standard-classes.md

+# 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](https://gitlab.haskell.org//haskell/prime/issues/101) or something similar, but such features are not yet implemented.
+
+## The Read class
+
+
+See [ReadClass](read-class).
+
+## 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 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.
+
+
+Proposals:
+
+- 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](http://www.haskell.org/ghc/dist/current/docs/libraries/base/Control-Applicative.html) 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.
+See also:
+
+- [ DoCon the Algebraic Domain Constructor](http://haskell.org/docon/)
+- [ Numeric prelude project](http://haskell.org/communities/06-2006/html/report.html#numericprelude)
+
+### The Num class
+
+
+Issues:
+
+- `Eq` and `Show` don't make sense 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`/`(-)`.
+- a ring-like subclass adding `(*)` and `one`/`fromInteger`, with the existing `Num` class as a further subclass.
+
+
+Note that the `Float` and `Double` instances will not satisfy the usual axioms for these structures.
+
+### The Integral class
+
+
+Issues:
+
+- `div` and `mod` also sense for rationals and polynomials, but `Ord`, `Num` and `toInteger` (and `toRational` for polynomials) don't.
+- `quot` and `rem` assume an ordering.
+
+### The Fractional class
+
+
+Issues:
+
+- `(/)` can be lifted to functions, but many of the pre-requisites can't be defined for these.
+
+
+Proposals:
+
+- Add a field-like superclass adding these operations to the ring-like class.
+- Add default
+
+  ```wiki
+  fromRational x = fromInteger (numerator x) / fromInteger (denominator x)
+  ```
+
+  This is independent of all the other proposals.
+
+## 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`.)