# Matrix and types

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## Matrix and types

 Hi,As an exercise I want to write a Matrix library.Multiplication of two matrices is only defined when the the number of columns in the first matrix equals the number of rows in the second matrix. i.e. c1 == r2So when writing the multiplication function I can check that  c1 == r2 and do something.However what I really want to do, if possible, is to have the compiler catch the error. I’d appreciate any advice on how to approach this. I don’t want a full description of exactly what to do as that way I won’t have struggled  or argued with the compiler - which for me is the best way to learn Haskell :)ThanksMike_______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
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## Re: Matrix and types

 Hello Mike, On Thu, Mar 14, 2019 at 11:10:06AM +0000, mike h wrote: > Multiplication of two matrices is only defined when the the number of columns in the first matrix > equals the number of rows in the second matrix. i.e. c1 == r2 > > So when writing the multiplication function I can check that  c1 == r2 and do something. > However what I really want to do, if possible, is to have the compiler catch the error. Type-level literals [1] or any kind of similar trickery should help you with having matrices checked at compile-time. [1] https://downloads.haskell.org/~ghc/7.10.1/docs/html/users_guide/type-level-literals.html_______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
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## Re: Matrix and types

 The (experimental) Static module of hmatrix seems (I've used the packaged but not that module) to do exactly that: http://hackage.haskell.org/package/hmatrix-0.19.0.0/docs/Numeric-LinearAlgebra-Static.htmlOn Thu, Mar 14, 2019, 12:37 PM Francesco Ariis <[hidden email]> wrote:Hello Mike, On Thu, Mar 14, 2019 at 11:10:06AM +0000, mike h wrote: > Multiplication of two matrices is only defined when the the number of columns in the first matrix > equals the number of rows in the second matrix. i.e. c1 == r2 > > So when writing the multiplication function I can check that  c1 == r2 and do something. > However what I really want to do, if possible, is to have the compiler catch the error. Type-level literals [1] or any kind of similar trickery should help you with having matrices checked at compile-time. [1] https://downloads.haskell.org/~ghc/7.10.1/docs/html/users_guide/type-level-literals.html _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners -- Frederic Cogny+33 7 83 12 61 69 _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
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## Re: Matrix and types

 Hi,Thanks for the pointers. So I’ve gotdata M (n :: Nat) a = M [a] deriving Showt2 :: M 2 Intt2  = M [1,2]t3 :: M 3 Intt3 = M [1,2,3]fx :: Num a => M n a -> M n a -> M n afx (M xs) (M ys) = M (zipWith (+) xs ys)and having g = fx t2 t3won’t compile. Which is what I want.However…t2 :: M 2 Intt2  = M [1,2]is ‘hardwired’ to 2 and clearly I could make t2 return  a list of any length. So what I then tried to look at was a general function that would take a list of Int and create the M type using the length of the supplied list. In other words if I supply a list, xs, of length n then I wan’t  M n xsLike thiscreateIntM xs = (M xs) :: M (length xs) Intwhich compile and has typeλ-> :t createIntM createIntM :: [Int] -> M (length xs) Intand all Ms created using createIntM  have the same type irrespective of the length of the supplied list.What’s the type jiggery I need or is this not the right way to go?ThanksMikeOn 14 Mar 2019, at 13:12, Frederic Cogny <[hidden email]> wrote:The (experimental) Static module of hmatrix seems (I've used the packaged but not that module) to do exactly that: http://hackage.haskell.org/package/hmatrix-0.19.0.0/docs/Numeric-LinearAlgebra-Static.htmlOn Thu, Mar 14, 2019, 12:37 PM Francesco Ariis <[hidden email]> wrote:Hello Mike, On Thu, Mar 14, 2019 at 11:10:06AM +0000, mike h wrote: > Multiplication of two matrices is only defined when the the number of columns in the first matrix > equals the number of rows in the second matrix. i.e. c1 == r2 > > So when writing the multiplication function I can check that  c1 == r2 and do something. > However what I really want to do, if possible, is to have the compiler catch the error. Type-level literals [1] or any kind of similar trickery should help you with having matrices checked at compile-time. [1] https://downloads.haskell.org/~ghc/7.10.1/docs/html/users_guide/type-level-literals.html _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners -- Frederic Cogny+33 7 83 12 61 69 _______________________________________________Beginners mailing list[hidden email]http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners_______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
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## Re: Matrix and types

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## Re: Matrix and types

 Hi, The problem is that Haskell lists don't carry their length in their type hence you cannot enforce their length at compile time. But you can define your M this way instead: {-# LANGUAGE TypeOperators #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE KindSignatures #-} import GHC.TypeNats import Data.Proxy data M (n :: Nat) a where    MNil  :: M 0 a    MCons :: a -> M (n-1) a -> M n a infixr 5 `MCons` toList :: M k a -> [a] toList MNil         = [] toList (MCons a as) = a:toList as instance (KnownNat n, Show a) => Show (M n a) where    show xs = mconcat       [ "M @"       , show (natVal (Proxy :: Proxy n))       , " "       , show (toList xs)       ] --t2 :: M 2 Integer t2 = 1 `MCons` 2 `MCons` MNil --t3 :: M 3 Integer t3 = 1 `MCons` 2 `MCons` 3 `MCons` MNil zipM :: (a -> b -> c) -> M n a -> M n b -> M n c zipM _f MNil         MNil         = MNil zipM  f (MCons a as) (MCons b bs) = MCons (f a b) (zipM f as bs) fx :: Num a => M n a -> M n a -> M n a fx = zipM (+) Test: > t2 M @2 [1,2] > fx t2 t2 M @2 [2,4] > fx t2 t3 :38:7: error:     • Couldn't match type ‘3’ with ‘2’       Expected type: M 2 Integer         Actual type: M 3 Integer Cheers, Sylvain On 15/03/2019 13:57, mike h wrote: Hi Frederic, Yeh, my explanation is a bit dubious :)  What I’m trying to say is: Looking at the type M (n::Nat)  If I want an M 2  of Ints say,  then I need to write the function with signature  f :: M 2 Int   If I want a M 3 then I need to explicitly write the function with signature M 3 Int and so on for every possible instance that I might want. What I would like to do is have just one function that is somehow parameterised to create the M tagged with the required value of (n::Nat) In pseudo Haskell create :: Int -> [Int] -> M n  create size ns = (M ns) ::  M size Int where  its trying to coerce (M ns) into the type (M size Int) where size is an Int but needs to be a Nat. It’s sort of like parameterising the signature of the function. Thanks Mike On 15 Mar 2019, at 11:37, Frederic Cogny <[hidden email]> wrote: I'm not sure I understand your question Mike. Are you saying createIntM behaves as desired but the data constructor M could let you build a data M with the wrong type. for instance M [1,2] :: M 1 Int ? If that is your question, then one way to handle this is to have a separate module where you define the data type and the proper constructor (here M and createIntM) but where you do not expose the type constructor. so something like module MyModule   ( M -- as opposed to M(..) to not expose the type constructor   , createIntM   ) where Then, outside of MyModule, you can not create an incorrect lentgh annotated list since the only way to build it is through createIntM Does that make sense? On Thu, Mar 14, 2019 at 4:19 PM mike h <[hidden email]> wrote: Hi, Thanks for the pointers. So I’ve got data M (n :: Nat) a = M [a] deriving Show t2 :: M 2 Int t2  = M [1,2] t3 :: M 3 Int t3 = M [1,2,3] fx :: Num a => M n a -> M n a -> M n a fx (M xs) (M ys) = M (zipWith (+) xs ys) and having  g = fx t2 t3 won’t compile. Which is what I want. However… t2 :: M 2 Int t2  = M [1,2] is ‘hardwired’ to 2 and clearly I could make t2 return  a list of any length.  So what I then tried to look at was a general function that would take a list of Int and create the M type using the length of the supplied list.  In other words if I supply a list, xs, of length n then I wan’t  M n xs Like this createIntM xs = (M xs) :: M (length xs) Int which compile and has type λ-> :t createIntM  createIntM :: [Int] -> M (length xs) Int and all Ms created using createIntM  have the same type irrespective of the length of the supplied list. What’s the type jiggery I need or is this not the right way to go? Thanks Mike On 14 Mar 2019, at 13:12, Frederic Cogny <[hidden email]> wrote: The (experimental) Static module of hmatrix seems (I've used the packaged but not that module) to do exactly that: http://hackage.haskell.org/package/hmatrix-0.19.0.0/docs/Numeric-LinearAlgebra-Static.html On Thu, Mar 14, 2019, 12:37 PM Francesco Ariis <[hidden email]> wrote: Hello Mike, On Thu, Mar 14, 2019 at 11:10:06AM +0000, mike h wrote: > Multiplication of two matrices is only defined when the the number of columns in the first matrix > equals the number of rows in the second matrix. i.e. c1 == r2 > > So when writing the multiplication function I can check that  c1 == r2 and do something. > However what I really want to do, if possible, is to have the compiler catch the error. Type-level literals [1] or any kind of similar trickery should help you with having matrices checked at compile-time. [1] https://downloads.haskell.org/~ghc/7.10.1/docs/html/users_guide/type-level-literals.html _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners -- Frederic Cogny +33 7 83 12 61 69 _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners -- Frederic Cogny +33 7 83 12 61 69 ```_______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners ``` _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
 Thanks.On 15 Mar 2019, at 13:48, Sylvain Henry <[hidden email]> wrote: Hi, The problem is that Haskell lists don't carry their length in their type hence you cannot enforce their length at compile time. But you can define your M this way instead:{-# LANGUAGE TypeOperators #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE KindSignatures #-} import GHC.TypeNats import Data.Proxy data M (n :: Nat) a where    MNil  :: M 0 a    MCons :: a -> M (n-1) a -> M n a infixr 5 `MCons` toList :: M k a -> [a] toList MNil         = [] toList (MCons a as) = a:toList as instance (KnownNat n, Show a) => Show (M n a) where    show xs = mconcat       [ "M @"       , show (natVal (Proxy :: Proxy n))       , " "       , show (toList xs)       ] --t2 :: M 2 Integer t2 = 1 `MCons` 2 `MCons` MNil --t3 :: M 3 Integer t3 = 1 `MCons` 2 `MCons` 3 `MCons` MNil zipM :: (a -> b -> c) -> M n a -> M n b -> M n c zipM _f MNil         MNil         = MNil zipM  f (MCons a as) (MCons b bs) = MCons (f a b) (zipM f as bs) fx :: Num a => M n a -> M n a -> M n a fx = zipM (+) Test:> t2 M @2 [1,2] > fx t2 t2 M @2 [2,4] > fx t2 t3 :38:7: error:     • Couldn't match type ‘3’ with ‘2’       Expected type: M 2 Integer         Actual type: M 3 Integer Cheers, Sylvain On 15/03/2019 13:57, mike h wrote: Hi Frederic, Yeh, my explanation is a bit dubious :)  What I’m trying to say is: Looking at the type M (n::Nat)  If I want an M 2  of Ints say,  then I need to write the function with signature  f :: M 2 Int   If I want a M 3 then I need to explicitly write the function with signature M 3 Int and so on for every possible instance that I might want. What I would like to do is have just one function that is somehow parameterised to create the M tagged with the required value of (n::Nat) In pseudo Haskell create :: Int -> [Int] -> M n  create size ns = (M ns) ::  M size Int where  its trying to coerce (M ns) into the type (M size Int) where size is an Int but needs to be a Nat. It’s sort of like parameterising the signature of the function. Thanks Mike On 15 Mar 2019, at 11:37, Frederic Cogny <[hidden email]> wrote: I'm not sure I understand your question Mike. Are you saying createIntM behaves as desired but the data constructor M could let you build a data M with the wrong type. for instance M [1,2] :: M 1 Int ? If that is your question, then one way to handle this is to have a separate module where you define the data type and the proper constructor (here M and createIntM) but where you do not expose the type constructor. so something like module MyModule   ( M -- as opposed to M(..) to not expose the type constructor   , createIntM   ) where Then, outside of MyModule, you can not create an incorrect lentgh annotated list since the only way to build it is through createIntM Does that make sense? On Thu, Mar 14, 2019 at 4:19 PM mike h <[hidden email]> wrote: Hi, Thanks for the pointers. So I’ve got data M (n :: Nat) a = M [a] deriving Show t2 :: M 2 Int t2  = M [1,2] t3 :: M 3 Int t3 = M [1,2,3] fx :: Num a => M n a -> M n a -> M n a fx (M xs) (M ys) = M (zipWith (+) xs ys) and having  g = fx t2 t3 won’t compile. Which is what I want. However… t2 :: M 2 Int t2  = M [1,2] is ‘hardwired’ to 2 and clearly I could make t2 return  a list of any length.  So what I then tried to look at was a general function that would take a list of Int and create the M type using the length of the supplied list.  In other words if I supply a list, xs, of length n then I wan’t  M n xs Like this createIntM xs = (M xs) :: M (length xs) Int which compile and has type λ-> :t createIntM  createIntM :: [Int] -> M (length xs) Int and all Ms created using createIntM  have the same type irrespective of the length of the supplied list. What’s the type jiggery I need or is this not the right way to go? Thanks Mike On 14 Mar 2019, at 13:12, Frederic Cogny <[hidden email]> wrote: The (experimental) Static module of hmatrix seems (I've used the packaged but not that module) to do exactly that: http://hackage.haskell.org/package/hmatrix-0.19.0.0/docs/Numeric-LinearAlgebra-Static.html On Thu, Mar 14, 2019, 12:37 PM Francesco Ariis <[hidden email]> wrote: Hello Mike, On Thu, Mar 14, 2019 at 11:10:06AM +0000, mike h wrote: > Multiplication of two matrices is only defined when the the number of columns in the first matrix > equals the number of rows in the second matrix. i.e. c1 == r2 > > So when writing the multiplication function I can check that  c1 == r2 and do something. > However what I really want to do, if possible, is to have the compiler catch the error. Type-level literals [1] or any kind of similar trickery should help you with having matrices checked at compile-time. [1] https://downloads.haskell.org/~ghc/7.10.1/docs/html/users_guide/type-level-literals.html _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners -- Frederic Cogny +33 7 83 12 61 69 _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners -- Frederic Cogny +33 7 83 12 61 69 ```_______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners ``` _______________________________________________Beginners mailing list[hidden email]http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners_______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners