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On Wednesday, January 12, 2005 12:00 PM you wrote: Ralf Hemmecke wrote:

Well, I haven't checked whether it should really work, but shouldn't be:

 Foo: with {
    g: (n: PositiveInteger, k: PositiveInteger) ->
       (P: PrimeFieldCategory, x: P)
 } == add {
    g(n: PositiveInteger, k: PositiveInteger ):
     (P: PrimeFieldCategory, x:P) == {
     (PrimeField(n), k::Integer::PrimeField(n)
    }
 }

be even better?

Later William Sit wrote:

In fact you just pointed a way to solve the problem! Notice that you are in effect constructing a domain! So first create this domain (call this anything else you like)

fricas
)abbrev domain PPF PointedPrimeField
--%PointedPrimeField
PointedPrimeField(n:PositiveInteger):Cat==Dog where
  Cat == FiniteFieldCategory with
    foo:PositiveInteger->PrimeField(n)
  Dog == PrimeField(n) add
    foo(k)==k::Integer::PrimeField(n)
fricas
Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3896265268149061013-25px.001.spad
      using old system compiler.
   PPF abbreviates domain PointedPrimeField 
------------------------------------------------------------------------
   initializing NRLIB PPF for PointedPrimeField 
   compiling into NRLIB PPF 
   compiling exported foo : PositiveInteger -> PrimeField n
Time: 0.03 SEC.
(time taken in buildFunctor: 0)
;;; *** |PointedPrimeField| REDEFINED
;;; *** |PointedPrimeField| REDEFINED Time: 0.02 SEC.
Cumulative Statistics for Constructor PointedPrimeField Time: 0.05 seconds
--------------non extending category---------------------- .. PointedPrimeField(#1) of cat (|Join| (|FiniteFieldCategory|) (CATEGORY |package| (SIGNATURE |foo| ((|PrimeField| |#1|) (|PositiveInteger|))))) has no (|FiniteAlgebraicExtensionField| $) finalizing NRLIB PPF Processing PointedPrimeField for Browser database: --->-->PointedPrimeField(constructor): Not documented!!!! --->-->PointedPrimeField((foo ((PrimeField n) (PositiveInteger)))): Not documented!!!! --->-->PointedPrimeField(): Missing Description ; compiling file "/var/aw/var/LatexWiki/PPF.NRLIB/PPF.lsp" (written 07 MAY 2016 12:50:03 PM):
; /var/aw/var/LatexWiki/PPF.NRLIB/PPF.fasl written ; compilation finished in 0:00:00.010 ------------------------------------------------------------------------ PointedPrimeField is now explicitly exposed in frame initial PointedPrimeField will be automatically loaded when needed from /var/aw/var/LatexWiki/PPF.NRLIB/PPF

After compiling, define in the interpreter

fricas
g(n,k)==foo(k)$PPF(n)
Type: Void
fricas
g(7,4)
Cannot compile a $-expression involving a local variable. FriCAS will attempt to step through and interpret the code.

\label{eq1}4(1)
Type: PrimeField?(7)

and it works (in Axiom)! (Do not declare the types for g because n is not defined).

Compiling g is still a problem in Axiom due to signature limitation. At least this way, inlining a complicated function is almost like a function call.

The idea is: Since in creating domains (or any other types of constructors), we are in effect creating a function(the domain constructor PPF is a function of sorts, or functor) and the compiler can take dependent types in its signature,structurally:

  PPF(n:PositiveInteger)==PrimeField(n) with foo

so it should be able to compile something like g by lifting it to the package level.

So here is another way using package.

spad
)abbrev package FOO Foo
Foo(n:PositiveInteger, k:Integer):with point:()->PrimeField(n)
  == add point()==k::PrimeField(n)
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6339949729126981292-25px003.spad
      using old system compiler.
   FOO abbreviates package Foo 
------------------------------------------------------------------------
   initializing NRLIB FOO for Foo 
   compiling into NRLIB FOO 
   compiling exported point : () -> PrimeField n
Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |Foo| REDEFINED
;;; *** |Foo| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor Foo Time: 0 seconds
finalizing NRLIB FOO Processing Foo for Browser database: --->-->Foo(constructor): Not documented!!!! --->-->Foo((point ((PrimeField n)))): Not documented!!!! --->-->Foo(): Missing Description ; compiling file "/var/aw/var/LatexWiki/FOO.NRLIB/FOO.lsp" (written 07 MAY 2016 12:50:03 PM):
; /var/aw/var/LatexWiki/FOO.NRLIB/FOO.fasl written ; compilation finished in 0:00:00.021 ------------------------------------------------------------------------ Foo is now explicitly exposed in frame initial Foo will be automatically loaded when needed from /var/aw/var/LatexWiki/FOO.NRLIB/FOO

After compiling, we can use:

  point()$Foo(n,k)

in any computation in compiler code (and in interpreter). In the interpreter you can call this bar(n,k):

fricas
bar(n,k) == point()$Foo(n,k)
Type: Void
fricas
bar(7,4)
Cannot compile a $-expression involving a local variable. FriCAS will attempt to step through and interpret the code.

\label{eq2}4(2)
Type: PrimeField?(7)

Can someone give an example where the signature of bar:

  bar: (n: PositiveInteger, k: PositiveInteger) -> PrimeField(n)

is actually needed?

spad
)abbrev package FOO2 Foo2
Foo2(n:PositiveInteger, k:IntegerMod(n)):with point:()->PrimeField(n)
  == add point()==convert(k)$IntegerMod(n)::PrimeField(n)
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3511022708306225656-25px005.spad
      using old system compiler.
   FOO2 abbreviates package Foo2 
------------------------------------------------------------------------
   initializing NRLIB FOO2 for Foo2 
   compiling into NRLIB FOO2 
   compiling exported point : () -> PrimeField n
Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |Foo2| REDEFINED
;;; *** |Foo2| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor Foo2 Time: 0 seconds
finalizing NRLIB FOO2 Processing Foo2 for Browser database: --->-->Foo2(constructor): Not documented!!!! --->-->Foo2((point ((PrimeField n)))): Not documented!!!! --->-->Foo2(): Missing Description ; compiling file "/var/aw/var/LatexWiki/FOO2.NRLIB/FOO2.lsp" (written 07 MAY 2016 12:50:03 PM):
; /var/aw/var/LatexWiki/FOO2.NRLIB/FOO2.fasl written ; compilation finished in 0:00:00.010 ------------------------------------------------------------------------ Foo2 is now explicitly exposed in frame initial Foo2 will be automatically loaded when needed from /var/aw/var/LatexWiki/FOO2.NRLIB/FOO2

fricas
point()$Foo2(13,2)

\label{eq3}2(3)
Type: PrimeField?(13)




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