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{-# LANGUAGE NoImplicitPrelude #-}
import Internals hiding ('Eq, (==))
infix 4 ==, /=, <
infixr 3 &&
infixr 2 ||
not True = False
not False = True
True && a = a
False && _ = False
False || a = a
True || _ = True
class Eq a where
(==) :: a -> a -> Bool
a /= b = not (a == b)
instance Eq Bool where
True == a = a
False == a = not a
[] ==. [] = True
(a:as) ==. (b:bs) = {-a == b && -} as ==. bs
_ ==. _ = False
{-
instance Eq t => Eq [t] where
[] == [] = True
a:as == b:bs = a == b && as == bs
_ == _ = False
-}
{-
Ord = \a -> Eq a & Ord' a -- so this is an alias, always subst.
cosmetics:
- subst. Ord' with Ord when presented to the user
- omit Eq whereever possible
- mark Ord-stemmed Eq as 'derived'
- 'derived' Eq overcomes other Eq
- eliminate all 'derived' Eq
Ord' Bool = 'Unit
Ord' [a] = Ord a
todo: mutual recursion
-}
{-
class Eq a => Ord a where
(<) :: a -> a -> Bool
instance Ord Bool where
_ < False = False
b < True = not b
instance Ord a => Ord [a] where
a:as < b:bs = a < b || a == b && as < bs
_ < [] = False
[] < _ = True
main = [False, True] == [False, True]
&& [False, True] /= [False, False]
&& [False, True] /= [False]
&& False < True
&& not (False < False)
&& [False] < [False, True]
&& [[False]] < [[False], []]
-}
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