standard-classes.md

@@ -4,6 +4,14 @@
 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
+- [ Algebraic structures](http://en.wikipedia.org/wiki/Algebraic_structure) in WikiPedia
+- [ DoCon the Algebraic Domain Constructor](http://www.haskell.org/docon/)
+- [ Numeric prelude project](http://www.haskell.org/communities/06-2006/html/report.html#numericprelude)
+
 ## Constructor classes
 
 ### The Functor class
@@ -38,10 +46,6 @@ Proposals:
 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
 
@@ -55,22 +59,13 @@ Issues:
 
 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.
+- 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.
 
 
 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, 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.
-
 ### The Fractional class
 
 
@@ -81,7 +76,9 @@ Issues:
 
 Proposals:
 
-- Add a field-like superclass adding these operations to the ring-like class.
+- 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.)
+- (Could be further split with a semiring subclass.)
 - Add default
 
   ```wiki
@@ -90,6 +87,15 @@ Proposals:
 
   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