Re: [Haskell-cafe] partially applied data constructor and corresponding type
Richard Eisenberg wrote:
There's a lot of recent work on GHC that might be helpful to you. Is it
possible for your application to use GHC 7.6.x? If so, you could so
something like this:
{-# LANGUAGE DataKinds, GADTs, KindSignatures #-}
data Nat = Zero | Succ Nat
type One = Succ Zero
type Two = Succ One
type Three = Succ Two
-- connects the type-level Nat with a term-level construct
data SNat :: Nat - * where
SZero :: SNat Zero
SSucc :: SNat n - SNat (Succ n)
zero = SZero
one = SSucc zero
two = SSucc one
three = SSucc two
data Tensor (n :: Nat) a = MkTensor { dims :: SNat n, items :: [a] }
type Vector = Tensor One
type Matrix = Tensor Two
mkVector :: [a] - Vector a
mkVector v = MkTensor { dims = one, items = v }
vector_prod :: Num a = Vector a - Vector a
vector_prod (MkTensor { items = v }) = ...
specializable :: Tensor n a - Tensor n a
specializable (MkTensor { dims = SSucc SZero, items = vec }) = ...
specializable (MkTensor { dims = SSucc (SSucc SZero), items = mat }) = ...
This is similar to other possible approaches with type-level numbers, but
it makes more use of the newer features of GHC that assist with type-level
computation. Unfortunately, there are no constructor synonyms or
pattern synonyms in GHC, so you can't pattern match on MkVector or
something similar in specializable. But, the pattern matches in
specializable are GADT pattern-matches, and so GHC knows what the value of
n, the type variable, is on the right-hand sides. This will allow you to
write and use instances of Tensor defined only at certain numbers of
dimensions.
I hope this is helpful. Please write back if this technique is unclear!
Thanks a lot! Those days I have read about DataKinds extension (with help
of Haskell-Cafe guys), and now I am able to understand your code. The
technique to connect the type-level and term-level integers allows to
duplicate information (duplicate information needed because of my more or
less clear requirements in my previous posts), but in a safe way (i.e. with
no copy/paste error): if I change one in two in the definition of the
smart constructor mkVector, I obtain an error, as expected because of the
use of type variable n on both sides of the equality in Tensor type
definition (and then we understand why the type constructor SNat has been
introduced).
This is a working example (this is not exactly what I will do at the end,
but it is very instructive! One more time, thanks!):
--
{-# LANGUAGE DataKinds, GADTs, KindSignatures, StandaloneDeriving #-}
data Nat = Zero | Succ Nat
type One = Succ Zero
type Two = Succ One
type Three = Succ Two
-- connects the type-level Nat with a term-level construct
data SNat :: Nat - * where
SZero :: SNat Zero
SSucc :: SNat n - SNat (Succ n)
deriving instance Show (SNat a)
zero = SZero
one = SSucc zero
two = SSucc one
three = SSucc two
data Tensor (n :: Nat) a = MkTensor { order :: SNat n, items :: [a] }
deriving Show
type Vector = Tensor One
type Matrix = Tensor Two
mkVector :: [a] - Vector a
mkVector v = MkTensor { order = one, items = v }
-- some dummy operation defined between two Vectors (and not other order
-- tensors), which results in a Vector.
some_operation :: Num a = Vector a - Vector a - Vector a
some_operation (MkTensor { items = v1 }) (MkTensor { items = v2 }) =
mkVector (v1 ++ v2)
main = do
let va = mkVector ([1,2,3] :: [Integer])
let vb = mkVector ([4,5,6] :: [Integer])
print $ some_operation va vb
print $ order va
print $ order vb
-
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Re: [Haskell-cafe] partially applied data constructor and corresponding type
Thanks for pointing to type level integers. With that I have found: http://www.haskell.org/haskellwiki/The_Monad.Reader/Issue5/Number_Param_Types For example: --- data Zero = Zero data Succ a = Succ a class Card c where c2num:: c - Integer cpred::(Succ c) - c cpred = undefined instance Card Zero where c2num _ = 0 instance (Card c) = Card (Succ c) where c2num x = 1 + c2num (cpred x) main = do putStrLn $ show $ c2num (Succ (Succ Zero)) --- I will continue to examine the topic in the following days, according to my needs. Thanks a lot, TP On Sunday, April 28, 2013 07:58:58 Stephen Tetley wrote: What you probably want are type level integers (naturals) Yury Sulsky used them in the message above - basically you can't use literal numbers 1,2,3,... etc as they are values of type Int (or Integer, etc...) instead you have to use type level numbers: data One data Two Work is ongoing for type level numbers in GHC and there are user libraries on Hackage so there is a lot of work to crib from. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] partially applied data constructor and corresponding type
There's a lot of recent work on GHC that might be helpful to you. Is it
possible for your application to use GHC 7.6.x? If so, you could so something
like this:
{-# LANGUAGE DataKinds, GADTs, KindSignatures #-}
data Nat = Zero | Succ Nat
type One = Succ Zero
type Two = Succ One
type Three = Succ Two
-- connects the type-level Nat with a term-level construct
data SNat :: Nat - * where
SZero :: SNat Zero
SSucc :: SNat n - SNat (Succ n)
zero = SZero
one = SSucc zero
two = SSucc one
three = SSucc two
data Tensor (n :: Nat) a = MkTensor { dims :: SNat n, items :: [a] }
type Vector = Tensor One
type Matrix = Tensor Two
mkVector :: [a] - Vector a
mkVector v = MkTensor { dims = one, items = v }
vector_prod :: Num a = Vector a - Vector a
vector_prod (MkTensor { items = v }) = ...
specializable :: Tensor n a - Tensor n a
specializable (MkTensor { dims = SSucc SZero, items = vec }) = ...
specializable (MkTensor { dims = SSucc (SSucc SZero), items = mat }) = ...
This is similar to other possible approaches with type-level numbers, but it
makes more use of the newer features of GHC that assist with type-level
computation. Unfortunately, there are no constructor synonyms or pattern
synonyms in GHC, so you can't pattern match on MkVector or something similar
in specializable. But, the pattern matches in specializable are GADT
pattern-matches, and so GHC knows what the value of n, the type variable, is on
the right-hand sides. This will allow you to write and use instances of Tensor
defined only at certain numbers of dimensions.
I hope this is helpful. Please write back if this technique is unclear!
Richard
On Apr 29, 2013, at 2:55 AM, TP paratribulati...@free.fr wrote:
Thanks for pointing to type level integers. With that I have found:
http://www.haskell.org/haskellwiki/The_Monad.Reader/Issue5/Number_Param_Types
For example:
---
data Zero = Zero
data Succ a = Succ a
class Card c where
c2num:: c - Integer
cpred::(Succ c) - c
cpred = undefined
instance Card Zero where
c2num _ = 0
instance (Card c) = Card (Succ c) where
c2num x = 1 + c2num (cpred x)
main = do
putStrLn $ show $ c2num (Succ (Succ Zero))
---
I will continue to examine the topic in the following days, according to my
needs.
Thanks a lot,
TP
On Sunday, April 28, 2013 07:58:58 Stephen Tetley wrote:
What you probably want are type level integers (naturals)
Yury Sulsky used them in the message above - basically you can't use
literal numbers 1,2,3,... etc as they are values of type Int (or
Integer, etc...) instead you have to use type level numbers:
data One
data Two
Work is ongoing for type level numbers in GHC and there are user
libraries on Hackage so there is a lot of work to crib from.
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Re: [Haskell-cafe] partially applied data constructor and corresponding type
Thanks a lot for your message.
I can use a recent version of GHC 7.6.x (I will install the last version of
Kubuntu for that purpose).
However, it will take me some time to understand correctly this code (e.g. I
do not know data kinds), I will go back to you if I encounter difficulties.
Thanks,
TP
On Monday, April 29, 2013 08:19:43 Richard Eisenberg wrote:
There's a lot of recent work on GHC that might be helpful to you. Is it
possible for your application to use GHC 7.6.x? If so, you could so
something like this:
{-# LANGUAGE DataKinds, GADTs, KindSignatures #-}
data Nat = Zero | Succ Nat
type One = Succ Zero
type Two = Succ One
type Three = Succ Two
-- connects the type-level Nat with a term-level construct
data SNat :: Nat - * where
SZero :: SNat Zero
SSucc :: SNat n - SNat (Succ n)
zero = SZero
one = SSucc zero
two = SSucc one
three = SSucc two
data Tensor (n :: Nat) a = MkTensor { dims :: SNat n, items :: [a] }
type Vector = Tensor One
type Matrix = Tensor Two
mkVector :: [a] - Vector a
mkVector v = MkTensor { dims = one, items = v }
vector_prod :: Num a = Vector a - Vector a
vector_prod (MkTensor { items = v }) = ...
specializable :: Tensor n a - Tensor n a
specializable (MkTensor { dims = SSucc SZero, items = vec }) = ...
specializable (MkTensor { dims = SSucc (SSucc SZero), items = mat }) = ...
This is similar to other possible approaches with type-level numbers, but it
makes more use of the newer features of GHC that assist with type-level
computation. Unfortunately, there are no constructor synonyms or pattern
synonyms in GHC, so you can't pattern match on MkVector or something
similar in specializable. But, the pattern matches in specializable are
GADT pattern-matches, and so GHC knows what the value of n, the type
variable, is on the right-hand sides. This will allow you to write and use
instances of Tensor defined only at certain numbers of dimensions.
I hope this is helpful. Please write back if this technique is unclear!
Richard
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Re: [Haskell-cafe] partially applied data constructor and corresponding type
What you probably want are type level integers (naturals) Yury Sulsky used them in the message above - basically you can't use literal numbers 1,2,3,... etc as they are values of type Int (or Integer, etc...) instead you have to use type level numbers: data One data Two Work is ongoing for type level numbers in GHC and there are user libraries on Hackage so there is a lot of work to crib from. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] partially applied data constructor and corresponding type
Hi TP,
Are you looking to use a phantom types here? Here's an example:
data One
data Two
data Tensor ndims a = Tensor { dims :: [Int], items :: [a] }
type Vector = Tensor One
type Matrix = Tensor Two
etc.
On Sat, Apr 27, 2013 at 3:33 PM, TP paratribulati...@free.fr wrote:
Hello,
I ask myself if there is a way to do the following.
Imagine that I have a dummy type:
data Tensor = TensorVar Int String
where the integer is the order, and the string is the name of the tensor.
I would like to make with the constructor TensorVar a type Vector, such
that, in pseudo-language:
data Vector = TensorVar 1 String
Because a vector is a tensor of order 1.
Is this possible? I have tried type synonyms and newtypes without any
success.
Thanks a lot,
TP
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Re: [Haskell-cafe] partially applied data constructor and corresponding type
Thanks Yury,
The problem with this solution is that if I have written a method for the
Tensor type (for example a method of a typeclass of which Tensor is an
instance) that uses the order of the tensor (your ndims) in a general way, I
cannot reuse it easily for a vector defined like that.
In fact, my problem is to be able to define:
* from my type Tensor, a type Vector, by specifying that the dimension
must be one to have a Vector type.
* from my constructor TensorVar, a constructor VectorVar, which
corresponds to TensorVar with the integer equal to 1.
The idea is to avoid duplicating code, by reusing the tensor type and data
constructor. At some place in my code, in some definition (say, of a vector
product), I want vectors and not more general tensors.
TP
On Saturday, April 27, 2013 16:16:49 Yury Sulsky wrote:
Hi TP,
Are you looking to use a phantom types here? Here's an example:
data One
data Two
data Tensor ndims a = Tensor { dims :: [Int], items :: [a] }
type Vector = Tensor One
type Matrix = Tensor Two
etc.
On Sat, Apr 27, 2013 at 3:33 PM, TP paratribulati...@free.fr wrote:
Hello,
I ask myself if there is a way to do the following.
Imagine that I have a dummy type:
data Tensor = TensorVar Int String
where the integer is the order, and the string is the name of the tensor.
I would like to make with the constructor TensorVar a type Vector, such
that, in pseudo-language:
data Vector = TensorVar 1 String
Because a vector is a tensor of order 1.
Is this possible? I have tried type synonyms and newtypes without any success.
Thanks a lot,
TP
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