On 04/09/2012, at 1:39 PM, john skaller wrote:
>
> On 04/09/2012, at 11:38 AM, john skaller wrote:
>
>> Last night i said to Shayne: "Felix needs more magic"
>
> ftp://ftp.cpsc.ucalgary.ca/pub/projects/charity/literature/manuals/manual.ps
So for a union like
union X [A,B] = | X1 of A | X2 of A * B | X3 of A+B ) ...
map is clearly:
fun map[A,B, A', B']
(fa: A -> A')
(fb: B -> B')
(x:X[A,B])
: X[A',B'] = {
match x with
| X1 ?a => X1 (fa a)
| X2 (?a,?b) => X2 (fa a, fb b)
| X3 (?k) => match k with
| case 0 ?a => case 0 (fa a)
| case 1 ?b => case 1 (fb b)
In more compact form, A * B can be handled itself by a (trivial) map,
as can A+B. If we run into an X[A,B] valued subterm, we just reapply
the map.
This machinery cannot handle exponentials, i.e. functions, i.e. terms
of type A -> B etc. Given some k: A -> B we can compose it:
inmap . k . outmap
where inmap: A' -> A, outmap B -> B'
We can take outmap as fb, but inmap would have to be the inverse of fa.
In general then, we have to provide, for each type variable, a pair of functions
which are inverses. Note this also applies to arrays (since they're
exponentials).
If run into a term of type X[ h (A,B), j (A,B) ] where h or j is not the first
or second projection, we have polymorphic recursion, and we have to
construct new fa, fb maps for h and j. Ouch!
Fold is similar. For one type variable it's trivial,
it's just a simple visitor.
--
john skaller
[email protected]
http://felix-lang.org
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