module UVMHS.Core.Classes.Order where

import UVMHS.Core.Init

import qualified Prelude as HS

infix 4 ≡,≢,⋚,≤,≥,<,>

(≡) ∷ (Eq a) ⇒ a → a → 𝔹
≡ :: forall a. Eq a => a -> a -> 𝔹
(≡) = a -> a -> 𝔹
forall a. Eq a => a -> a -> 𝔹
(HS.==)

(≢) ∷ (Eq a) ⇒ a → a → 𝔹
≢ :: forall a. Eq a => a -> a -> 𝔹
(≢) = a -> a -> 𝔹
forall a. Eq a => a -> a -> 𝔹
(HS./=)

(⋚) ∷ (Ord a) ⇒ a → a → Ordering
⋚ :: forall a. Ord a => a -> a -> Ordering
(⋚) = a -> a -> Ordering
forall a. Ord a => a -> a -> Ordering
compare

(≤) ∷ (Ord a) ⇒ a → a → 𝔹
a
x ≤ :: forall a. Ord a => a -> a -> 𝔹
≤ a
y = case a
x a -> a -> Ordering
forall a. Ord a => a -> a -> Ordering
⋚ a
y of {Ordering
LT → 𝔹
True;Ordering
EQ → 𝔹
True;Ordering
GT → 𝔹
False}

(≥) ∷ (Ord a) ⇒ a → a → 𝔹
a
x ≥ :: forall a. Ord a => a -> a -> 𝔹
≥ a
y = case a
x a -> a -> Ordering
forall a. Ord a => a -> a -> Ordering
⋚ a
y of {Ordering
LT → 𝔹
False;Ordering
EQ → 𝔹
True;Ordering
GT → 𝔹
True}

(<) ∷ (Ord a) ⇒ a → a → 𝔹
< :: forall a. Ord a => a -> a -> 𝔹
(<) = a -> a -> 𝔹
forall a. Ord a => a -> a -> 𝔹
(HS.<)

(>) ∷ (Ord a) ⇒ a → a → 𝔹
> :: forall a. Ord a => a -> a -> 𝔹
(>) = a -> a -> 𝔹
forall a. Ord a => a -> a -> 𝔹
(HS.>)

(⩏) ∷ (Ord a) ⇒ a → a → a
a
x ⩏ :: forall a. Ord a => a -> a -> a
⩏ a
y 
  | a
x a -> a -> 𝔹
forall a. Ord a => a -> a -> 𝔹
≤ a
y = a
y
  | 𝔹
otherwise = a
x

(⩎) ∷ (Ord a) ⇒ a → a → a
a
x ⩎ :: forall a. Ord a => a -> a -> a
⩎ a
y 
  | a
x a -> a -> 𝔹
forall a. Ord a => a -> a -> 𝔹
≤ a
y = a
x
  | 𝔹
otherwise = a
y

minBy ∷ (Ord b) ⇒ (a → b) → a → a → a
minBy :: forall b a. Ord b => (a -> b) -> a -> a -> a
minBy a -> b
f a
x a
y 
  | a -> b
f a
x b -> b -> 𝔹
forall a. Ord a => a -> a -> 𝔹
≤ a -> b
f a
y = a
x
  | 𝔹
otherwise = a
y

maxBy ∷ (Ord b) ⇒ (a → b) → a → a → a
maxBy :: forall b a. Ord b => (a -> b) -> a -> a -> a
maxBy a -> b
f a
x a
y 
  | a -> b
f a
x b -> b -> 𝔹
forall a. Ord a => a -> a -> 𝔹
≥ a -> b
f a
y = a
x
  | 𝔹
otherwise = a
y