Bertram and Liying:
You have hit upon something that has bothered me for some time, and have expressed it better than I ever did... There are several examples of this tension in the Ptolemy II library. E.g., the FFT actor has type <double> --> <double>. Why isn't it <[double]> --> <[double]>? It could just as well be, and I don't know of any way to choose between these...
In practice, we've relied on just making a choice, clearly documenting it, and then judiciously using SequenceToArray and ArrayToSequence actors. These have type <a> --> <[a]> and <[a]> --> <a>. But this solution has its problems. For SDF, the ArrayToSequence actor needs to set a static input array size, but this is not represented in the type system... Similarly, SequenceToArray has a parameter arrayLength that has to be static for SDF.
Steve Neuendorffer introduced a solution to this in version 4.0 where parameters that affect scheduling can change dynamically, and it is well-defined when schedules have to be recomputed, but this still doesn't help in deciding whether types should be streams or streams of arrays...
The short answer is that we don't have to conclude that <<a>> == <a>. We can instead insist that ArrayToSequence or SequenceToArray be used to convert types, which is what the type system does today (modulo type inference, which can create unexpected answers if you don't know whether you are dealing with <<a>> or <a>).
But the long answer is harder... I don't have it... Interesting question though...
Edward
At 01:08 PM 5/25/2004 -0700, 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:
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> produce a process MYACTOR :: <a> --> <b> which thus can be explained as a "special map" over streams with the type identity <<b>> = <b> ??
Thanks in advance!
Bertram and Liying
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