Re: [Haskell-cafe] Monad instance for partially applied type constructor?
On Wednesday 29 September 2010 2:52:21 pm Christopher Done wrote: > LiberalTypeSynonyms lets you partially apply type synonyms. Not in general. LiberalTypeSynonyms only allows synonyms to be partially applied when expansions of other type synonyms will eventually cause them to become fully applied (or discarded, probably). So, for instance: type Foo a = (a, a) type Bar f = f Int Bar Foo ==> Foo Int ==> (Int, Int) -- valid It does not make partially applied synonyms first class, such that they'd be able to be made instances, or parameters to datatypes, etc. -- Dan ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Monad instance for partially applied type constructor?
On 29 September 2010 20:48, Ryan Ingram wrote:
> But it doesn't let you partially apply the type synonym.
>
> On the other hand, if you did this:
>
> newtype Compose f g a = O { unO :: f (g a) }
> type Poly k = Compose (Vect k) Monomial
>
> instance Monad (Poly k) where ...
>
> would work, but now you have to wrap/unwrap Compose in the instance
> definition.
LiberalTypeSynonyms lets you partially apply type synonyms.
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Re: [Haskell-cafe] Monad instance for partially applied type constructor?
On Wed, Sep 29, 2010 at 11:08 AM, DavidA wrote:
> Hi,
>
> I have the following code:
>
> {-# LANGUAGE TypeSynonymInstances #-}
>
> data Vect k b = V [(k,b)]
> -- vector space over field k with basis b
> -- for example, V [(5, E 1), (7, E 2)] would represent the vector 5 e1 + 7 e2
>
> data Monomial v = M [(v,Int)]
> -- monomials over variables v
> -- for example, M [(A,3), (B,5)] would represent the monomial a^3 b^5
>
> type Poly k v = Vect k (Monomial v)
> -- multivariate polynomials over field k and variables v
>
> instance Monad (Poly k) where
> return v = V [(1, M [(v,1)])]
> p >>= f = ... -- variable substitution
>
> So my thinking is:
> 1. The Monad type class is for one parameter type constructors (eg [], IO)
> 2. Poly is a two-parameter type constructor
> 3. So Poly k is a one-parameter type constructor
> 4. What I'm trying to express, that polynomials over field k are a monad,
> is true.
>
> However, GHC 6.12.2 complains:
>
> Type synonym `Poly' should have 2 arguments, but has been given 1
> In the instance declaration for `Monad (Poly k)'
>
> What is going wrong?
Haskell doesn't have true type functions; what you are really saying is
instance Monad (\v -> Vect k (Monomial v))
TypeSynonymInstances just lets you write stuff like this
type Foo = [Int]
instance C Foo where ...
instead of
type Foo = [Int]
instance C [Int] where ...
But it doesn't let you partially apply the type synonym.
On the other hand, if you did this:
newtype Compose f g a = O { unO :: f (g a) }
type Poly k = Compose (Vect k) Monomial
instance Monad (Poly k) where ...
would work, but now you have to wrap/unwrap Compose in the instance definition.
-- ryan
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Re: [Haskell-cafe] Monad instance for partially applied type constructor?
Maybe -XLiberalTypeSynonyms is an option:
http://www.haskell.org/ghc/docs/6.12.2/html/users_guide/data-type-extensions.html#type-synonyms
On 29 September 2010 20:08, DavidA wrote:
> Hi,
>
> I have the following code:
>
> {-# LANGUAGE TypeSynonymInstances #-}
>
> data Vect k b = V [(k,b)]
> -- vector space over field k with basis b
> -- for example, V [(5, E 1), (7, E 2)] would represent the vector 5 e1 + 7 e2
>
> data Monomial v = M [(v,Int)]
> -- monomials over variables v
> -- for example, M [(A,3), (B,5)] would represent the monomial a^3 b^5
>
> type Poly k v = Vect k (Monomial v)
> -- multivariate polynomials over field k and variables v
>
> instance Monad (Poly k) where
> return v = V [(1, M [(v,1)])]
> p >>= f = ... -- variable substitution
>
> So my thinking is:
> 1. The Monad type class is for one parameter type constructors (eg [], IO)
> 2. Poly is a two-parameter type constructor
> 3. So Poly k is a one-parameter type constructor
> 4. What I'm trying to express, that polynomials over field k are a monad,
> is true.
>
> However, GHC 6.12.2 complains:
>
> Type synonym `Poly' should have 2 arguments, but has been given 1
> In the instance declaration for `Monad (Poly k)'
>
> What is going wrong?
>
>
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> Haskell-Cafe mailing list
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[Haskell-cafe] Monad instance for partially applied type constructor?
Hi,
I have the following code:
{-# LANGUAGE TypeSynonymInstances #-}
data Vect k b = V [(k,b)]
-- vector space over field k with basis b
-- for example, V [(5, E 1), (7, E 2)] would represent the vector 5 e1 + 7 e2
data Monomial v = M [(v,Int)]
-- monomials over variables v
-- for example, M [(A,3), (B,5)] would represent the monomial a^3 b^5
type Poly k v = Vect k (Monomial v)
-- multivariate polynomials over field k and variables v
instance Monad (Poly k) where
return v = V [(1, M [(v,1)])]
p >>= f = ... -- variable substitution
So my thinking is:
1. The Monad type class is for one parameter type constructors (eg [], IO)
2. Poly is a two-parameter type constructor
3. So Poly k is a one-parameter type constructor
4. What I'm trying to express, that polynomials over field k are a monad,
is true.
However, GHC 6.12.2 complains:
Type synonym `Poly' should have 2 arguments, but has been given 1
In the instance declaration for `Monad (Poly k)'
What is going wrong?
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