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