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Merge pull request #2918 from buzden/min-max-gen-for-connex

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[ new ] Add generalisations of `min` and `max` for `StronglyConnex`
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André Videla 2023-06-16 15:27:06 +01:00 committed by GitHub
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2 changed files with 76 additions and 2 deletions
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6
CHANGELOG.md
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@ -166,6 +166,8 @@
* Implemented `Ord` for `Language.Reflection.TT.Name`, `Language.Reflection.TT.Namespace`
and `Language.Reflection.TT.UserName`.
* Adds `leftmost` and `rightmost` to `Control.Order`, a generalisation of `min` and `max`.
#### System
* Changes `getNProcessors` to return the number of online processors rather than
@ -177,9 +179,9 @@
* Adds `Data.List.Sufficient`, a small library defining a structurally inductive view of lists.
* Remove Data.List.HasLength from contrib library but add it to the base library
* Remove `Data.List.HasLength` from `contrib` library but add it to the `base` library
with the type signature from the compiler codebase and some of the naming
from the contrib library. The type ended up being `HasLength n xs` rather than
from the `contrib` library. The type ended up being `HasLength n xs` rather than
`HasLength xs n`.
* Adds an implementation for `Functor Text.Lexer.Tokenizer.Tokenizer`.

72
libs/base/Control/Order.idr
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@ -40,3 +40,75 @@ interface (PartialOrder ty rel, Connex ty rel) => LinearOrder ty rel where
||| Every equivalence relation is a preorder.
public export
[EP] Equivalence ty rel => Preorder ty rel where
--- Derivaties of order-based stuff ---
||| Gives the leftmost of a strongly connex relation among the given two elements, generalisation of `min`.
|||
||| That is, leftmost x y ~ x and leftmost x y ~ y, and `leftmost x y` is either `x` or `y`
public export
leftmost : (0 rel : _) -> StronglyConnex ty rel => ty -> ty -> ty
leftmost rel x y = either (const x) (const y) $ order {rel} x y
||| Gives the rightmost of a strongly connex relation among the given two elements, generalisation of `max`.
|||
||| That is, x ~ rightmost x y and y ~ rightmost x y, and `rightmost x y` is either `x` or `y`
public export
rightmost : (0 rel : _) -> StronglyConnex ty rel => ty -> ty -> ty
rightmost rel x y = either (const y) (const x) $ order {rel} x y
-- properties --
export
leftmostRelL : (0 rel : _) -> Reflexive ty rel => StronglyConnex ty rel => (x, y : ty) -> leftmost rel x y `rel` x
leftmostRelL rel x y with (order {rel} x y)
_ | Left _ = reflexive {rel}
_ | Right yx = yx
export
leftmostRelR : (0 rel : _) -> Reflexive ty rel => StronglyConnex ty rel => (x, y : ty) -> leftmost rel x y `rel` y
leftmostRelR rel x y with (order {rel} x y)
_ | Left xy = xy
_ | Right _ = reflexive {rel}
export
leftmostPreserves : (0 rel : _) -> StronglyConnex ty rel => (x, y : ty) -> Either (leftmost rel x y = x) (leftmost rel x y = y)
leftmostPreserves rel x y with (order {rel} x y)
_ | Left _ = Left Refl
_ | Right _ = Right Refl
export
leftmostIsRightmostLeft : (0 rel : _) -> StronglyConnex ty rel =>
(x, y : ty) ->
(z : ty) -> (z `rel` x) -> (z `rel` y) ->
(z `rel` leftmost rel x y)
leftmostIsRightmostLeft rel x y z zx zy with (order {rel} x y)
_ | Left _ = zx
_ | Right _ = zy
export
rightmostRelL : (0 rel : _) -> Reflexive ty rel => StronglyConnex ty rel => (x, y : ty) -> x `rel` rightmost rel x y
rightmostRelL rel x y with (order {rel} x y)
_ | Left xy = xy
_ | Right _ = reflexive {rel}
export
rightmostRelR : (0 rel : _) -> Reflexive ty rel => StronglyConnex ty rel => (x, y : ty) -> y `rel` rightmost rel x y
rightmostRelR rel x y with (order {rel} x y)
_ | Left _ = reflexive {rel}
_ | Right yx = yx
export
rightmostPreserves : (0 rel : _) -> StronglyConnex ty rel => (x, y : ty) -> Either (rightmost rel x y = x) (rightmost rel x y = y)
rightmostPreserves rel x y with (order {rel} x y)
_ | Left _ = Right Refl
_ | Right _ = Left Refl
export
rightmostIsLeftmostRight : (0 rel : _) -> StronglyConnex ty rel =>
(x, y : ty) ->
(z : ty) -> (x `rel` z) -> (y `rel` z) ->
(leftmost rel x y `rel` z)
rightmostIsLeftmostRight rel x y z zx zy with (order {rel} x y)
_ | Left _ = zx
_ | Right _ = zy