On 5 February 2012 20:04, Marshall Lochbaum <mwlochb...@gmail.com> wrote:
> ...
> I'm not sure what you mean about Haskell's "deriving" descriptor. If I
> understand typeclasses at all, what "deriving" accomplishes is rather weak
> and not at all related to implicit mapping.
Here is a typical example.
The following is a datatype describing a binary tree with nodes
of type a.
data Btree a = E | Bt a (Btree a) (Btree a) deriving Eq
It derives from Eq, so trees can be compared for equality by
comparing the values at their nodes pairwise: if t1 and t2 are
trees of, say, integers, then t1==t2 is computed by applying ==
pairwise on the nodes of t1 and t2, i.e. by implicitly mapping ==.
If the nodes are themselves trees or other complex structures,
the mapping takes place first at the items of the items, etc.
This is not the usual mapping, as the result of t1==t2 is a single
Boolean rather than a tree of Booleans (a more precise term is
‘lifting’) but essentially it is (implicit) mapping anyway.
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