### 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 - ___ 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

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

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 ___ 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

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

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