Equality test between types that returns type-level Bool ?

Takayuki Muranushi

25 Nov 2012 25 Nov '12

3:36 a.m.

Is it possible to write type family SameType a b :: Bool which returns True if a and b are the same type, and False otherwise? I encountered this problem when I was practicing promoted lists and tuples in ghc-7.6.1. One of my goal for practice is to write more "modular" version of extensible-dimensional calculations, and to understand whether ghc-7.6.1 is capable of it. http://hackage.haskell.org/packages/archive/dimensional/0.10.2/doc/html/Nume... Some of my attempts: https://github.com/nushio3/dimensional-tf/blob/master/attic/list-02.hs This fails because :==: is not an equality test between a and b, but is a equality test within a (promoted) kind. https://github.com/nushio3/dimensional-tf/blob/master/attic/list-03.hs This fails because type instance declarations are not read from top to bottom. (not like function declarations.) https://github.com/nushio3/dimensional-tf/blob/master/attic/map-03.hs I could define a lookup using class constraints, but when I use it, results in overlapping instances. So, will somebody teach me which of the following is correct? * We can write a type family SameType a b :: Bool * We cannot do that because of theoretical reason (that leads to non-termination etc.) * We cannot write SameType, but there are ways to write functions like 'filter' and 'merge' , over type-level lists, without using SameType. Always grateful to your help, -- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

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Gábor Lehel

25 Nov 25 Nov

10:51 a.m.

New subject: Equality test between types that returns type-level Bool ?

On Sun, Nov 25, 2012 at 9:36 AM, Takayuki Muranushi wrote:

...

Is it possible to write

type family SameType a b :: Bool

which returns True if a and b are the same type, and False otherwise?

I encountered this problem when I was practicing promoted lists and tuples in ghc-7.6.1. One of my goal for practice is to write more "modular" version of extensible-dimensional calculations, and to understand whether ghc-7.6.1 is capable of it.

http://hackage.haskell.org/packages/archive/dimensional/0.10.2/doc/html/Nume...

Some of my attempts:

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-02.hs This fails because :==: is not an equality test between a and b, but is a equality test within a (promoted) kind.

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-03.hs This fails because type instance declarations are not read from top to bottom. (not like function declarations.)

https://github.com/nushio3/dimensional-tf/blob/master/attic/map-03.hs I could define a lookup using class constraints, but when I use it, results in overlapping instances.

So, will somebody teach me which of the following is correct?

* We can write a type family SameType a b :: Bool * We cannot do that because of theoretical reason (that leads to non-termination etc.)

This is correct. It's not currently possible to have overlapping type family instances without breaking the soundness of the type system. There's some work on changing it: http://hackage.haskell.org/trac/ghc/wiki/NewAxioms

...

* We cannot write SameType, but there are ways to write functions like 'filter' and 'merge' , over type-level lists, without using SameType.

Not easily that I know of. There's no way to write a general "else", "otherwise", "if not", etc. case. You have to explicitly enumerate every type you want to use it with. It _is_ possible with type classes and OverlappingInstances, but beyond the trivial cases it tends to make my head hurt (and there's no way to get a result "out" of a type class "computation" and into a type family).

...

Always grateful to your help, -- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

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-- Your ship was destroyed in a monadic eruption.

Erik Hesselink

26 Nov 26 Nov

4:18 p.m.

New subject: Equality test between types that returns type-level Bool ?

If you're up for it, Oleg has a lot of interesting material about this subject [1]. Regards, Erik [1] http://okmij.org/ftp/Haskell/typeEQ.html On Sun, Nov 25, 2012 at 9:36 AM, Takayuki Muranushi wrote:

...

Is it possible to write

type family SameType a b :: Bool

which returns True if a and b are the same type, and False otherwise?

I encountered this problem when I was practicing promoted lists and tuples in ghc-7.6.1. One of my goal for practice is to write more "modular" version of extensible-dimensional calculations, and to understand whether ghc-7.6.1 is capable of it.

http://hackage.haskell.org/packages/archive/dimensional/0.10.2/doc/html/Nume...

Some of my attempts:

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-02.hs This fails because :==: is not an equality test between a and b, but is a equality test within a (promoted) kind.

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-03.hs This fails because type instance declarations are not read from top to bottom. (not like function declarations.)

https://github.com/nushio3/dimensional-tf/blob/master/attic/map-03.hs I could define a lookup using class constraints, but when I use it, results in overlapping instances.

So, will somebody teach me which of the following is correct?

* We can write a type family SameType a b :: Bool * We cannot do that because of theoretical reason (that leads to non-termination etc.) * We cannot write SameType, but there are ways to write functions like 'filter' and 'merge' , over type-level lists, without using SameType.

Always grateful to your help, -- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

Takayuki Muranushi

6:42 p.m.

New subject: Equality test between types that returns type-level Bool ?

Dear Gábor, Erik, and Oleg, Thank you for your advices. Also what I have wanted, the extensible dimensional type system, has just been released. http://hackage.haskell.org/package/unittyped-0.1 Now I have homeworks to test these, thank you! 2012/11/27 Erik Hesselink

...

If you're up for it, Oleg has a lot of interesting material about this subject [1].

Regards,

Erik

[1] http://okmij.org/ftp/Haskell/typeEQ.html

On Sun, Nov 25, 2012 at 9:36 AM, Takayuki Muranushi wrote:

...
Is it possible to write

type family SameType a b :: Bool

which returns True if a and b are the same type, and False otherwise?

I encountered this problem when I was practicing promoted lists and tuples in ghc-7.6.1. One of my goal for practice is to write more "modular" version of extensible-dimensional calculations, and to understand whether ghc-7.6.1 is capable of it.

http://hackage.haskell.org/packages/archive/dimensional/0.10.2/doc/html/Nume...

Some of my attempts:

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-02.hs This fails because :==: is not an equality test between a and b, but is a equality test within a (promoted) kind.

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-03.hs This fails because type instance declarations are not read from top to bottom. (not like function declarations.)

https://github.com/nushio3/dimensional-tf/blob/master/attic/map-03.hs I could define a lookup using class constraints, but when I use it, results in overlapping instances.

So, will somebody teach me which of the following is correct?

* We can write a type family SameType a b :: Bool * We cannot do that because of theoretical reason (that leads to non-termination etc.) * We cannot write SameType, but there are ways to write functions like 'filter' and 'merge' , over type-level lists, without using SameType.

Always grateful to your help, -- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

-- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

Takayuki Muranushi

28 Nov 28 Nov

10:47 a.m.

New subject: Equality test between types that returns type-level Bool ?

By tracing how unittyped produced the 'True-s and 'False-s in the error messages, and by Oleg's lecture,

...

1 meter + 5 second

<interactive>:17:9: Couldn't match type 'False with 'True When using functional dependencies to combine UnitTyped.And 'False 'False 'False, arising from the dependency `a b -> c' in the instance declaration in `UnitTyped' UnitTyped.And 'False 'False 'True, arising from a use of `+' at <interactive>:17:9 In the expression: 1 meter + 5 second In an equation for `it': it = 1 meter + 5 second I understood how type-level equalities https://github.com/nushio3/dimensional-tf/blob/master/attic/typeeq-01.hs and type-level list lookups https://github.com/nushio3/dimensional-tf/blob/master/attic/typeeq-03.hs can be implemented using overlapped instances. Thank you for the instructions. and I'm looking forward to see TYPEREP with ghc7.6.1's promoted integers and TH pretty soon! 2012/11/27 Takayuki Muranushi

...

Dear Gábor, Erik, and Oleg,

Thank you for your advices. Also what I have wanted, the extensible dimensional type system, has just been released.

http://hackage.haskell.org/package/unittyped-0.1

Now I have homeworks to test these, thank you!

2012/11/27 Erik Hesselink

...
If you're up for it, Oleg has a lot of interesting material about this subject [1].

Regards,

Erik

[1] http://okmij.org/ftp/Haskell/typeEQ.html

On Sun, Nov 25, 2012 at 9:36 AM, Takayuki Muranushi wrote:

...
Is it possible to write

type family SameType a b :: Bool

which returns True if a and b are the same type, and False otherwise?

I encountered this problem when I was practicing promoted lists and tuples in ghc-7.6.1. One of my goal for practice is to write more "modular" version of extensible-dimensional calculations, and to understand whether ghc-7.6.1 is capable of it.

http://hackage.haskell.org/packages/archive/dimensional/0.10.2/doc/html/Nume...

Some of my attempts:

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-02.hs This fails because :==: is not an equality test between a and b, but is a equality test within a (promoted) kind.

https://github.com/nushio3/dimensional-tf/blob/master/attic/list-03.hs This fails because type instance declarations are not read from top to bottom. (not like function declarations.)

https://github.com/nushio3/dimensional-tf/blob/master/attic/map-03.hs I could define a lookup using class constraints, but when I use it, results in overlapping instances.

So, will somebody teach me which of the following is correct?

* We can write a type family SameType a b :: Bool * We cannot do that because of theoretical reason (that leads to non-termination etc.) * We cannot write SameType, but there are ways to write functions like 'filter' and 'merge' , over type-level lists, without using SameType.

Always grateful to your help, -- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

-- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

-- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html

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Erik Hesselink
Gábor Lehel
Takayuki Muranushi