Re: [Axiom-developer] typo in the guessing package pamphlet, was: Re: Algebra and literate documentation

[Gabriel Dos Reis]

On Wed, 8 Aug 2007, Bill Page wrote:

| On 08 Aug 2007 06:56:46 +0200, Martin Rubey wrote:
| > Gabriel Dos Reis writes:
| > ...
| > > More specifically:
| > >
| > >  * short hand for unnamed functions do not work properly, so one has
| > >    to use the syntax x +-> f(x)
| >
| > Could you tell me in what places that happens, and what "do not work 
properly"
| > means exactly?  I depend on unnamed functions quite a bit, since at a few
| > points I actually construct such functions by code.  I do recall vividly 
that
| > these functions were extremely hard to compile.
| 
| Well, just picking an example at random from your code (not
| necessarily one that compiled with errors):
| 
| In mantepse.spad.pamphlet chunk <<implementation: Guess - Hermite-Pade
| - Operators>>=
| ...
|     diffHP(q: Symbol): (LGOPT -> HPSPEC) ==
|         if displayAsGF(#1)$GOPT0 then
|             partitions := FilteredPartitionStream #1
|             [ADEguessStream(#1, partitions, qDiffDS(q, #1, #2), 1$UFPSF), _
|              repeating([0$NNI])$Stream(NNI), _
|              ADEtestStream(#1, partitions, qDiffDSF(q, #1, #2), 1$UFPSSUPF), _
|              ADEEXPRRStream(#1, #2, partitions, qDiffDX(q, #1, #2,
| #3), diff1X), _
|              diffA, diffAF, diffAX, diffC]$HPSPEC
|         else
|             error "Guess: guessADE supports only displayAsGF"
| 
| ----
| 
| where reference is made to the following definitions:
| 
|     LGOPT ==> List GuessOption
| 
|     HPSPEC ==> Record(guessStream:  UFPSF -> Stream UFPSF,
|                       degreeStream: Stream NNI,
|                       testStream:   UFPSSUPF -> Stream UFPSSUPF,
|                       exprStream:   (EXPRR, Symbol) -> Stream EXPRR,
|                       A:  DIFFSPECA,
|                       AF: DIFFSPECAF,
|                       AX: DIFFSPECAX,
|                       C:  DIFFSPECC)
| 
| UFPSF ==> UnivariateFormalPowerSeries F
| 
| ADEguessStream(f: UFPSF, partitions: Stream List Integer,
|                DS: DIFFSPECS, D1: DIFFSPEC1): Stream UFPSF ==
|     map(termAsUFPSF(f, #1, DS, D1), partitions)
|        $StreamFunctions2(List Integer, UFPSF)
| 
| ---
| 
| Why do you use macros for types like HPSPEC?
| 
| What do expect the meaning of #2 and #3 to be?
| 
| As I understand Spad syntax, if I write
| 
|    ( #1 + #2 + #3 )
| 
| this is a shorthand for the following anonymous function
| 
|   (x,y,z) +-> x + y + z
| 
| Is that correct?

I think so.

Note however, that in nested context, I believe the rules are a bit different.
That is:

    f(#1, g(#1, #2))

would be equivalent to

   x +-> f(x, (y, z) +-> g(y, z))

However, I can't find a documentation for that.

-- Gaby