At 01:08 PM 5/25/2004, Bertram Ludaescher wrote:
Hi:
Liying Sui and I recently came across the following typing problem:
Consider an actor, say "factors" which computes for a given int I, all the prime factors of I. For example factors(20) = [2,2,5]
Thus, the signature of factors is:
factors :: int --> [int]
Now assume factors is to be applied on a stream <x1, x2, x3, ...> of integers, denoted <int>
It seems tempting to view the *process* Factors that is so created as applying the higher-order map function to factors, i.e., Factors = map(factors)
There are some interesting typing issues. Let's say map has the following type on streams:
map :: (a-->b) --> <a> --> <b>
That is, map takes a function of type (a-->b) and a stream of a's (denoted <a>) and returns a stream of b's. Therefore the type of the Factors process can be determined to be
Factors :: <int> --> < [int] >
Example: Factors( <4, 6, 10, ... > ) = < [2,2], [2,3], [2,5], ... >
So far so good -- no information is lost.
It seems, however, that in practise sometimes another process is created: Factors'( <4, 6, 10, ... > ) = < 2,2,2,3,2,5, ... >
Clearly this process Factors' does lose some information (the grouping of result tuples into list of prime factors). While for this specific example, Factors' is not desirable, such a "flattening" behavior seems to be used in practise:
I'm confused: Are you saying that this is what Ptolemy does, and you don't like
it, or that Ptolemy does not do this, and you would like it to?
Could you consider this to be another higher-order function that takes expandArray :: <[int]> -> <int>?
Let say we change our original function factors to produce not a list of ints, but a stream of them:
factors' :: int --> <int>
This correspond to a token consumption/production pattern of " 1:* " (for each input token, we might get multiple output tokens).
Is it correct that in Ptolemy II using factors' with an SDF director produces a process Factors' on streams that has the signature:
Factors' :: <int> --> <int>
In order to make this behavior type-correct it seems we may have to say that <<int>> = <int>, because we get
map(factors') = Factors'
and the former has the type
map(factors') :: <int> --> < <int> >
Note that the type of map(factors') is obtained by using the general type of map above:
map :: (a-->b) --> <a> --> <b>
and the applying this to factors' :: int --> <int> (hence a = int and b = <int>)
So if indeed Factors' is of the said type we must accept (whether we like it or not ;-) that <<int>> = <int> (or in general, nesting streams in this way yields a "flat" stream).
Comments?? Does Ptolemy II with an SDF director and an actor of type myactor :: a --> <b>
I don't think this makes sence... SDF actor functions don't have access to the whole stream... they have access to a fixed length prefix of the stream.
produce a process
MYACTOR :: <a> --> <b>
which thus can be explained as a "special map" over streams with the
type identity <<b>> = <b> ??
why not another HOF: expandStream :: <<b>> -> <b> ?
I think that the advantage of expandArray over expandStream is that arrays are generally finite, while
streams are not, and hence it is more likely that the computation I've specified actually processes the
data being created... Note that there are two ways to implement expandStream (does it produce an infinite stream consisting of the first element of each input stream, or does it produce an infinite stream that begins with the first
infinite input stream, and then never gets to the other ones?)
Thanks in advance!
Bertram and Liying
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