We can add laws while recognizing that some existing instances are not
lawful.
On Wed, Feb 6, 2019, 9:43 PM Carter Schonwald We cant add laws at the moment unless we change how the Ord instances for
Float and Double are defined. (which i think SHOULd happen, but needs some
care and has lots of implications) there are several possible semantics we can choose that act as we expect
on +/- infity and finite floats, but differ in the handling of nans option 1) use the total order defined in floating point standard 2008,
section 5.10, which defines negative nans below -infity, positive nans
above +infty
(this has the nice property that you could check for not nan by -infty
<= x && x <= infty) option 2) shift haskell/ GHC to having signalling NAN semantics by
default, so the only "fully evaluated" floating point values are in the
interval from negative to positive infinity , option 3) some mixture of the above I am slowly doing some patches to improve floating point bits in ghc (and
pave the way towards doing something like one of the above), though theres
still much to do also: the current definitions of min/max via compare aren't commutative if
either argument is nan (they become right biased or left biased, i forget
which) http://www.dsc.ufcg.edu.br/~cnum/modulos/Modulo2/IEEE754_2008.pdf is a
copy of ieee floating point 2008 (easy to google up a copy if that link
doesnt work) On Wed, Feb 6, 2019 at 4:31 PM chessai . Sure. There are no explicit mention of the laws of Ord. I think they
should be explicitly stated in the report, perhaps like so: ---------- start proposed change
class (Eq a) => Ord a where
compare :: a -> a -> Ordering
(<), (<=), (>), (>=) :: a -> a -> Bool
max, min :: a -> a -> a compare x y = if x == y then EQ
else if x <= y then LT
else GT x < y = case compare x y of { LT -> True; _ -> False }
x <= y = case compare x y of { GT -> False; _ -> True }
x > y = case compare x y of { GT -> True; _ -> False }
x >= y = case compare x y of { LT -> False; _ -> True } max x y = if x <= y then y else x
min x y = if x <= y then x else y
{-# MINIMAL compare | (<=) #-} The `Ord` class is used for totally ordered datatypes. Instances of
'Ord' can be derived for any user-defined datatype whose constituent
types are in 'Ord'. The declared order of the constructors in the data
declaration determines the ordering in the derived 'Ord' instances.
The 'Ordering' datatype allows a single comparison to determine the
precise ordering of two objects. A minimal instance of 'Ord' implements either 'compare' or '<=', and
is expected to adhere to the following laws: Antisymmetry (a <= b && b <= a = a == b)
Transitivity (a <= b && b <= c = a <= c)
Totality (a <= b || b <= a = True) An additional law, Reflexity, is implied by Totality. It states (x <= x =
True).
---------- end proposed change I don't particularly like the bit in the current documentation about
(<=) implementing a non-strict partial ordering, because if (<=)
constitutes a minimal definition of Ord and is required only to be a
partial ordering on the type parameterised by Ord, then why is Ord
required to be a total ordering? That seems sort of confusing. It
seems to me that the current documentation leans more toward 'Ord'
implementing a partial order than a total order. I can't speak for
others, but when I think of 'Ord' I usually think of a total ordering. Additionally, Reflexity is strictly weaker than Totality, so
specifying their relationship (Reflexivity is implied by Totality) and
also writing out what Totality means in the context of Ord makes sense
to me. For Eq, the report currently states: ----------begin report quote
class Eq a where
(==), (/=) :: a -> a -> Bool x /= y = not (x == y)
x == y = not (x /= y) The Eq class provides equality (==) and inequality (/=) methods. All
basic datatypes except for functions and IO are instances of this
class. Instances of Eq can be derived for any user-defined datatype
whose constituents are also instances of Eq. This declaration gives default method declarations for both /= and ==,
each being defined in terms of the other. If an instance declaration
for Eq defines neither == nor /=, then both will loop. If one is
defined, the default method for the other will make use of the one
that is defined. If both are defined, neither default method is used.
----------end report quote I think the following changes make sense: ---------- begin proposed changes class Eq a where
(==), (/=) :: a -> a -> Bool
x /= y = not (x == y)
x == y = not (x /= y) The 'Eq' class defines equality ('==') and inequality ('/=').
All the basic datatypes exported by the "Prelude" are instances of 'Eq',
and 'Eq' may be derived for any datatype whose constituents are also
instances of 'Eq'. '==' implements an equivalence relationship where two values comparing
equal
are considered indistinguishable. A minimal instance of 'Eq'
implements either '==' or '/=', and must adhere to the following laws: Reflexivity (x == x = True)
Symmetry (x == y = y == x)
Transitivity (x == y && y == z = x == z)
Substitutivity (x == y = f x == f y)
Negation (x /= y = not (x = y)
---------- end proposed changes On Wed, Feb 6, 2019 at 3:52 PM Herbert Valerio Riedel
On Wed, Feb 6, 2019 at 9:43 PM chessai . Per GHC.Classes (haddock-viewable from Data.Ord) "The Haskell Report defines no laws for Ord. However, <= is
customarily expected to implement a non-strict partial order and have
the following properties:" I propose that in the next report that the expected typeclass laws for
Ord be added. They're generally agreed upon/understood. Can you spell out the concrete change to the report wording you're suggesting? For reference, the current wording used in the 2010 Haskell
Report is quoted below. While at it, you might also want to take into
account the `Eq` class definition in the report. 6.3.2 The Ord Class class (Eq a) => Ord a where
compare :: a -> a -> Ordering
(<), (<=), (>=), (>) :: a -> a -> Bool
max, min :: a -> a -> a compare x y | x == y = EQ
| x <= y = LT
| otherwise = GT x <= y = compare x y /= GT
x < y = compare x y == LT
x >= y = compare x y /= LT
x > y = compare x y == GT -- Note that (min x y, max x y) = (x,y) or (y,x)
max x y | x <= y = y
| otherwise = x
min x y | x <= y = x
| otherwise = y The Ord class is used for totally ordered datatypes. All basic datatypes except for functions, IO, and IOError, are instances of this
class. Instances of Ord can be derived for any user-defined datatype whose
constituent types are in Ord. The declared order of the constructors in the
data declaration determines the ordering in derived Ord instances. The
Ordering datatype allows a single comparison to determine the precise
ordering of two objects. The default declarations allow a user to create an Ord instance either with a type-specific compare function or with type-specific == and <=
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