Does the wording of the report specify "totally ordered" as a law? I think it would be good to make that explicit, laying out the axioms for what a total order is—similar to the current documentation in Data.Ord but explicitly as the laws for the class. The relationship between Eq and Ord should be explicitly specified too, if it isn't. On Wed, Feb 6, 2019, 12:53 Herbert Valerio Riedel

On Wed, Feb 6, 2019 at 9:43 PM chessai . wrote:

...

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 <= functions.

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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 . wrote:

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 wrote:

...

On Wed, Feb 6, 2019 at 9:43 PM chessai . wrote:

...

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 <= functions.

...

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

true, i just actually WANT to fixup those corners of float, assuming impact can be managed suitably On Wed, Feb 6, 2019 at 10:30 PM David Feuer wrote:

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 . wrote:

...

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 wrote:

...

On Wed, Feb 6, 2019 at 9:43 PM chessai .

wrote:

...

...

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 <= functions.

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

I guess the OTHER important reason is: any code that assumes those putative laws will break horribly on floating point data types in the presence of NAN values for any code that assumes those laws (but only when NANs happen ) On Wed, Feb 6, 2019 at 10:46 PM Carter Schonwald wrote:

(and to be even clearer, its definitely something where any help on determining impact and minimizing it would be a pure joy to have )

On Wed, Feb 6, 2019 at 10:42 PM Carter Schonwald < carter.schonwald@gmail.com> wrote:

...

true, i just actually WANT to fixup those corners of float, assuming impact can be managed suitably

On Wed, Feb 6, 2019 at 10:30 PM David Feuer wrote:

...

We can add laws while recognizing that some existing instances are not lawful.

On Wed, Feb 6, 2019, 9:43 PM Carter Schonwald < carter.schonwald@gmail.com wrote:

...

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 . wrote:

...

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 wrote:

...

On Wed, Feb 6, 2019 at 9:43 PM chessai .

wrote:

...

> > 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 <= functions.

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

I was discussing this with Carter on IRC, so to chime in with my two cents: I think the default behaviour for Float/Double should use a trapping NaN. The current value NaN is as if every Double value has an implicit "fromJust" and finding out which part of larger computations/pipelines introduced the NaNs in your output is a pain. Trapping NaN would also eliminate the brokenness of Ord. If some people are really attached to value NaNs (why?!? What's wrong with you?) we could allow disabling trapping at compile or runtime so they get the old behaviour. Cheers, Merijn

On 7 Feb 2019, at 03:43, Carter Schonwald wrote:

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 . wrote: 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 wrote:

...

On Wed, Feb 6, 2019 at 9:43 PM chessai . wrote:

...

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 <= functions.

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Given that compare :: ... -> Ordering and Ordering = LT | EQ | GT, then the current Ord class has to support *total* orders, as there is no way to indicate when two elements are incomparable. Imagine trying to define the obvious partial ordering on sets - i.e. subset-or-equal using the Ord class. What should be the result, for Instance Ord (Set Int) of compare (fromList [1]) (fromList [2]) or fromList [2] <= fromList [1] ? Cheers, Andrew

On 7 Feb 2019, at 16:21, Elliot Cameron wrote:

While I'm sure it would be a lot of churn, couldn't we introduce a `TotalOrd` class and guard it more carefully?

On Thu, Feb 7, 2019 at 10:45 AM Merijn Verstraaten mailto:merijn@inconsistent.nl> wrote: I was discussing this with Carter on IRC, so to chime in with my two cents:

I think the default behaviour for Float/Double should use a trapping NaN. The current value NaN is as if every Double value has an implicit "fromJust" and finding out which part of larger computations/pipelines introduced the NaNs in your output is a pain.

Trapping NaN would also eliminate the brokenness of Ord. If some people are really attached to value NaNs (why?!? What's wrong with you?) we could allow disabling trapping at compile or runtime so they get the old behaviour.

Cheers, Merijn

...

On 7 Feb 2019, at 03:43, Carter Schonwald mailto:carter.schonwald@gmail.com> wrote:

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 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 . mailto:chessai1996@gmail.com> wrote: 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 mailto:hvriedel@gmail.com> wrote:

...

On Wed, Feb 6, 2019 at 9:43 PM chessai . mailto:chessai1996@gmail.com> wrote:

...

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 <= functions.

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-------------------------------------------------------------------- Andrew Butterfield Tel: +353-1-896-2517 Fax: +353-1-677-2204 Lero@TCD, Head of Foundations & Methods Research Group School of Computer Science and Statistics, Room G.39, O'Reilly Institute, Trinity College, University of Dublin http://www.scss.tcd.ie/Andrew.Butterfield/ --------------------------------------------------------------------

On Thu, 7 Feb 2019, Andrew Butterfield wrote:

Imagine trying to define the obvious partial ordering on sets - i.e. subset-or-equal using the Ord class. What should be the result, for Instance Ord (Set Int) of

compare (fromList [1]) (fromList [2])    or  fromList [2] <= fromList [1] ?

Partial ordering means to me that the comparison function is partial. I.e. fromList [2] <= fromList [1] would be "undefined".

On Fri, 8 Feb 2019, Oliver Charles wrote:

On Fri, 8 Feb 2019, 12:20 am Henning Thielemann, wrote:

On Thu, 7 Feb 2019, Andrew Butterfield wrote:

> Imagine trying to define the obvious partial ordering on sets - i.e. > subset-or-equal using the Ord class. What should be the result, for > Instance Ord (Set Int) of > > compare (fromList [1]) (fromList [2])    or  fromList [2] <= fromList [1] ?

Partial ordering means to me that the comparison function is partial. I.e. fromList [2] <= fromList [1] would be "undefined".__________________

Oh heavens no! It's very useful to ask whether two elements are comparable, that's  a nightmare with this approach.

With the signature of 'compare' we can hardly do it better. That's why it is certainly better to leave Ord for total orderings and define class PartialOrd a where maybeCompare :: a -> a -> Maybe Ordering

On Thu, 7 Feb 2019, Merijn Verstraaten wrote:

I think the default behaviour for Float/Double should use a trapping NaN. The current value NaN is as if every Double value has an implicit "fromJust"

I like to think of it like all operations are lifted to (Maybe Float).

Trapping NaN would also eliminate the brokenness of Ord. If some people are really attached to value NaNs (why?!? What's wrong with you?) we could allow disabling trapping at compile or runtime so they get the old behaviour.

What about calling into foreign code? If I call a BLAS routine and one element of the result vector is NaN, shall this be trapped? Or shall it be trapped once I access the NaN element?

@sven and @henning : i'm actually doing some preliminary work to add save and restore for FPU state to the GHC RTS, at the green/haskell thread layer. after first ripping out x87 code gen, which just needs some more docs written out before its merged in. note that i'm speaking specifically of the MXCSR register save and restore, not the more hefty operations you might be thinking. FPU mode state save and restore is done already on EVERY OS when switching threads/processes, and in the agner fog latency tables the cost of manipulating mxcsr registers is pretty small! https://www.agner.org/optimize/instruction_tables.pdf LDMXCSR (restore) and STMXCSR (save) have cpu latencies at like 5-20 cycles (more often 8-15), so having the current C ffi calls set the default C FPU environment (as we currently have ordinarily) is super doable to ensure no breakage of existing C bindings, plus have a new ccall variant that inherits the host haskell thread FPU state. we're talking sub 10 nanosecond overhead on x86 and x86_64 platforms (and either way, on those platforms soon ghc will only be using the sse2 or higher ). point being: aside from like AMD piledriver micro architecture and some stuff from VIA, the performance of the CPU instruction for the signalling nans state setup and related rounding mode etc, should work perfectly well, @Daniel Cartwright I do not support documenting false laws in any enshrined way, it will result in broken code. (Also i'm actually working to do some fixes, if you reread my remarks and merijn's, and i think we can have our cake and eat it, with the finest floats). Lets fix stuff and then document true laws! On Thu, Feb 7, 2019 at 12:05 PM Sven Panne wrote:

Am Do., 7. Feb. 2019 um 17:22 Uhr schrieb Henning Thielemann < lemming@henning-thielemann.de>:

...

[...] What about calling into foreign code? If I call a BLAS routine and one element of the result vector is NaN, shall this be trapped? Or shall it be trapped once I access the NaN element?

IMHO this is the biggest show stopper for some exotic NaN handling, as correct as it may be mathematically or aesthetically: The floating point environment is a thread-local (i.e. basically global) entity on most platforms, and most programming language runtimes expect a "default" environment, i.e. no traps when NaNs are encountered. So if Haskell wants to do things differently, the FPE has to be set/reset around foreign calls and for around every Haskell callback. I am not sure if this is really worth the trouble and the performance loss. For some special applications it might be OK or even important, but my gut feeling is that trapping NaNs is the wrong default in our current world... _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Even if Ord becomes lawful for floating point, there will still be massive problems reasoning about it because the Num instances can't support the ring laws, let alone the ordered ring laws. What should `compare NaN n` be? If it's an exception, then the ordering is not total, you can't store NaN in a Set, etc. If it's LT or GT, then you get a total ordering, but a rather weird one. So yeah, you'd be able to store NaN in a Set and have an NaN key in a Map, but then as soon as you start looking at where these are coming from and where they're going, everything goes weird and you need type-specific code anyway. On Thu, Feb 7, 2019, 4:29 PM Carter Schonwald

to further add weight, i'm still doing preliminary hackery on the signalling approach, but the signalling for FP state stuff seems to be OS thread local, so it can be treated as an exception perfectly well!

On Thu, Feb 7, 2019 at 4:27 PM Carter Schonwald < carter.schonwald@gmail.com> wrote:

...

@sven and @henning : i'm actually doing some preliminary work to add save and restore for FPU state to the GHC RTS, at the green/haskell thread layer. after first ripping out x87 code gen, which just needs some more docs written out before its merged in. note that i'm speaking specifically of the MXCSR register save and restore, not the more hefty operations you might be thinking.

FPU mode state save and restore is done already on EVERY OS when switching threads/processes, and in the agner fog latency tables the cost of manipulating mxcsr registers is pretty small! https://www.agner.org/optimize/instruction_tables.pdf

LDMXCSR (restore) and STMXCSR (save) have cpu latencies at like 5-20 cycles (more often 8-15), so having the current C ffi calls set the default C FPU environment (as we currently have ordinarily) is super doable to ensure no breakage of existing C bindings, plus have a new ccall variant that inherits the host haskell thread FPU state. we're talking sub 10 nanosecond overhead on x86 and x86_64 platforms (and either way, on those platforms soon ghc will only be using the sse2 or higher ).

point being: aside from like AMD piledriver micro architecture and some stuff from VIA, the performance of the CPU instruction for the signalling nans state setup and related rounding mode etc, should work perfectly well,

@Daniel Cartwright I do not support documenting false laws in any enshrined way, it will result in broken code. (Also i'm actually working to do some fixes, if you reread my remarks and merijn's, and i think we can have our cake and eat it, with the finest floats). Lets fix stuff and then document true laws!

On Thu, Feb 7, 2019 at 12:05 PM Sven Panne wrote:

...

Am Do., 7. Feb. 2019 um 17:22 Uhr schrieb Henning Thielemann < lemming@henning-thielemann.de>:

...

[...] What about calling into foreign code? If I call a BLAS routine and one element of the result vector is NaN, shall this be trapped? Or shall it be trapped once I access the NaN element?

IMHO this is the biggest show stopper for some exotic NaN handling, as correct as it may be mathematically or aesthetically: The floating point environment is a thread-local (i.e. basically global) entity on most platforms, and most programming language runtimes expect a "default" environment, i.e. no traps when NaNs are encountered. So if Haskell wants to do things differently, the FPE has to be set/reset around foreign calls and for around every Haskell callback. I am not sure if this is really worth the trouble and the performance loss. For some special applications it might be OK or even important, but my gut feeling is that trapping NaNs is the wrong default in our current world... _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

On 7 Feb 2019, at 22:41, David Feuer wrote:

Even if Ord becomes lawful for floating point, there will still be massive problems reasoning about it because the Num instances can't support the ring laws, let alone the ordered ring laws. What should `compare NaN n` be?

Our goal is to make "compare NaN n" impossible to happen. You can only (try) to compare with NaN if you can *get* a NaN value. But IEEE-754 pretty clearly does *NOT* require computations that evaluate to NaN to be represented as values. "Trap representations" (i.e., anything vaguely exception like) are an acceptable IEEE-754 compliant way of implementing NaN. All the major CPU platforms support trapping floating point exceptions, not many languages make use of this.

If it's an exception, then the ordering is not total, you can't store NaN in a Set, etc.

I think this argument is without merit. Yes, it would mean you can't store NaN in a Set anymore (because you wouldn't even be able to have a NaN value...). But that's like complaining Int is broken because I can't store "(5 `div` 0)" in a Set. So far everyone seems perfectly ok with the exception raised by division by zero, so why not NaN?

If it's LT or GT, then you get a total ordering, but a rather weird one. So yeah, you'd be able to store NaN in a Set and have an NaN key in a Map, but then as soon as you start looking at where these are coming from and where they're going, everything goes weird and you need type-specific code anyway.

If we accept value NaN's (as opposed to trapping NaNs) then we can't have Ord anyway, at least not without giving up on IEEE-754 compliance, as IEEE-754 demands "NaN" compares unequal with itself, which breaks any sort of ordering based function (even simple things like sort, as I painfully discovered in Python...) Cheers, Merijn

I think we've gotten a bit off-track here. Certainly we have disagreements about what should be done regarding floating-point values in GHC over the longer term, but that shouldn't hold up the report. I would prefer to see the total order laws added as Daniel suggested, while documenting that Float and Double have non-lawful instances due to NaNs. If the handling of doubles is later improved we can simply delete that line of documentation. On Fri, 8 Feb 2019 at 08:34, Carter Schonwald wrote:

additionally (for posterity), merjin pointed out to me that we do want x/0 to not be an exception when abs(x)!= 0, because +/- infinity are perfectly valid and useful mathematical objects

On Thu, Feb 7, 2019 at 5:31 PM Merijn Verstraaten wrote:

...

...

On 7 Feb 2019, at 22:41, David Feuer wrote:

Even if Ord becomes lawful for floating point, there will still be massive problems reasoning about it because the Num instances can't support the ring laws, let alone the ordered ring laws. What should `compare NaN n` be?

Our goal is to make "compare NaN n" impossible to happen. You can only (try) to compare with NaN if you can *get* a NaN value. But IEEE-754 pretty clearly does *NOT* require computations that evaluate to NaN to be represented as values.

"Trap representations" (i.e., anything vaguely exception like) are an acceptable IEEE-754 compliant way of implementing NaN. All the major CPU platforms support trapping floating point exceptions, not many languages make use of this.

...

If it's an exception, then the ordering is not total, you can't store NaN in a Set, etc.

I think this argument is without merit. Yes, it would mean you can't store NaN in a Set anymore (because you wouldn't even be able to have a NaN value...). But that's like complaining Int is broken because I can't store "(5 `div` 0)" in a Set. So far everyone seems perfectly ok with the exception raised by division by zero, so why not NaN?

...

If it's LT or GT, then you get a total ordering, but a rather weird one. So yeah, you'd be able to store NaN in a Set and have an NaN key in a Map, but then as soon as you start looking at where these are coming from and where they're going, everything goes weird and you need type-specific code anyway.

If we accept value NaN's (as opposed to trapping NaNs) then we can't have Ord anyway, at least not without giving up on IEEE-754 compliance, as IEEE-754 demands "NaN" compares unequal with itself, which breaks any sort of ordering based function (even simple things like sort, as I painfully discovered in Python...)

Cheers, Merijn

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Yes, quite. This is only about clarifications to the report. All this other stuff seems mostly tangential, and should probably be another thread. On Thu, Feb 7, 2019, 5:44 PM George Wilson

I think we've gotten a bit off-track here. Certainly we have disagreements about what should be done regarding floating-point values in GHC over the longer term, but that shouldn't hold up the report. I would prefer to see the total order laws added as Daniel suggested, while documenting that Float and Double have non-lawful instances due to NaNs. If the handling of doubles is later improved we can simply delete that line of documentation.

On Fri, 8 Feb 2019 at 08:34, Carter Schonwald wrote:

...

additionally (for posterity), merjin pointed out to me that we do want

x/0 to not be an exception when abs(x)!= 0, because +/- infinity are perfectly valid and useful mathematical objects

...

On Thu, Feb 7, 2019 at 5:31 PM Merijn Verstraaten <

...

...

...

On 7 Feb 2019, at 22:41, David Feuer wrote:

Even if Ord becomes lawful for floating point, there will still be

massive problems reasoning about it because the Num instances can't support

...

...

Our goal is to make "compare NaN n" impossible to happen. You can only

(try) to compare with NaN if you can *get* a NaN value. But IEEE-754 pretty clearly does *NOT* require computations that evaluate to NaN to be represented as values.

...

"Trap representations" (i.e., anything vaguely exception like) are an

acceptable IEEE-754 compliant way of implementing NaN. All the major CPU

merijn@inconsistent.nl> wrote: the ring laws, let alone the ordered ring laws. What should `compare NaN n` be? platforms support trapping floating point exceptions, not many languages make use of this.

...

...

...

If it's an exception, then the ordering is not total, you can't store

NaN in a Set, etc.

...

I think this argument is without merit. Yes, it would mean you can't

store NaN in a Set anymore (because you wouldn't even be able to have a NaN value...). But that's like complaining Int is broken because I can't store "(5 `div` 0)" in a Set. So far everyone seems perfectly ok with the exception raised by division by zero, so why not NaN?

...

...

If it's LT or GT, then you get a total ordering, but a rather weird

one. So yeah, you'd be able to store NaN in a Set and have an NaN key in a Map, but then as soon as you start looking at where these are coming from and where they're going, everything goes weird and you need type-specific code anyway.

...

If we accept value NaN's (as opposed to trapping NaNs) then we can't

have Ord anyway, at least not without giving up on IEEE-754 compliance, as IEEE-754 demands "NaN" compares unequal with itself, which breaks any sort of ordering based function (even simple things like sort, as I painfully discovered in Python...)

...

Cheers, Merijn

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---

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On 8 Feb 2019, at 10:57, Sven Panne wrote:

Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten : Our goal is to make "compare NaN n" impossible to happen. [...]

Well, what is supposed to happen then when you *do* see a NaN, e.g. one produced from a foreign call? You *will* see NaNs in Haskell if you interact with other languages, most of them take a far less religious approach to floating points calculations.

This is not true. As Carter pointed out we can setup the CPU to trap NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. Doing this we can simply convert the trap into an exception at the FFI boundary. Now, there are cases were this is problematic, so as said before we will probably need to allow people to optionally switch on 'value NaNs', because the foreign code isn't exception safe or for other reasons, but this is manageable. Via, for example having an annotation on foreign imports whether you want to trap or not. In the scenario where someone switches to value NaNs, we are *still* not worse off than we are now. The things you suggest already happen *now*, so the only thing we're advocating is making it possible to have more sane behaviour in the future. Any IEEE-754 compliant implementation of Double that doesn't use trapping NaN can, by definition, never ever be a sane implementation of Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't apply to NaNs and there is *no* safe way to sort/order data containing NaNs. I've run into several nasty issues of trying to sort lists containing NaNs (not just Haskell, also Python and C) and it's *not* just the NaNs that are affected, entire subsequences end up getting sorted wrong based on the comparison with NaN and you end up with completely garbled and unsorted data. In other words, there are only two ways to get sane behaviour from Double with regards to ordering: 1. Trapping NaN represenation 2. Deviate from IEEE-754 semantics To me, option 2 is out of the question, it's the one consistent thing across language we have when it comes to floating point. I understand that *always* using trap representation isn't feasible, but allowing people to optionally switch to value NaNs leaves us no worse off than we are *right now*, and per above, there is literally no way to improve the situation wrt value NaNs without sacrificing IEEE-754 compliance. Cheers, Merijn

I would *hate* to lose quiet NaNs. They can be very useful. But I’d be fine having them as a separate type. And while we’re at it, why not make Int overflow and underflow cause a trap as well? With a different type if you want to wrap. On Fri, Feb 8, 2019 at 08:34 Carter Schonwald wrote:

Thanks for eloquently summarizing , better than I would , what I thought I had laid out.

Ieee floating point has fantastic hardware support . May as well be the first real language to actually use it correctly. :)

On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten wrote:

...

...

On 8 Feb 2019, at 10:57, Sven Panne wrote:

Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten < merijn@inconsistent.nl>: Our goal is to make "compare NaN n" impossible to happen. [...]

Well, what is supposed to happen then when you *do* see a NaN, e.g. one produced from a foreign call? You *will* see NaNs in Haskell if you interact with other languages, most of them take a far less religious approach to floating points calculations.

This is not true. As Carter pointed out we can setup the CPU to trap NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. Doing this we can simply convert the trap into an exception at the FFI boundary.

Now, there are cases were this is problematic, so as said before we will probably need to allow people to optionally switch on 'value NaNs', because the foreign code isn't exception safe or for other reasons, but this is manageable. Via, for example having an annotation on foreign imports whether you want to trap or not.

In the scenario where someone switches to value NaNs, we are *still* not worse off than we are now. The things you suggest already happen *now*, so the only thing we're advocating is making it possible to have more sane behaviour in the future.

Any IEEE-754 compliant implementation of Double that doesn't use trapping NaN can, by definition, never ever be a sane implementation of Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't apply to NaNs and there is *no* safe way to sort/order data containing NaNs.

I've run into several nasty issues of trying to sort lists containing NaNs (not just Haskell, also Python and C) and it's *not* just the NaNs that are affected, entire subsequences end up getting sorted wrong based on the comparison with NaN and you end up with completely garbled and unsorted data.

In other words, there are only two ways to get sane behaviour from Double with regards to ordering:

1. Trapping NaN represenation 2. Deviate from IEEE-754 semantics

To me, option 2 is out of the question, it's the one consistent thing across language we have when it comes to floating point. I understand that *always* using trap representation isn't feasible, but allowing people to optionally switch to value NaNs leaves us no worse off than we are *right now*, and per above, there is literally no way to improve the situation wrt value NaNs without sacrificing IEEE-754 compliance.

Cheers, Merijn _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

I’m not sure if they currently have full ring structure , but I do agree that trapping and non trapping int and word are useful. Simple example where all the finite signed ints work wrong today : There’s no proper additive inverse for minBound :: int Likewise , what’s our current definition of negate on finite word types? On Fri, Feb 8, 2019 at 2:12 PM David Feuer wrote:

No, no, no. Int and Word are *rings*, which let's us apply a ton of mathematical reasoning to their arithmetic. Trapping overflow would throw all that completely out the window. If you want to trap overflow, please use different types!

On Fri, Feb 8, 2019, 2:07 PM Lennart Augustsson

...

I would *hate* to lose quiet NaNs. They can be very useful. But I’d be fine having them as a separate type.

And while we’re at it, why not make Int overflow and underflow cause a trap as well? With a different type if you want to wrap.

On Fri, Feb 8, 2019 at 08:34 Carter Schonwald wrote:

...

Thanks for eloquently summarizing , better than I would , what I thought I had laid out.

Ieee floating point has fantastic hardware support . May as well be the first real language to actually use it correctly. :)

On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten < merijn@inconsistent.nl> wrote:

...

...

On 8 Feb 2019, at 10:57, Sven Panne wrote:

Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten < merijn@inconsistent.nl>: Our goal is to make "compare NaN n" impossible to happen. [...]

Well, what is supposed to happen then when you *do* see a NaN, e.g. one produced from a foreign call? You *will* see NaNs in Haskell if you interact with other languages, most of them take a far less religious approach to floating points calculations.

This is not true. As Carter pointed out we can setup the CPU to trap NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. Doing this we can simply convert the trap into an exception at the FFI boundary.

Now, there are cases were this is problematic, so as said before we will probably need to allow people to optionally switch on 'value NaNs', because the foreign code isn't exception safe or for other reasons, but this is manageable. Via, for example having an annotation on foreign imports whether you want to trap or not.

In the scenario where someone switches to value NaNs, we are *still* not worse off than we are now. The things you suggest already happen *now*, so the only thing we're advocating is making it possible to have more sane behaviour in the future.

Any IEEE-754 compliant implementation of Double that doesn't use trapping NaN can, by definition, never ever be a sane implementation of Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't apply to NaNs and there is *no* safe way to sort/order data containing NaNs.

I've run into several nasty issues of trying to sort lists containing NaNs (not just Haskell, also Python and C) and it's *not* just the NaNs that are affected, entire subsequences end up getting sorted wrong based on the comparison with NaN and you end up with completely garbled and unsorted data.

In other words, there are only two ways to get sane behaviour from Double with regards to ordering:

1. Trapping NaN represenation 2. Deviate from IEEE-754 semantics

To me, option 2 is out of the question, it's the one consistent thing across language we have when it comes to floating point. I understand that *always* using trap representation isn't feasible, but allowing people to optionally switch to value NaNs leaves us no worse off than we are *right now*, and per above, there is literally no way to improve the situation wrt value NaNs without sacrificing IEEE-754 compliance.

Cheers, Merijn _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

minBound + minBound :: Int 0 negate minBound == (minBound :: Int) True 42 + negate 17 :: Word 25

Int and Word are currently rings. What proportion actually uses them as such would be interesting to know but I guess it is very small. I wouldn't dare to reason about Int and Word as rings as there is no guarantee on which ring they are. Int64 and Word64 and so on; yes, those can be reasoned about. I'd be very happy to see a separate type for signalling integral types. Personally, I'd make them the default choice. On Fri, 8 Feb 2019 at 19:27, Carter Schonwald wrote:

I’m not sure if they currently have full ring structure , but I do agree that trapping and non trapping int and word are useful.

Simple example where all the finite signed ints work wrong today :

There’s no proper additive inverse for minBound :: int

Likewise , what’s our current definition of negate on finite word types?

On Fri, Feb 8, 2019 at 2:12 PM David Feuer wrote:

...

No, no, no. Int and Word are *rings*, which let's us apply a ton of mathematical reasoning to their arithmetic. Trapping overflow would throw all that completely out the window. If you want to trap overflow, please use different types!

On Fri, Feb 8, 2019, 2:07 PM Lennart Augustsson

...

I would *hate* to lose quiet NaNs. They can be very useful. But I’d be fine having them as a separate type.

And while we’re at it, why not make Int overflow and underflow cause a trap as well? With a different type if you want to wrap.

On Fri, Feb 8, 2019 at 08:34 Carter Schonwald < carter.schonwald@gmail.com> wrote:

...

Thanks for eloquently summarizing , better than I would , what I thought I had laid out.

Ieee floating point has fantastic hardware support . May as well be the first real language to actually use it correctly. :)

On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten < merijn@inconsistent.nl> wrote:

...

...

On 8 Feb 2019, at 10:57, Sven Panne wrote:

Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten < merijn@inconsistent.nl>: Our goal is to make "compare NaN n" impossible to happen. [...]

Well, what is supposed to happen then when you *do* see a NaN, e.g. one produced from a foreign call? You *will* see NaNs in Haskell if you interact with other languages, most of them take a far less religious approach to floating points calculations.

This is not true. As Carter pointed out we can setup the CPU to trap NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. Doing this we can simply convert the trap into an exception at the FFI boundary.

Now, there are cases were this is problematic, so as said before we will probably need to allow people to optionally switch on 'value NaNs', because the foreign code isn't exception safe or for other reasons, but this is manageable. Via, for example having an annotation on foreign imports whether you want to trap or not.

In the scenario where someone switches to value NaNs, we are *still* not worse off than we are now. The things you suggest already happen *now*, so the only thing we're advocating is making it possible to have more sane behaviour in the future.

Any IEEE-754 compliant implementation of Double that doesn't use trapping NaN can, by definition, never ever be a sane implementation of Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't apply to NaNs and there is *no* safe way to sort/order data containing NaNs.

I've run into several nasty issues of trying to sort lists containing NaNs (not just Haskell, also Python and C) and it's *not* just the NaNs that are affected, entire subsequences end up getting sorted wrong based on the comparison with NaN and you end up with completely garbled and unsorted data.

In other words, there are only two ways to get sane behaviour from Double with regards to ordering:

1. Trapping NaN represenation 2. Deviate from IEEE-754 semantics

To me, option 2 is out of the question, it's the one consistent thing across language we have when it comes to floating point. I understand that *always* using trap representation isn't feasible, but allowing people to optionally switch to value NaNs leaves us no worse off than we are *right now*, and per above, there is literally no way to improve the situation wrt value NaNs without sacrificing IEEE-754 compliance.

Cheers, Merijn _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

I think the algebraic property we usually want for nice integer ish things is intergral domain. Which is a stronger property than ring. Pardon the confusion On Fri, Feb 8, 2019 at 3:03 PM Carter Schonwald wrote:

No. A ring can’t have 2x=0 for x not zero. Thus int can’t be

And by ring I mean an algebraic structure where you have a multiplicative group that doesn’t generate zero from products of nonzero elements ...

Phrased differently: Int doesn’t have a multiplicative group structure on the nonzero elements. That makes it a pretty nasty ring. Negate on minBound should be an overflow exception so you can have actual sane semantics. This is an old dead horse with lots of blood written about it.

https://ghc.haskell.org/trac/ghc/ticket/8695 has some related discussions

On Fri, Feb 8, 2019 at 2:53 PM Jens Blanck wrote:

...

...

minBound + minBound :: Int 0 negate minBound == (minBound :: Int) True 42 + negate 17 :: Word 25

Int and Word are currently rings. What proportion actually uses them as such would be interesting to know but I guess it is very small. I wouldn't dare to reason about Int and Word as rings as there is no guarantee on which ring they are. Int64 and Word64 and so on; yes, those can be reasoned about.

I'd be very happy to see a separate type for signalling integral types. Personally, I'd make them the default choice.

On Fri, 8 Feb 2019 at 19:27, Carter Schonwald wrote:

...

I’m not sure if they currently have full ring structure , but I do agree that trapping and non trapping int and word are useful.

Simple example where all the finite signed ints work wrong today :

There’s no proper additive inverse for minBound :: int

Likewise , what’s our current definition of negate on finite word types?

On Fri, Feb 8, 2019 at 2:12 PM David Feuer wrote:

...

No, no, no. Int and Word are *rings*, which let's us apply a ton of mathematical reasoning to their arithmetic. Trapping overflow would throw all that completely out the window. If you want to trap overflow, please use different types!

On Fri, Feb 8, 2019, 2:07 PM Lennart Augustsson

...

I would *hate* to lose quiet NaNs. They can be very useful. But I’d be fine having them as a separate type.

And while we’re at it, why not make Int overflow and underflow cause a trap as well? With a different type if you want to wrap.

On Fri, Feb 8, 2019 at 08:34 Carter Schonwald < carter.schonwald@gmail.com> wrote:

...

Thanks for eloquently summarizing , better than I would , what I thought I had laid out.

Ieee floating point has fantastic hardware support . May as well be the first real language to actually use it correctly. :)

On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten < merijn@inconsistent.nl> wrote:

> > > > On 8 Feb 2019, at 10:57, Sven Panne wrote: > > > > Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten < > merijn@inconsistent.nl>: > > Our goal is to make "compare NaN n" impossible to happen. [...] > > > > Well, what is supposed to happen then when you *do* see a NaN, > e.g. one produced from a foreign call? You *will* see NaNs in Haskell if > you interact with other languages, most of them take a far less religious > approach to floating points calculations. > > This is not true. As Carter pointed out we can setup the CPU to trap > NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. > Doing this we can simply convert the trap into an exception at the FFI > boundary. > > Now, there are cases were this is problematic, so as said before we > will probably need to allow people to optionally switch on 'value NaNs', > because the foreign code isn't exception safe or for other reasons, but > this is manageable. Via, for example having an annotation on foreign > imports whether you want to trap or not. > > In the scenario where someone switches to value NaNs, we are *still* > not worse off than we are now. The things you suggest already happen *now*, > so the only thing we're advocating is making it possible to have more sane > behaviour in the future. > > Any IEEE-754 compliant implementation of Double that doesn't use > trapping NaN can, by definition, never ever be a sane implementation of > Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't > apply to NaNs and there is *no* safe way to sort/order data containing NaNs. > > I've run into several nasty issues of trying to sort lists > containing NaNs (not just Haskell, also Python and C) and it's *not* just > the NaNs that are affected, entire subsequences end up getting sorted wrong > based on the comparison with NaN and you end up with completely garbled and > unsorted data. > > In other words, there are only two ways to get sane behaviour from > Double with regards to ordering: > > 1. Trapping NaN represenation > 2. Deviate from IEEE-754 semantics > > To me, option 2 is out of the question, it's the one consistent > thing across language we have when it comes to floating point. I understand > that *always* using trap representation isn't feasible, but allowing people > to optionally switch to value NaNs leaves us no worse off than we are > *right now*, and per above, there is literally no way to improve the > situation wrt value NaNs without sacrificing IEEE-754 compliance. > > Cheers, > Merijn > _______________________________________________ > Libraries mailing list > Libraries@haskell.org > http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries > _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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Wouldn't both versions throw an exception in that case? Am I missing something? On 2/8/19 2:26 PM, David Feuer wrote:

Yes, but a ring is sufficient for lots of very basic and important manipulations. When I'm writing code with Int and Word, I don't even think about whether the associative and distributive laws apply--I just use them to simplify my definitions. With trapping overflow, I need to watch for ranges every time I apply one. Horrible!

On Fri, Feb 8, 2019, 3:05 PM Carter Schonwald mailto:carter.schonwald@gmail.com wrote:

I think the algebraic property we usually want for nice integer ish things is intergral domain. Which is a stronger property than ring. Pardon the confusion 

On Fri, Feb 8, 2019 at 3:03 PM Carter Schonwald mailto:carter.schonwald@gmail.com> wrote:

No.  A ring can’t have 2x=0 for x not zero.  Thus int can’t  be 

And by ring I mean an algebraic structure where you have a multiplicative group that doesn’t generate zero from products of nonzero elements ... 

Phrased differently: Int doesn’t have a multiplicative group structure on the nonzero elements. That makes it a pretty nasty ring. Negate on minBound should be an overflow exception so you can have actual sane semantics.  This is an old dead horse with lots of blood written about it. 

https://ghc.haskell.org/trac/ghc/ticket/8695 has some related discussions 

On Fri, Feb 8, 2019 at 2:53 PM Jens Blanck mailto:jens.blanck@gmail.com> wrote:

> minBound + minBound :: Int 0 > negate minBound == (minBound :: Int) True > 42 + negate 17 :: Word 25

Int and Word are currently rings. What proportion actually uses them as such would be interesting to know but I guess it is very small. I wouldn't dare to reason about Int and Word as rings as there is no guarantee on which ring they are. Int64 and Word64 and so on; yes, those can be reasoned about.

I'd be very happy to see a separate type for signalling integral types. Personally, I'd make them the default choice.

On Fri, 8 Feb 2019 at 19:27, Carter Schonwald mailto:carter.schonwald@gmail.com> wrote:

I’m not sure if they currently have full ring structure , but  I do agree that trapping and non trapping int and word are useful. 

Simple example where all the finite signed ints work wrong today : 

There’s no proper additive inverse for minBound :: int 

Likewise , what’s our current definition of negate on finite word types?

On Fri, Feb 8, 2019 at 2:12 PM David Feuer mailto:david.feuer@gmail.com> wrote:

No, no, no. Int and Word are *rings*, which let's us apply a ton of mathematical reasoning to their arithmetic. Trapping overflow would throw all that completely out the window. If you want to trap overflow, please use different types!

On Fri, Feb 8, 2019, 2:07 PM Lennart Augustsson mailto:lennart@augustsson.net wrote:

I would *hate* to lose quiet NaNs.  They can be very useful.  But I’d be fine having them as a separate type.

And while we’re at it, why not make Int overflow and underflow cause a trap as well?  With a different type if you want to wrap. 

On Fri, Feb 8, 2019 at 08:34 Carter Schonwald mailto:carter.schonwald@gmail.com> wrote:

Thanks for eloquently summarizing , better than I would , what I thought I had laid out. 

Ieee floating point has fantastic hardware support .  May as well be the first real language to actually use it correctly. :)

On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten mailto:merijn@inconsistent.nl> wrote:

> On 8 Feb 2019, at 10:57, Sven Panne mailto:svenpanne@gmail.com> wrote: > > Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten mailto:merijn@inconsistent.nl>: > Our goal is to make "compare NaN n" impossible to happen. [...] > > Well, what is supposed to happen then when you *do* see a NaN, e.g. one produced from a foreign call? You *will* see NaNs in Haskell if you interact with other languages, most of them take a far less religious approach to floating points calculations.

This is not true. As Carter pointed out we can setup the CPU to trap NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. Doing this we can simply convert the trap into an exception at the FFI boundary.

Now, there are cases were this is problematic, so as said before we will probably need to allow people to optionally switch on 'value NaNs', because the foreign code isn't exception safe or for other reasons, but this is manageable. Via, for example having an annotation on foreign imports whether you want to trap or not.

In the scenario where someone switches to value NaNs, we are *still* not worse off than we are now. The things you suggest already happen *now*, so the only thing we're advocating is making it possible to have more sane behaviour in the future.

Any IEEE-754 compliant implementation of Double that doesn't use trapping NaN can, by definition, never ever be a sane implementation of Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't apply to NaNs and there is *no* safe way to sort/order data containing NaNs.

I've run into several nasty issues of trying to sort lists containing NaNs (not just Haskell, also Python and C) and it's *not* just the NaNs that are affected, entire subsequences end up getting sorted wrong based on the comparison with NaN and you end up with completely garbled and unsorted data.

In other words, there are only two ways to get sane behaviour from Double with regards to ordering:

1. Trapping NaN represenation 2. Deviate from IEEE-754 semantics

To me, option 2 is out of the question, it's the one consistent thing across language we have when it comes to floating point. I understand that *always* using trap representation isn't feasible, but allowing people to optionally switch to value NaNs leaves us no worse off than we are *right now*, and per above, there is literally no way to improve the situation wrt value NaNs without sacrificing IEEE-754 compliance.

Cheers, Merijn _______________________________________________ Libraries mailing list Libraries@haskell.org mailto:Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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I absolutely agree. Before any user visible stuff happens the first step would be rts support for better managing floating point flags / rounding mode / trap bits. Could you list some contexts / examples where you want quiet or signaling nans respectively? The more examples written down and shared the better! :) On Fri, Feb 8, 2019 at 2:07 PM Lennart Augustsson wrote:

I would *hate* to lose quiet NaNs. They can be very useful. But I’d be fine having them as a separate type.

And while we’re at it, why not make Int overflow and underflow cause a trap as well? With a different type if you want to wrap.

On Fri, Feb 8, 2019 at 08:34 Carter Schonwald wrote:

...

Thanks for eloquently summarizing , better than I would , what I thought I had laid out.

Ieee floating point has fantastic hardware support . May as well be the first real language to actually use it correctly. :)

On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten wrote:

...

...

On 8 Feb 2019, at 10:57, Sven Panne wrote:

Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten < merijn@inconsistent.nl>: Our goal is to make "compare NaN n" impossible to happen. [...]

Well, what is supposed to happen then when you *do* see a NaN, e.g. one produced from a foreign call? You *will* see NaNs in Haskell if you interact with other languages, most of them take a far less religious approach to floating points calculations.

This is not true. As Carter pointed out we can setup the CPU to trap NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. Doing this we can simply convert the trap into an exception at the FFI boundary.

Now, there are cases were this is problematic, so as said before we will probably need to allow people to optionally switch on 'value NaNs', because the foreign code isn't exception safe or for other reasons, but this is manageable. Via, for example having an annotation on foreign imports whether you want to trap or not.

In the scenario where someone switches to value NaNs, we are *still* not worse off than we are now. The things you suggest already happen *now*, so the only thing we're advocating is making it possible to have more sane behaviour in the future.

Any IEEE-754 compliant implementation of Double that doesn't use trapping NaN can, by definition, never ever be a sane implementation of Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't apply to NaNs and there is *no* safe way to sort/order data containing NaNs.

I've run into several nasty issues of trying to sort lists containing NaNs (not just Haskell, also Python and C) and it's *not* just the NaNs that are affected, entire subsequences end up getting sorted wrong based on the comparison with NaN and you end up with completely garbled and unsorted data.

In other words, there are only two ways to get sane behaviour from Double with regards to ordering:

1. Trapping NaN represenation 2. Deviate from IEEE-754 semantics

To me, option 2 is out of the question, it's the one consistent thing across language we have when it comes to floating point. I understand that *always* using trap representation isn't feasible, but allowing people to optionally switch to value NaNs leaves us no worse off than we are *right now*, and per above, there is literally no way to improve the situation wrt value NaNs without sacrificing IEEE-754 compliance.

Cheers, Merijn _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Wouldn't having both quiet and signalling NaN types imply wrapping all the primitive operations for one or other type in a CPU state switch? Maybe the compiler could then optimise some away. On 08/02/2019 19:07, Lennart Augustsson wrote:

I would *hate* to lose quiet NaNs.  They can be very useful.  But I’d be fine having them as a separate type.

And while we’re at it, why not make Int overflow and underflow cause a trap as well?  With a different type if you want to wrap. 

On Fri, Feb 8, 2019 at 08:34 Carter Schonwald mailto:carter.schonwald@gmail.com> wrote:

Thanks for eloquently summarizing , better than I would , what I thought I had laid out. 

Ieee floating point has fantastic hardware support .  May as well be the first real language to actually use it correctly. :)

On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten mailto:merijn@inconsistent.nl> wrote:

> On 8 Feb 2019, at 10:57, Sven Panne mailto:svenpanne@gmail.com> wrote: > > Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten mailto:merijn@inconsistent.nl>: > Our goal is to make "compare NaN n" impossible to happen. [...] > > Well, what is supposed to happen then when you *do* see a NaN, e.g. one produced from a foreign call? You *will* see NaNs in Haskell if you interact with other languages, most of them take a far less religious approach to floating points calculations.

This is not true. As Carter pointed out we can setup the CPU to trap NaNs *even in foreign calls*. So, in theory we CAN rule this out safely. Doing this we can simply convert the trap into an exception at the FFI boundary.

Now, there are cases were this is problematic, so as said before we will probably need to allow people to optionally switch on 'value NaNs', because the foreign code isn't exception safe or for other reasons, but this is manageable. Via, for example having an annotation on foreign imports whether you want to trap or not.

In the scenario where someone switches to value NaNs, we are *still* not worse off than we are now. The things you suggest already happen *now*, so the only thing we're advocating is making it possible to have more sane behaviour in the future.

Any IEEE-754 compliant implementation of Double that doesn't use trapping NaN can, by definition, never ever be a sane implementation of Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't apply to NaNs and there is *no* safe way to sort/order data containing NaNs.

I've run into several nasty issues of trying to sort lists containing NaNs (not just Haskell, also Python and C) and it's *not* just the NaNs that are affected, entire subsequences end up getting sorted wrong based on the comparison with NaN and you end up with completely garbled and unsorted data.

In other words, there are only two ways to get sane behaviour from Double with regards to ordering:

1. Trapping NaN represenation 2. Deviate from IEEE-754 semantics

To me, option 2 is out of the question, it's the one consistent thing across language we have when it comes to floating point. I understand that *always* using trap representation isn't feasible, but allowing people to optionally switch to value NaNs leaves us no worse off than we are *right now*, and per above, there is literally no way to improve the situation wrt value NaNs without sacrificing IEEE-754 compliance.

Cheers, Merijn _______________________________________________ Libraries mailing list Libraries@haskell.org mailto:Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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