09a5b34931
This PR adjusts the experimental module system to make `private` the default visibility modifier in `module`s, introducing `public` as a new modifier instead. `public section` can be used to revert the default for an entire section, though this is more intended to ease gradual adoption of the new semantics such as in `Init` (and soon `Std`) where they should be replaced by a future decl-by-decl re-review of visibilities.
70 lines
1.5 KiB
Text
70 lines
1.5 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 identity Monad.
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-/
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module
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prelude
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public import Init.Core
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public section
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universe u
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/--
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The identity function on types, used primarily for its `Monad` instance.
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The identity monad is useful together with monad transformers to construct monads for particular
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purposes. Additionally, it can be used with `do`-notation in order to use control structures such as
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local mutability, `for`-loops, and early returns in code that does not otherwise use monads.
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Examples:
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```lean example
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def containsFive (xs : List Nat) : Bool := Id.run do
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for x in xs do
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if x == 5 then return true
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return false
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```
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```lean example
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#eval containsFive [1, 3, 5, 7]
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```
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```output
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true
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```
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-/
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@[expose] def Id (type : Type u) : Type u := type
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namespace Id
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@[always_inline]
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instance : Monad Id where
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pure x := x
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bind x f := f x
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map f x := f x
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/--
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The identity monad has a `bind` operator.
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-/
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def hasBind : Bind Id :=
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inferInstance
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/--
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Runs a computation in the identity monad.
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This function is the identity function. Because its parameter has type `Id α`, it causes
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`do`-notation in its arguments to use the `Monad Id` instance.
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-/
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@[always_inline, inline, expose]
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protected def run (x : Id α) : α := x
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instance [OfNat α n] : OfNat (Id α) n :=
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inferInstanceAs (OfNat α n)
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instance {m : Type u → Type v} [Pure m] : MonadLiftT Id m where
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monadLift x := pure x.run
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end Id
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