Difference list

This file provides a few results about DList, which is defined in Std.

A difference list is a function that, given a list, returns the original content of the difference list prepended to the given list. It is useful to represent elements of a given type as a₁ + ... + aₙ where + : α → α → α→ α → α→ α is any operation, without actually computing.

This structure supports O(1) append and concat operations on lists, making it useful for append-heavy uses such as logging and pretty printing.

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def Std.DList.join {α : Type u_1} : List (Std.DList α) → Std.DList α

Concatenates a list of difference lists to form a single difference list. Similar to List.join.

Equations

• Std.DList.join [] = Std.DList.empty
• Std.DList.join (x_1 :: xs) = x_1 ++ Std.DList.join xs

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def Std.DList.lazy_ofList {α : Type u_1} (l : Thunk (List α)) : Std.DList α

Convert a lazily-evaluated List to a DList

Equations

• Std.DList.lazy_ofList l = { apply := fun xs => Thunk.get l ++ xs, invariant := (_ : ∀ (t : List α), Thunk.get l ++ t = Thunk.get l ++ [] ++ t) }

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@[simp]

theorem Std.DList_singleton {α : Type u_1} {a : α} : Std.DList.singleton a = Std.DList.lazy_ofList { fn := fun x => [a] }

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@[simp]

theorem Std.DList_lazy {α : Type u_1} {l : List α} : Std.DList.lazy_ofList { fn := fun x => l } = Std.DList.ofList l

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theorem Std.DList.toList_ofList {α : Type u_1} (l : List α) : Std.DList.toList (Std.DList.ofList l) = l

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theorem Std.DList.ofList_toList {α : Type u_1} (l : Std.DList α) : Std.DList.ofList (Std.DList.toList l) = l