error-less io

gen/apply.lean

@@ -1,4 +1,4 @@
-import init.lean.config system.io
+import init.lean.config init.io
 open io
 
 @[reducible] def m := reader_t handle io

library/init/coe.lean

@@ -88,8 +88,8 @@ universes u₁ u₂ u₃
 instance lift_trans {a : Sort u₁} {b : Sort u₂} {c : Sort u₃} [has_lift a b] [has_lift_t b c] : has_lift_t a c :=
 ⟨λ x, lift_t (lift x : b)⟩
 
-instance lift_base {a : Sort u} {b : Sort v} [has_lift a b] : has_lift_t a b :=
-⟨lift⟩
+instance lift_refl {a : Sort u} : has_lift_t a a :=
+⟨id⟩
 
 instance coe_trans {a : Sort u₁} {b : Sort u₂} {c : Sort u₃} [has_coe a b] [has_coe_t b c] : has_coe_t a c :=
 ⟨λ x, coe_t (coe_b x : b)⟩

library/init/control/coroutine_io.lean

@@ -0,0 +1,113 @@
+/-
+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 }
+
+instance : monad_io (coroutine_io α δ) :=
+{ monad_lift := λ _ x, mk (λ _, done <$> x) }
+
+end coroutine_io

library/init/control/except.lean

@@ -7,6 +7,7 @@ The except monad transformer.
 -/
 prelude
 import init.control.alternative init.control.lift init.data.to_string
+import init.control.monad_fail
 universes u v w
 
 inductive except (ε : Type u) (α : Type v)
@@ -131,8 +132,12 @@ catch t₁ $ λ _, t₂
 
 /-- Alternative orelse operator that allows to select which exception should be used.
     The default is to use the first exception since the standard `orelse` uses the second. -/
-meta def orelse' [monad_except ε m] {α : Type v} (t₁ t₂ : m α) (use_first_ex := tt) : m α :=
+def orelse' [monad_except ε m] {α : Type v} (t₁ t₂ : m α) (use_first_ex := tt) : m α :=
 catch t₁ $ λ e₁, catch t₂ $ λ e₂, throw (if use_first_ex then e₁ else e₂)
+
+def lift_except {ε' : Type u} [monad_except ε m] [has_lift_t ε' ε] [monad m] {α : Type v} : except ε' α → m α
+| (except.error e) := throw ↑e
+| (except.ok a)    := pure a
 end monad_except
 
 export monad_except (throw catch)
@@ -167,3 +172,7 @@ end
 
 instance (ε m out) [monad_run out m] : monad_run (λ α, out (except ε α)) (except_t ε m) :=
 ⟨λ α, run ∘ except_t.run⟩
+
+-- useful for implicit failures in do-notation
+instance (m) [monad m] : monad_fail (except_t string m) :=
+⟨λ _, throw⟩

library/init/default.lean

@@ -6,4 +6,4 @@ Authors: Leonardo de Moura
 prelude
 import init.core init.control init.data.basic init.version
 import init.function init.util init.coe init.wf init.meta
-import init.meta.well_founded_tactics init.data
+import init.meta.well_founded_tactics init.data init.io