155 lines
5.3 KiB
Text
155 lines
5.3 KiB
Text
/-
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Copyright (c) 2019 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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Authors: Leonardo de Moura
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-/
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prelude
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import Init.Control.State
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import Init.Control.Except
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universes u v
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namespace EStateM
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inductive Result (ε σ α : Type u)
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| ok {} : α → σ → Result
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| error {} : ε → σ → Result
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variables {ε σ α : Type u}
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protected def Result.toString [HasToString ε] [HasToString α] : Result ε σ α → String
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| Result.ok a _ => "ok: " ++ toString a
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| Result.error e _ => "error: " ++ toString e
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protected def Result.repr [HasRepr ε] [HasRepr α] : Result ε σ α → String
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| Result.error e _ => "(error " ++ repr e ++ ")"
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| Result.ok a _ => "(ok " ++ repr a ++ ")"
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instance [HasToString ε] [HasToString α] : HasToString (Result ε σ α) := ⟨Result.toString⟩
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instance [HasRepr ε] [HasRepr α] : HasRepr (Result ε σ α) := ⟨Result.repr⟩
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end EStateM
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def EStateM (ε σ α : Type u) := σ → EStateM.Result ε σ α
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namespace EStateM
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variables {ε σ α β : Type u}
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instance [Inhabited ε] : Inhabited (EStateM ε σ α) :=
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⟨fun s => Result.error (arbitrary ε) s⟩
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@[inline] protected def pure (a : α) : EStateM ε σ α :=
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fun s => Result.ok a s
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@[inline] protected def set (s : σ) : EStateM ε σ PUnit :=
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fun _ => Result.ok ⟨⟩ s
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@[inline] protected def get : EStateM ε σ σ :=
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fun s => Result.ok s s
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@[inline] protected def modifyGet (f : σ → α × σ) : EStateM ε σ α :=
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fun s =>
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match f s with
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| (a, s) => Result.ok a s
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@[inline] protected def throw (e : ε) : EStateM ε σ α :=
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fun s => Result.error e s
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/-- Auxiliary instance for saving/restoring the "backtrackable" part of the state. -/
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class Backtrackable (δ : outParam $ Type u) (σ : Type u) :=
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(save : σ → δ)
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(restore : σ → δ → σ)
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@[inline] protected def catch {δ} [Backtrackable δ σ] {α} (x : EStateM ε σ α) (handle : ε → EStateM ε σ α) : EStateM ε σ α :=
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fun s =>
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let d := Backtrackable.save s;
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match x s with
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| Result.error e s => handle e (Backtrackable.restore s d)
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| ok => ok
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@[inline] protected def orelse {δ} [Backtrackable δ σ] (x₁ x₂ : EStateM ε σ α) : EStateM ε σ α :=
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fun s =>
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let d := Backtrackable.save s;
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match x₁ s with
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| Result.error _ s => x₂ (Backtrackable.restore s d)
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| ok => ok
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/-- Alternative orelse operator that allows to select which exception should be used.
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The default is to use the first exception since the standard `orelse` uses the second. -/
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@[inline] protected def orelse' {δ} [Backtrackable δ σ] (x₁ x₂ : EStateM ε σ α) (useFirstEx := true) : EStateM ε σ α :=
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fun s =>
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let d := Backtrackable.save s;
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match x₁ s with
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| Result.error e₁ s₁ =>
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match x₂ (Backtrackable.restore s₁ d) with
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| Result.error e₂ s₂ => Result.error (if useFirstEx then e₁ else e₂) s₂
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| ok => ok
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| ok => ok
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@[inline] def adaptExcept {ε' : Type u} [HasLift ε ε'] (x : EStateM ε σ α) : EStateM ε' σ α :=
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fun s => match x s with
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| Result.error e s => Result.error (lift e) s
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| Result.ok a s => Result.ok a s
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@[inline] protected def bind (x : EStateM ε σ α) (f : α → EStateM ε σ β) : EStateM ε σ β :=
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fun s => match x s with
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| Result.ok a s => f a s
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| Result.error e s => Result.error e s
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@[inline] protected def map (f : α → β) (x : EStateM ε σ α) : EStateM ε σ β :=
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fun s => match x s with
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| Result.ok a s => Result.ok (f a) s
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| Result.error e s => Result.error e s
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@[inline] protected def seqRight (x : EStateM ε σ α) (y : EStateM ε σ β) : EStateM ε σ β :=
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fun s => match x s with
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| Result.ok _ s => y s
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| Result.error e s => Result.error e s
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instance : Monad (EStateM ε σ) :=
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{ bind := @EStateM.bind _ _, pure := @EStateM.pure _ _, map := @EStateM.map _ _, seqRight := @EStateM.seqRight _ _ }
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instance {δ} [Backtrackable δ σ] : HasOrelse (EStateM ε σ α) :=
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{ orelse := @EStateM.orelse _ _ _ _ _ }
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instance : MonadState σ (EStateM ε σ) :=
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{ set := @EStateM.set _ _, get := @EStateM.get _ _, modifyGet := @EStateM.modifyGet _ _ }
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instance {δ} [Backtrackable δ σ] : MonadExcept ε (EStateM ε σ) :=
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{ throw := @EStateM.throw _ _, catch := @EStateM.catch _ _ _ _ }
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@[inline] def adaptState {σ₁ σ₂} (split : σ → σ₁ × σ₂) (merge : σ₁ → σ₂ → σ) (x : EStateM ε σ₁ α) : EStateM ε σ α :=
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fun s =>
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let (s₁, s₂) := split s;
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match x s₁ with
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| Result.ok a s₁ => Result.ok a (merge s₁ s₂)
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| Result.error e s₁ => Result.error e (merge s₁ s₂)
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instance {ε σ σ'} : MonadStateAdapter σ σ' (EStateM ε σ) (EStateM ε σ') :=
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⟨fun σ'' α => EStateM.adaptState⟩
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@[inline] def fromStateM {ε σ α : Type} (x : StateM σ α) : EStateM ε σ α :=
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fun s =>
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match x.run s with
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| (a, s') => EStateM.Result.ok a s'
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@[inline] def run (x : EStateM ε σ α) (s : σ) : Result ε σ α :=
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x s
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@[inline] def run' (x : EStateM ε σ α) (s : σ) : Option α :=
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match run x s with
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| Result.ok v _ => some v
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| Result.error _ _ => none
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@[inline] def dummySave : σ → PUnit :=
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fun _ => ⟨⟩
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@[inline] def dummyRestore : σ → PUnit → σ :=
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fun s _ => s
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/- Dummy default instance -/
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instance nonBacktrackable : Backtrackable PUnit σ :=
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{ save := dummySave,
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restore := dummyRestore }
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end EStateM
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