Version 9 (modified by ross@…, 8 years ago) (diff) |
---|

# Issues with Standard Classes

This page collects issues and proposals for the standard classes. Many of the proposals involve additional superclasses, which would be less burdensome with class aliases or something similar, but such features are not yet implemented.

## References

- Standard Haskell Classes of Haskell 98
- Standard Prelude of Haskell 98
- Algebraic structures in WikiPedia
- DoCon the Algebraic Domain Constructor
- Numeric prelude project

## Constructor classes

### The Functor class

Proposal:

- Add instances for
`((->) a)`,`((,) a)`and`Either a`.

### The Monad class

Issues:

- Monads are really functors, but programmers can't always assume that
`fmap`is defined for them, and so must use`liftM`instead. Similarly, code parameterized by`Functor`cannot be used with monads. - The
`fail`method was added to the class in Haskell 98 to implement pattern match failure in`do`expressions. However the assumption that errors are strings can be problematic (e.g. cf the`Error`class in Control.Monad.Error, or for internationalization).

Proposals:

- Add instance for
`((->) a)`. - Make
`Functor`a superclass of`Monad`. This would impose an extra burden on those who just want to define a`Monad`. - Make
`join`a method of`Monad`, interdefined with`(>>=)`. - A more extreme step down this road would be to interpose the new Applicative class between
`Functor`and`Monad`, with corresponding renaming of methods.

## Numbers

The Haskell 98 numeric classes are adequate for Haskell 98 numeric types, but other mathematical objects do not fit. If the Haskell 98 classes were retained for backwards compatibility, but with a more refined class hierarchy, the change would impact mostly on those defining instances (and these are the people inconvenienced by the current system). Clients of the classes would notice only some more general types.

### The Num class

Issues:

`Eq`and`Show`don't make sense for functions under lifting.`(*)`doesn't make sense for vectors.`abs`and`signum`don't make sense for`Complex Integer`(Gaussian integers), vectors, matrices, etc.

Proposals:

- A group-like class with
`zero`,`(+)`and`negate`/`(-)`. - (Could be further split with a monoid sub-class.)
- A ring-like subclass adding
`(*)`and`one`/`fromInteger`, with the existing`Num`class as a further subclass. - (Could be further split with a semiring subclass, e.g. for natural numbers.)

Note that the `Float` and `Double` instances will not satisfy the usual axioms for these structures.

### The Fractional class

Issues:

`(/)`,`recip`and`fromRational`can be lifted to functions, but many of the pre-requisites can't be defined for these.

Proposals:

- Add a division ring-like superclass adding these operations to the ring-like class. (A division ring has the same operations as a field, but does not assume commutative multiplication, allowing structures such as quaternions.)
- Add default
fromRational x = fromInteger (numerator x) / fromInteger (denominator x)

This is independent of all the other proposals.

### The Integral class

Issues:

`div`and`mod`also sense for rationals, polynomials and Gaussian integers, but`toInteger`does not.`Ord`,`Num(abs, signum)`and`toRational`don't make sense for polynomials and Gaussian integers.`quot`and`rem`assume an ordering.

## Other standard classes

### The Read class

See ReadClass.

### The Enum class

Issues:

`succ`and`pred`are unused.- The default definitions of
`enum`* would make more sense if`toEnum`and`fromEnum`used`Integer`instead of`Int`.

### The Ix class

Issues:

- There is no portable way to report indexing errors accurately.

Proposal:

- Make
`Show`a superclass of`Ix`, so that the offending index and range can be shown in exceptions. (All instances of`Ix`in the`base`package are also instances of`Show`.)