[Haskell-cafe] Comparing programs

[Harry Chesley]

This is more of an algorithm question than a language question, but any 
insights would be much appreciated.

The problem is to input a series of programs and find previous 
occurrences of the same algorithm.

The programs consist of a set of input parameters (a, b, c, ...), and a 
set of side-effect-free functions (f, g, h, ...). Since the functions 
are side-effect-free, they can be reordered without changing the 
algorithm ("f(a), g(b)" is the same as "g(b), f(a)"). Subsequent calls 
of the same function with the same parameters have no effect ("f(a), 
f(a)" is the same as "f(a)"); in fact, you can assume duplicates have 
been removed in earlier processing.

But here's the thing that makes it hard (at least for me): two programs 
are considered the same if they can be made to match by rearranging the 
order of the input parameters. I.e., "f(a), g(b)" is the same as "f(b), 
g(a)". Although parameters can be reordered, they cannot be substituted 
("f(a), g(b)" is _not_ the same as "f(a), g(a)").

Example: "f(a), g(b), h(a, b)" is the same as "f(b), g(a), h(b, a)" but 
_not_ the same as "f(a), g(b), h(b, a)".

I need a way to compare the input programs, and preferably to order them.

In Haskell terms, given the programs are represented by a type Prog, I 
want Prog to be a member of class Ord, letting me use tools like 
Data.Map to look up information about previous instances.

I can do a brute-force compare by trying all the parameter permutations, 
but that only gives me Eq, not Ord, and seems terribly inelegant as well.