Data declaration with constraint
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....