feat(library/init/control/coroutine_io): coroutine_io

library/init/control/coroutine_io.lean

@@ -0,0 +1,110 @@
+/-
+Copyright (c) 2018 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura, Sebastian Ullrich
+-/
+prelude
+import init.io init.control.coroutine
+
+/-! A variant of `coroutine` on top of `io`. Implementation. -/
+
+universes u v w r s
+
+namespace coroutine_io
+variables {α δ β γ : Type}
+
+export coroutine_result_io (done yielded)
+
+/-- `resume c a` resumes/invokes the coroutine_io `c` with input `a`. -/
+@[inline] def resume : coroutine_io α δ β → α → io (coroutine_result_io α δ β)
+| (mk k) a := k a
+
+@[inline] protected def pure (b : β) : coroutine_io α δ β :=
+mk $ λ _, pure (done b)
+
+/-- Read the input argument passed to the coroutine.
+    Remark: should we use a different name? I added an instance [monad_reader] later. -/
+@[inline] protected def read : coroutine_io α δ α :=
+mk $ λ a, pure (done a)
+
+/-- Return the control to the invoker with result `d` -/
+@[inline] protected def yield (d : δ) : coroutine_io α δ punit :=
+mk $ λ a : α, pure $ yielded d (coroutine_io.pure ⟨⟩)
+
+/-
+TODO(Leo): following relations have been commented because Lean4 is currently
+accepting non-terminating programs.
+
+/-- Auxiliary relation for showing that bind/pipe terminate -/
+inductive direct_subcoroutine_io : coroutine_io α δ β → coroutine_io α δ β → Prop
+| mk : ∀ (k : α → coroutine_result α δ β) (a : α) (d : δ) (c : coroutine_io α δ β), k a = yielded d c → direct_subcoroutine_io c (mk k)
+
+theorem direct_subcoroutine_wf : well_founded (@direct_subcoroutine_io α δ β) :=
+begin
+  constructor, intro c,
+  apply @coroutine.ind _ _ _
+          (λ c, acc direct_subcoroutine_io c)
+          (λ r, ∀ (d : δ) (c : coroutine_io α δ β), r = yielded d c → acc direct_subcoroutine_io c),
+  { intros k ih, dsimp at ih, constructor, intros c' h, cases h, apply ih h_a h_d, assumption },
+  { intros, contradiction },
+  { intros d c ih d₁ c₁ heq, injection heq, subst c, assumption }
+end
+
+/-- Transitive closure of direct_subcoroutine. It is not used here, but may be useful when defining
+    more complex procedures. -/
+def subcoroutine_io : coroutine_io α δ β → coroutine_io α δ β → Prop :=
+tc direct_subcoroutine_io
+
+theorem subcoroutine_wf : well_founded (@subcoroutine_io α δ β) :=
+tc.wf direct_subcoroutine_wf
+
+-- Local instances for proving termination by well founded relation
+
+def bind_wf_inst : has_well_founded (Σ' a : coroutine_io α δ β, (β → coroutine_io α δ γ)) :=
+{ r  := psigma.lex direct_subcoroutine_io (λ _, empty_relation),
+  wf := psigma.lex_wf direct_subcoroutine_wf (λ _, empty_wf) }
+
+def pipe_wf_inst : has_well_founded (Σ' a : coroutine_io α δ β, coroutine_io δ γ β) :=
+{ r  := psigma.lex direct_subcoroutine_io (λ _, empty_relation),
+  wf := psigma.lex_wf direct_subcoroutine_wf (λ _, empty_wf) }
+
+local attribute [instance] wf_inst₁ wf_inst₂
+
+open well_founded_tactics
+
+-/
+
+protected def bind : coroutine_io α δ β → (β → coroutine_io α δ γ) → coroutine_io α δ γ
+| (mk k) f := mk $ λ a, k a >>= λ r,
+    match r, rfl : ∀ (n : _), n = r → _ with
+    | done b, _      := coroutine_io.resume (f b) a
+    | yielded d c, h :=
+      -- have direct_subcoroutine_io c (mk k), { apply direct_subcoroutine.mk k a d, rw h },
+      pure $ yielded d (bind c f)
+--  using_well_founded { dec_tac := unfold_wf_rel >> process_lex (tactic.assumption) }
+
+def pipe : coroutine_io α δ β → coroutine_io δ γ β → coroutine_io α γ β
+| (mk k₁) (mk k₂) := mk $ λ a, do
+  r ← k₁ a,
+  match r, rfl : ∀ (n : _), n = r → _ with
+  | done b, h        := pure (done b)
+  | yielded d k₁', h := do
+    r ← k₂ d,
+    pure $ match r with
+    | done b        := done b
+    | yielded r k₂' :=
+      -- have direct_subcoroutine_io k₁' (mk k₁), { apply direct_subcoroutine.mk k₁ a d, rw h },
+      yielded r (pipe k₁' k₂')
+-- using_well_founded { dec_tac := unfold_wf_rel >> process_lex (tactic.assumption) }
+
+instance : monad (coroutine_io α δ) :=
+{ pure := @coroutine_io.pure _ _,
+  bind := @coroutine_io.bind _ _ }
+
+instance : monad_reader α (coroutine_io α δ) :=
+{ read := @coroutine_io.read _ _ }
+
+instance (α δ : Type) : coroutine.monad_coroutine α δ (coroutine_io α δ) :=
+{ yield  := coroutine_io.yield }
+
+end coroutine_io

library/init/io.lean

@@ -341,3 +341,13 @@ meta instance eio_unit.has_eval {ε : Type} [has_to_format ε] : has_eval (excep
   match r with
   | except.error e := tactic.fail e
   | except.ok a    := pure ()⟩
+
+
+local attribute [reducible] io
+/-- A variant of `coroutine` on top of `io` -/
+mutual inductive coroutine_io, coroutine_result_io (α δ β: Type)
+with coroutine_io : Type
+| mk    {} : (α → io coroutine_result_io) → coroutine_io
+with coroutine_result_io : Type
+| done     {} : β → coroutine_result_io
+| yielded {}  : δ → coroutine_io → coroutine_result_io