# Data declaration with constraint

## Contents

## Problem

### Question

I have declared

```
data C a => T a = Cons a
```

and I hoped that now the type checker knows that every value of type `T a`

satisfies the type constraint on `a`

.
I like to declare an instance for an type constructor class for the type constructor `T`

but its methods require type constraints that depend on the particular type constructor `T`

.

For example:

```
instance Vector T where
add (Cons x) (Cons y) = Cons (x+y) -- requires Num constraint on type a
```

### Answer

In Haskell 98, only functions can have type constraints.
The type constraint of a `data`

only refers to the constructors.
The designers of Haskell 98 do now think, that it was a bad decision to allow constraints on constructors. GHC as of version 7.2 disallows them by default (turn back on with `-XDatatypeContexts`

).

## Solution

You could use ghc's Generalised Algebraic Data Structures (GADTs) to add an implicit context to the data constructors:

```
data T a where
Cons :: C a => a -> T a
```

This way, functions using `T`

no longer need a constraint. Instead, constructing a `T a`

using `Cons`

needs a `C a`

context, and when something pattern matches a `Cons x`

, the context comes with it.

There has been some discussion about whether it is sensible to want this.

A Haskell 98 workaround is to use multi-parameter type classes, where `T a`

and `a`

are separate arguments.

## See also

- Henning Thielemann in Haskell-Cafe: Context for type parameters of type constructors
- Mark Nicholls in Haskell-Cafe: nice simple problem for someone struggling....