtTreeMap α β cmp) : m δ :=
|
||
t.inner.foldrM f init
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.foldr]
|
||
def foldr [TransCmp cmp] (f : (a : α) → β → δ → δ) (init : δ) (t : ExtTreeMap α β cmp) : δ :=
|
||
t.inner.foldr f init
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.partition]
|
||
def partition [TransCmp cmp] (f : (a : α) → β → Bool) (t : ExtTreeMap α β cmp) :
|
||
ExtTreeMap α β cmp × ExtTreeMap α β cmp :=
|
||
let p := t.inner.partition f; (⟨p.1⟩, ⟨p.2⟩)
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.forM]
|
||
def forM [TransCmp cmp] (f : α → β → m PUnit) (t : ExtTreeMap α β cmp) : m PUnit :=
|
||
t.inner.forM f
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.forIn]
|
||
def forIn [TransCmp cmp] (f : α → β → δ → m (ForInStep δ)) (init : δ) (t : ExtTreeMap α β cmp) : m δ :=
|
||
t.inner.forIn (fun a b c => f a b c) init
|
||
|
||
instance [TransCmp cmp] [Monad m] [LawfulMonad m] : ForM m (ExtTreeMap α β cmp) (α × β) where
|
||
forM t f := forM (fun a b => f ⟨a, b⟩) t
|
||
|
||
instance [TransCmp cmp] [Monad m] [LawfulMonad m] : ForIn m (ExtTreeMap α β cmp) (α × β) where
|
||
forIn m init f := forIn (fun a b acc => f ⟨a, b⟩ acc) init m
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.any]
|
||
def any [TransCmp cmp] (t : ExtTreeMap α β cmp) (p : α → β → Bool) : Bool :=
|
||
t.inner.any p
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.all]
|
||
def all [TransCmp cmp] (t : ExtTreeMap α β cmp) (p : α → β → Bool) : Bool :=
|
||
t.inner.all p
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.keys]
|
||
def keys [TransCmp cmp] (t : ExtTreeMap α β cmp) : List α :=
|
||
t.inner.keys
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.keysArray]
|
||
def keysArray [TransCmp cmp] (t : ExtTreeMap α β cmp) : Array α :=
|
||
t.inner.keysArray
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.values]
|
||
def values [TransCmp cmp] (t : ExtTreeMap α β cmp) : List β :=
|
||
t.inner.values
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.valuesArray]
|
||
def valuesArray [TransCmp cmp] (t : ExtTreeMap α β cmp) : Array β :=
|
||
t.inner.valuesArray
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.toList]
|
||
def toList [TransCmp cmp] (t : ExtTreeMap α β cmp) : List (α × β) :=
|
||
ExtDTreeMap.Const.toList t.inner
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.ofList]
|
||
def ofList (l : List (α × β)) (cmp : α → α → Ordering := by exact compare) : ExtTreeMap α β cmp :=
|
||
⟨ExtDTreeMap.Const.ofList l cmp⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.unitOfList]
|
||
def unitOfList (l : List α) (cmp : α → α → Ordering := by exact compare) : ExtTreeMap α Unit cmp :=
|
||
⟨ExtDTreeMap.Const.unitOfList l cmp⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.toArray]
|
||
def toArray [TransCmp cmp] (t : ExtTreeMap α β cmp) : Array (α × β) :=
|
||
ExtDTreeMap.Const.toArray t.inner
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.ofArray]
|
||
def ofArray (a : Array (α × β)) (cmp : α → α → Ordering := by exact compare) : ExtTreeMap α β cmp :=
|
||
⟨ExtDTreeMap.Const.ofArray a cmp⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.unitOfArray]
|
||
def unitOfArray (a : Array α) (cmp : α → α → Ordering := by exact compare) : ExtTreeMap α Unit cmp :=
|
||
⟨ExtDTreeMap.Const.unitOfArray a cmp⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.modify]
|
||
def modify [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (f : β → β) : ExtTreeMap α β cmp :=
|
||
⟨ExtDTreeMap.Const.modify t.inner a f⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.alter]
|
||
def alter [TransCmp cmp] (t : ExtTreeMap α β cmp) (a : α) (f : Option β → Option β) : ExtTreeMap α β cmp :=
|
||
⟨ExtDTreeMap.Const.alter t.inner a f⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.mergeWith]
|
||
def mergeWith [TransCmp cmp] (mergeFn : α → β → β → β) (t₁ t₂ : ExtTreeMap α β cmp) : ExtTreeMap α β cmp :=
|
||
⟨ExtDTreeMap.Const.mergeWith mergeFn t₁.inner t₂.inner⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.insertMany]
|
||
def insertMany [TransCmp cmp] {ρ} [ForIn Id ρ (α × β)] (t : ExtTreeMap α β cmp) (l : ρ) : ExtTreeMap α β cmp :=
|
||
⟨ExtDTreeMap.Const.insertMany t.inner l⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.Const.insertManyIfNewUnit]
|
||
def insertManyIfNewUnit [TransCmp cmp] {ρ} [ForIn Id ρ α] (t : ExtTreeMap α Unit cmp) (l : ρ) : ExtTreeMap α Unit cmp :=
|
||
⟨ExtDTreeMap.Const.insertManyIfNewUnit t.inner l⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.union]
|
||
def union [TransCmp cmp] (t₁ t₂ : ExtTreeMap α β cmp) : ExtTreeMap α β cmp := ⟨ExtDTreeMap.union t₁.inner t₂.inner⟩
|
||
|
||
instance [TransCmp cmp] : Union (ExtTreeMap α β cmp) := ⟨union⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.inter]
|
||
def inter [TransCmp cmp] (t₁ t₂ : ExtTreeMap α β cmp) : ExtTreeMap α β cmp := ⟨ExtDTreeMap.inter t₁.inner t₂.inner⟩
|
||
|
||
instance [TransCmp cmp] : Inter (ExtTreeMap α β cmp) := ⟨inter⟩
|
||
|
||
instance [TransCmp cmp] [BEq β] : BEq (ExtTreeMap α β cmp) where
|
||
beq m₁ m₂ := ExtDTreeMap.Const.beq m₁.inner m₂.inner
|
||
|
||
instance [TransCmp cmp] [BEq β] [ReflBEq β] : ReflBEq (ExtTreeMap α β cmp) where
|
||
rfl := ExtDTreeMap.Const.beq_of_eq _ _ rfl
|
||
|
||
instance [TransCmp cmp] [LawfulEqCmp cmp] [BEq β] [LawfulBEq β] : LawfulBEq (ExtTreeMap α β cmp) where
|
||
eq_of_beq {a} {b} hyp := by
|
||
have ⟨_⟩ := a
|
||
have ⟨_⟩ := b
|
||
simp only [mk.injEq]
|
||
exact ExtDTreeMap.Const.eq_of_beq _ _ hyp
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.diff]
|
||
def diff [TransCmp cmp] (t₁ t₂ : ExtTreeMap α β cmp) : ExtTreeMap α β cmp := ⟨ExtDTreeMap.diff t₁.inner t₂.inner⟩
|
||
|
||
instance [TransCmp cmp] : SDiff (ExtTreeMap α β cmp) := ⟨diff⟩
|
||
|
||
@[inline, inherit_doc ExtDTreeMap.eraseMany]
|
||
def eraseMany [TransCmp cmp] {ρ} [ForIn Id ρ α] (t : ExtTreeMap α β cmp) (l : ρ) : ExtTreeMap α β cmp :=
|
||
⟨t.inner.eraseMany l⟩
|
||
|
||
instance [TransCmp cmp] [Repr α] [Repr β] : Repr (ExtTreeMap α β cmp) where
|
||
reprPrec m prec := Repr.addAppParen ("Std.ExtTreeMap.ofList " ++ repr m.toList) prec
|
||
|
||
end ExtTreeMap
|
||
|
||
end Std
|