feat(data/mllist): monadic lazy lists

src/data/mllist.lean

@@ -0,0 +1,83 @@
+/-
+Copyright (c) 2018 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Author: Mario Carnerio, Keeley Hoek, Scott Morrison
+
+Monadic lazy lists.
+
+The inductive construction is not allowed outside of meta (indeed, we can build infinite objects).
+This isn't so bad, as the typical use is with the tactic monad, in any case.
+
+As we're in meta anyway, we don't bother with proofs about these constructions.
+-/
+
+universes u v
+
+meta inductive mllist (m : Type u → Type u) (α : Type u) : Type u
+| nil {} : mllist
+| cons : α → m mllist → mllist
+
+namespace mllist
+
+meta def empty {m} [monad m] {α : Type u} : mllist m α → bool
+| nil := ff
+| (cons _ _) := tt
+
+meta def fix {m : Type u → Type u} [alternative m]
+  {α} (f : α → m α) : α → m (mllist m α)
+| x := (λ a, cons a (fix a)) <$> f x <|> pure nil
+
+meta def of_list {m} [monad m] {α : Type u} : list α → mllist m α
+| [] := nil
+| (h :: t) := cons h (pure (of_list t))
+
+meta def m_of_list {m} [monad m] {α : Type u} : list (m α) → m (mllist m α)
+| [] := return nil
+| (h :: t) := do a ← h, return (cons a (m_of_list t))
+
+meta def force {m} [monad m] {α} : mllist m α → m (list α)
+| nil := pure []
+| (cons a l) := list.cons a <$> (l >>= force)
+
+meta def map {m} [monad m] {α β : Type u} (f : α → β) : mllist m α → m (mllist m β)
+| nil := pure nil
+| (cons a l) := do r ← l, return (cons (f a) (map r))
+
+meta def mmap {m} [monad m] [alternative m] {α β : Type u} (f : α → m β) : mllist m α → m (mllist m β)
+| nil := pure nil
+| (cons a l) := do r ← l, b ← f a, return (cons b (mmap r))
+
+meta def filter {m} [monad m] {α : Type u} (p : α → Prop) [decidable_pred p] : mllist m α → m (mllist m α)
+| nil := pure nil
+| (cons a l) := do r ← l, if p a then return (cons a (filter r)) else filter r
+
+meta def mfilter {m} [monad m] [alternative m] {α β : Type} (p : α → m β) : mllist m α → m (mllist m α)
+| nil := pure nil
+| (cons a l) := do r ← l, (p a >> return (cons a (mfilter r))) <|> mfilter r
+
+meta def filter_map {m} [monad m] {α β : Type u} (f : α → option β) : mllist m α → m (mllist m β)
+| nil := pure nil
+| (cons a l) := do r ← l, match f a with
+  | (some b) := return (cons b (filter_map r))
+  | none := filter_map r
+  end
+
+meta def mfilter_map {m} [monad m] [alternative m] {α β : Type u} (f : α → m β) : mllist m α → m (mllist m β)
+| nil := pure nil
+| (cons a l) := do r ← l, (f a >>= (λ b, return (cons b (mfilter_map r)))) <|> mfilter_map r
+
+meta def join {m} [monad m] {α : Type u} : mllist m (mllist m α) → m (mllist m α)
+| nil := pure nil
+| (cons nil l) := do r ← l, join r
+| (cons (cons a m) l) := do n ← m, return (cons a (join (cons n l)))
+
+meta def enum_from {m} [monad m] {α : Type u} : ℕ → mllist m α → m (mllist m (ℕ × α))
+| _ nil := return nil
+| n (cons a l) := do r ← l, return (cons (n, a) (enum_from (n + 1) r))
+
+meta def enum {m} [monad m] {α : Type u} : mllist m α → m (mllist m (ℕ × α)) := enum_from 0
+
+meta def concat {m} [monad m] {α : Type u} : mllist m α → α → m (mllist m α)
+| L a := (mllist.of_list [L, mllist.of_list [a]]).join
+
+end mllist