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.
 
-## References
 
-- [ Standard Haskell Classes](http://www.haskell.org/onlinereport/basic.html#sect6.3) of Haskell 98
-- [ Standard Prelude](http://www.haskell.org/onlinereport/standard-prelude.html) of Haskell 98
+## The Read class
 
-## Constructor classes
 
-### The Functor class
 
+See [ReadClass](read-class).
 
-Proposal:
 
-- Add instances for `((->) a)`, `((,) a)` and `Either a`.
+## The Enum class
 
-### The Monad 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.
-- 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](http://www.haskell.org/ghc/docs/6.4-latest/html/libraries/mtl/Control-Monad-Error.html), 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 `(>>=)`.
@@ -40,49 +45,82 @@ Proposals:
 ## Numbers
 
 
-See [NumericClasses](numeric-classes).
 
-## Other standard classes
+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:
 
-### The Read class
 
+- [ DoCon the Algebraic Domain Constructor](http://haskell.org/docon/)
+- [ Numeric prelude project](http://haskell.org/communities/06-2006/html/report.html#numericprelude)
 
-See [ReadClass](read-class).
+### The Num 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`.
-- Some doubt that it makes sense to have `Float` and `Double` instances.
-- It is wierd that `[0,3..20]::[Rational]` includes `21`.
 
-### The Ix class
+- `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.
 
 
-Issues:
+Proposals:
 
-- There is no portable way to report indexing errors accurately.
 
+- 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.
 
-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`.)
+Note that the `Float` and `Double` instances will not satisfy the usual axioms for these structures.
+
+
+### The Integral class
 
-### The Bits class
 
 
 Issues:
 
-- The `Num` superclass may unduly restrict instances.  The only thing actually needed from `Num` is 0.
-- The `bitSize` method is not defined for all instances, and there is no general way to test whether it can be safely called.
 
-### The Storable class
+- `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:
 
-- Some interfaces require clients to manage the memory for objects, but to treat them abstractly.  In such cases one wants to define `sizeOf` and `alignment` (to use `malloc` or `alloca`), but not `peek` or `poke`.
+
+- `(/)` 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`.)