I wonder if we should collect some example code and make it presentable.
I think we should.
By that I mean there should be the classification of the example, brief description, and, mainly, sample test data and the expected results. And, of course, implementations for these examples in various generic programming approaches. Incidentally, the `expressibility' section in the library description can simply enumerate which examples the library can implement. _Some_ of the examples may become the part of the benchmarking suite (at this point I'm simply interested in what is possible).
Here's what I have gleaned so far, from a couple of SYB papers and the code already in DARCS:
generic show: essential type is t -> String [I say essential because there may be additional arguments, say, for type representation] Description: display the term; special processing for Strings, as opposed to general arrays. Category: closed Cartesian [sorry, couldn't resist] I mean, `consumer', reduce a generic term to a value of the fixed type, String. LIGD has the implementation; no test data though.
generic size: essential type t -> Int Give the size of a term (in terms of data constructors). The user should be able to assign size matrix to specific data types (like strings). Category: consumer, reduce a generic term to a value of the fixed type, Int. SYB3 example, also used in Smash. I have test data and expected results (part of syb4.hs) This example is quite similar to gshow above; I personally prefer this over gshow, because the Show class already provides the latter, so it's hard to get excited over gshow.
Maybe not, but gshow is a good example of a function that uses the constructor names of a data type. And I think it is interesting to see how the different approaches provide access to constructor names (and possibly even also data type name, although that is not used in gshow).
Salary Raise: essential type t -> t Transform a term (representing an `organization' or an XML document) into the term of the same type, but with different values of some primitive fields. Ralf's dream example, from SYB1. category: type-preserving transformer Variation: uniform transformation (raise everybody's salary by 10%); or the transformation should affect only specific parts of the term. Transformation can be context-independent (increment each float field by 10%) or context- (that is, traversal history) dependent (increment each float until the money runs out). Test data can be extracted from Ralf's web site.
generic minimum: essential type t Provides the 'minimal' value of any term in the universe of discourse. category: pure producer Variation: functional term may or may not be handled. LIGD example. test data can be easily extracted from it.
Replace all Ints with Floats in a term: essential type t -> t' where t' = f(t). category: transformer, to a term of a different type. The output type is the function of the input type. variation: replace all Ints with Floats and negate all booleans, in a single traversal (that is, `compose' multiple compatible processing steps) Smash example; test data are available in the syb4.hs
generic equality: essential type t -> t -> Bool category: binary function over two generic arguments of the same type. Variation: try essential type t -> t' -> Bool Variation: permit the user supply their own comparison procedure for some data types Variation: local extensibility [as explained in Stefan Holdermans] LIGD example (including specific comparison of integers mod 2). Need test data though.
something of the type t1 -> t2 -> t3 where t3 = f(t1, t2). Generalization of zip/zipWith. I have never seen that example.
Obviously a lot is missing in the above -- in particular, good names for the examples, and the test data. And the idea how to organize the files with examples and test data within our DARCS repository.
I think these are good examples. The only thing I miss is a generic variant of map :: (a->b) -> [a]->[b]. -- Johan