[Haskell-beginners] Data structure for Propositional Logic formulas

[Benedict Eastaugh]

On 13 October 2011 10:12, Christian Maeder <Christian.Maeder at dfki.de> wrote:

> Why do most people like duplicate or repeated code?

Hi Christian,

I can't speak for most people, but I like my data types to encode the
semantics of the domain. In this case, the connectives are logical
devices that allow the formation of new well-formed formulae from old
ones. I also think it's a mistake to consider them, in their guise as
operators, to be any different from negation save in their arity. In
my code they are on a par, and any extension to include new n-ary
connectives would be straightforward and natural.

(There are other unary and binary logical operators which happen not
to be listed; I simply included the most commonly used ones, rather
than add NAND, XOR, etc. As Daniel pointed out, merely including
negation and disjunction allows the formation of a truth-functionally
complete system. One can also do this with just NAND or NOR.)

The duplication is, ultimately, fairly minor, so doing what you
suggest also seems like overkill: it's not as though I'm going to be
adding another five or ten connectives any time soon. Your version,
while admittedly shorter, makes the code more complex and less
readable, for no gain in expressiveness and a very minor improvement
in brevity.

Benedict