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.
52 lines
1.4 KiB
Text
52 lines
1.4 KiB
Text
/-
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Copyright (c) 2021 Gabriel Ebner. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Gabriel Ebner, Mario Carneiro
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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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/-!
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Instances converting between `Zero α` and `OfNat α (nat_lit 0)`.
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-/
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instance (priority := 300) Zero.toOfNat0 {α} [Zero α] : OfNat α (nat_lit 0) where
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ofNat := ‹Zero α›.1
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instance (priority := 200) Zero.ofOfNat0 {α} [OfNat α (nat_lit 0)] : Zero α where
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zero := 0
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/-!
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Instances converting between `One α` and `OfNat α (nat_lit 1)`.
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-/
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instance (priority := 300) One.toOfNat1 {α} [One α] : OfNat α (nat_lit 1) where
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ofNat := ‹One α›.1
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instance (priority := 200) One.ofOfNat1 {α} [OfNat α (nat_lit 1)] : One α where
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one := 1
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/--
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The fundamental power operation in a monoid.
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`npowRec n a = a*a*...*a` n times.
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This function should not be used directly; it is often used to implement a `Pow M Nat` instance,
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but end users should use the `a ^ n` notation instead.
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-/
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@[expose]
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def npowRec [One M] [Mul M] : Nat → M → M
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| 0, _ => 1
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| n + 1, a => npowRec n a * a
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/--
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The fundamental scalar multiplication in an additive monoid.
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`nsmulRec n a = a+a+...+a` n times.
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This function should not be used directly;
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it is often used to implement an instance for scalar multiplication.
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-/
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def nsmulRec [Zero M] [Add M] : Nat → M → M
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| 0, _ => 0
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| n + 1, a => nsmulRec n a + a
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