146 lines
6 KiB
Text
146 lines
6 KiB
Text
/-
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Copyright (c) 2018 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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-/
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prelude
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import init.control.monad init.wf init.control.reader
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universes u v w r s
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inductive coroutine_result_core (coroutine : Type (max u v w)) (α : Type u) (δ : Type v) (β : Type w) : Type (max u v w)
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| done {} : β → coroutine_result_core
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| yielded {} : δ → coroutine → coroutine_result_core
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/--
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Asymmetric coroutines `coroutine α δ β` takes inputs of type `α`, yields elements of type `δ`,
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and produces an element of type `β`.
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Asymmetric coroutines are so called because they involve two types of control transfer operations:
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one for resuming/invoking a coroutine and one for suspending it, the latter returning
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control to the coroutine invoker. An asymmetric coroutine can be regarded as subordinate
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to its caller, the relationship between them being similar to that between a called and
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a calling routine.
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-/
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inductive coroutine (α : Type u) (δ : Type v) (β : Type w) : Type (max u v w)
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| mk {} : (α → coroutine_result_core coroutine α δ β) → coroutine
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abbreviation coroutine_result (α : Type u) (δ : Type v) (β : Type w) : Type (max u v w) :=
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coroutine_result_core (coroutine α δ β) α δ β
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namespace coroutine
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variables {α : Type u} {δ : Type v} {β γ : Type w}
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export coroutine_result_core (done yielded)
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/-- `resume c a` resumes/invokes the coroutine `c` with input `a`. -/
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@[inline] def resume : coroutine α δ β → α → coroutine_result α δ β
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| (mk k) a := k a
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@[inline] protected def pure (b : β) : coroutine α δ β :=
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mk $ λ _, done b
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/-- Read the input argument passed to the coroutine.
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Remark: should we use a different name? I added an instance [monad_reader] later. -/
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@[inline] protected def read : coroutine α δ α :=
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mk $ λ a, done a
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/-- Return the control to the invoker with result `d` -/
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@[inline] protected def yield (d : δ) : coroutine α δ punit :=
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mk $ λ a : α, yielded d (coroutine.pure ⟨⟩)
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/-
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TODO(Leo): following relations have been commented because Lean4 is currently
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accepting non-terminating programs.
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/-- Auxiliary relation for showing that bind/pipe terminate -/
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inductive direct_subcoroutine : coroutine α δ β → coroutine α δ β → Prop
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| mk : ∀ (k : α → coroutine_result α δ β) (a : α) (d : δ) (c : coroutine α δ β), k a = yielded d c → direct_subcoroutine c (mk k)
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theorem direct_subcoroutine_wf : well_founded (@direct_subcoroutine α δ β) :=
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begin
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constructor, intro c,
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apply @coroutine.ind _ _ _
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(λ c, acc direct_subcoroutine c)
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(λ r, ∀ (d : δ) (c : coroutine α δ β), r = yielded d c → acc direct_subcoroutine c),
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{ intros k ih, dsimp at ih, constructor, intros c' h, cases h, apply ih h_a h_d, assumption },
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{ intros, contradiction },
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{ intros d c ih d₁ c₁ heq, injection heq, subst c, assumption }
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end
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/-- Transitive closure of direct_subcoroutine. It is not used here, but may be useful when defining
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more complex procedures. -/
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def subcoroutine : coroutine α δ β → coroutine α δ β → Prop :=
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tc direct_subcoroutine
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theorem subcoroutine_wf : well_founded (@subcoroutine α δ β) :=
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tc.wf direct_subcoroutine_wf
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-- Local instances for proving termination by well founded relation
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def bind_wf_inst : has_well_founded (Σ' a : coroutine α δ β, (β → coroutine α δ γ)) :=
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{ r := psigma.lex direct_subcoroutine (λ _, empty_relation),
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wf := psigma.lex_wf direct_subcoroutine_wf (λ _, empty_wf) }
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def pipe_wf_inst : has_well_founded (Σ' a : coroutine α δ β, coroutine δ γ β) :=
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{ r := psigma.lex direct_subcoroutine (λ _, empty_relation),
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wf := psigma.lex_wf direct_subcoroutine_wf (λ _, empty_wf) }
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local attribute [instance] wf_inst₁ wf_inst₂
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open well_founded_tactics
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-/
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protected def bind : coroutine α δ β → (β → coroutine α δ γ) → coroutine α δ γ
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| (mk k) f := mk $ λ a,
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match k a, rfl : ∀ (n : _), n = k a → _ with
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| done b, _ := coroutine.resume (f b) a
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| yielded d c, h :=
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-- have direct_subcoroutine c (mk k), { apply direct_subcoroutine.mk k a d, rw h },
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yielded d (bind c f)
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-- using_well_founded { dec_tac := unfold_wf_rel >> process_lex (tactic.assumption) }
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def pipe : coroutine α δ β → coroutine δ γ β → coroutine α γ β
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| (mk k₁) (mk k₂) := mk $ λ a,
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match k₁ a, rfl : ∀ (n : _), n = k₁ a → _ with
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| done b, h := done b
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| yielded d k₁', h :=
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match k₂ d with
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| done b := done b
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| yielded r k₂' :=
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-- have direct_subcoroutine k₁' (mk k₁), { apply direct_subcoroutine.mk k₁ a d, rw h },
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yielded r (pipe k₁' k₂')
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-- using_well_founded { dec_tac := unfold_wf_rel >> process_lex (tactic.assumption) }
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private def finish_aux (f : δ → α) : coroutine α δ β → α → list δ → list δ × β
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| (mk k) a ds :=
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match k a with
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| done b := (ds.reverse, b)
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| yielded d k' := finish_aux k' (f d) (d::ds)
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/-- Run a coroutine to completion, feeding back yielded items after transforming them with `f`. -/
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def finish (f : δ → α) : coroutine α δ β → α → list δ × β :=
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λ k a, finish_aux f k a []
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instance : monad (coroutine α δ) :=
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{ pure := @coroutine.pure _ _,
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bind := @coroutine.bind _ _ }
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instance : monad_reader α (coroutine α δ) :=
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{ read := @coroutine.read _ _ }
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/-- Auxiliary class for lifiting `yield` -/
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class monad_coroutine (α : out_param (Type u)) (δ : out_param (Type v)) (m : Type w → Type r) :=
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(yield {} : δ → m punit)
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instance (α : Type u) (δ : Type v) : monad_coroutine α δ (coroutine α δ) :=
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{ yield := coroutine.yield }
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instance monad_coroutine_trans (α : Type u) (δ : Type v) (m : Type w → Type r) (n : Type w → Type s)
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[has_monad_lift m n] [monad_coroutine α δ m] : monad_coroutine α δ n :=
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{ yield := λ d, monad_lift (monad_coroutine.yield d : m _) }
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export monad_coroutine (yield)
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end coroutine
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