135 lines
5.4 KiB
Text
135 lines
5.4 KiB
Text
/-
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Copyright (c) 2017 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: Sebastian Ullrich
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The reader monad transformer for passing immutable state.
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-/
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prelude
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import init.control.lift init.control.id init.control.alternative init.control.except
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universes u v w
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/-- An implementation of [ReaderT](https://hackage.haskell.org/package/transformers-0.5.5.0/docs/Control-Monad-Trans-Reader.html#t:ReaderT) -/
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structure reader_t (ρ : Type u) (m : Type u → Type v) (α : Type u) : Type (max u v) :=
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(run : ρ → m α)
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@[reducible] def reader (ρ : Type u) := reader_t ρ id
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attribute [pp_using_anonymous_constructor] reader_t
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namespace reader_t
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section
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variable {ρ : Type u}
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variable {m : Type u → Type v}
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variable [monad m]
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variables {α β : Type u}
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@[inline] protected def read : reader_t ρ m ρ :=
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⟨pure⟩
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@[inline] protected def pure (a : α) : reader_t ρ m α :=
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⟨λ r, pure a⟩
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@[inline] protected def bind (x : reader_t ρ m α) (f : α → reader_t ρ m β) : reader_t ρ m β :=
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⟨λ r, do a ← x.run r,
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(f a).run r⟩
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instance : monad (reader_t ρ m) :=
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{ pure := @reader_t.pure _ _ _, bind := @reader_t.bind _ _ _ }
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@[inline] protected def lift (a : m α) : reader_t ρ m α :=
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⟨λ r, a⟩
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instance (m) [monad m] : has_monad_lift m (reader_t ρ m) :=
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⟨@reader_t.lift ρ m _⟩
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@[inline] protected def monad_map {ρ m m'} [monad m] [monad m'] {α} (f : Π {α}, m α → m' α) : reader_t ρ m α → reader_t ρ m' α :=
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λ x, ⟨λ r, f (x.run r)⟩
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instance (ρ m m') [monad m] [monad m'] : monad_functor m m' (reader_t ρ m) (reader_t ρ m') :=
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⟨@reader_t.monad_map ρ m m' _ _⟩
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@[inline] protected def adapt {ρ' : Type u} [monad m] {α : Type u} (f : ρ' → ρ) : reader_t ρ m α → reader_t ρ' m α :=
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λ x, ⟨λ r, x.run (f r)⟩
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protected def orelse [alternative m] {α : Type u} (x₁ x₂ : reader_t ρ m α) : reader_t ρ m α :=
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⟨λ s, x₁.run s <|> x₂.run s⟩
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protected def failure [alternative m] {α : Type u} : reader_t ρ m α :=
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⟨λ s, failure⟩
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instance [alternative m] : alternative (reader_t ρ m) :=
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{ failure := @reader_t.failure _ _ _ _,
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orelse := @reader_t.orelse _ _ _ _ }
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instance (ε) [monad m] [monad_except ε m] : monad_except ε (reader_t ρ m) :=
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{ throw := λ α, reader_t.lift ∘ throw,
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catch := λ α x c, ⟨λ r, catch (x.run r) (λ e, (c e).run r)⟩ }
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end
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end reader_t
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/-- An implementation of [MonadReader](https://hackage.haskell.org/package/mtl-2.2.2/docs/Control-Monad-Reader-Class.html#t:MonadReader).
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It does not contain `local` because this function cannot be lifted using `monad_lift`.
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Instead, the `monad_reader_adapter` class provides the more general `adapt_reader` function.
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Note: This class can be seen as a simplification of the more "principled" definition
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```
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class monad_reader (ρ : out_param (Type u)) (n : Type u → Type u) :=
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(lift {} {α : Type u} : (∀ {m : Type u → Type u} [monad m], reader_t ρ m α) → n α)
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```
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-/
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class monad_reader (ρ : out_param (Type u)) (m : Type u → Type v) :=
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(read {} : m ρ)
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export monad_reader (read)
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instance monad_reader_trans {ρ : Type u} {m : Type u → Type v} {n : Type u → Type w}
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[has_monad_lift m n] [monad_reader ρ m] : monad_reader ρ n :=
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⟨monad_lift (monad_reader.read : m ρ)⟩
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instance {ρ : Type u} {m : Type u → Type v} [monad m] : monad_reader ρ (reader_t ρ m) :=
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⟨reader_t.read⟩
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/-- Adapt a monad stack, changing the type of its top-most environment.
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This class is comparable to [Control.Lens.Magnify](https://hackage.haskell.org/package/lens-4.15.4/docs/Control-Lens-Zoom.html#t:Magnify), but does not use lenses (why would it), and is derived automatically for any transformer implementing `monad_functor`.
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Note: This class can be seen as a simplification of the more "principled" definition
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```
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class monad_reader_functor (ρ ρ' : out_param (Type u)) (n n' : Type u → Type u) :=
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(map {} {α : Type u} : (∀ {m : Type u → Type u} [monad m], reader_t ρ m α → reader_t ρ' m α) → n α → n' α)
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```
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-/
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class monad_reader_adapter (ρ ρ' : out_param (Type u)) (m m' : Type u → Type v) :=
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(adapt_reader {} {α : Type u} : (ρ' → ρ) → m α → m' α)
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export monad_reader_adapter (adapt_reader)
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section
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variables {ρ ρ' : Type u} {m m' : Type u → Type v}
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instance monad_reader_adapter_trans {n n' : Type u → Type v} [monad_functor m m' n n'] [monad_reader_adapter ρ ρ' m m'] : monad_reader_adapter ρ ρ' n n' :=
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⟨λ α f, monad_map (λ α, (adapt_reader f : m α → m' α))⟩
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instance [monad m] : monad_reader_adapter ρ ρ' (reader_t ρ m) (reader_t ρ' m) :=
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⟨λ α, reader_t.adapt⟩
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end
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instance (ρ : Type u) (m out) [monad_run out m] : monad_run (λ α, ρ → out α) (reader_t ρ m) :=
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⟨λ α x, run ∘ x.run⟩
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class monad_reader_runner (ρ : Type u) (m m' : Type u → Type u) :=
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(run_reader {} {α : Type u} : m α → ρ → m' α)
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export monad_reader_runner (run_reader)
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section
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variables {ρ ρ' : Type u} {m m' : Type u → Type u}
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instance monad_reader_runner_trans {n n' : Type u → Type u} [monad_functor m m' n n'] [monad_reader_runner ρ m m'] : monad_reader_runner ρ n n' :=
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⟨λ α x r, monad_map (λ α (y : m α), (run_reader y r : m' α)) x⟩
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instance reader_t.monad_state_runner [monad m] : monad_reader_runner ρ (reader_t ρ m) m :=
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⟨λ α x r, x.run r⟩
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end
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