MathAction SandBoxRemember

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On Tue, Oct 27, 2009 at 4:19 PM, Franz Lehner wrote:

  ok here is a minimal example how to get remembering function.
  I am however not sure if hash tables are actually used.

This example sub-classes Table to create a domain whose values are cached functions.

fricas

(1) -> <spad>

fricas

)abbrev domain FWC FunctionWithCache
FunctionWithCache(A:SetCategory,F:Partition->A):Exports == Implementation where
    Exports ==> TableAggregate(SExpression,A) with 
        apply:(%,Partition)-> A
        ++ \spad{f(p)} computes the value of the function f
        ++ remembering its values
    Implementation ==> Table(SExpression,A) add 
        Rep := Table(SExpression,A)

        rep(x:%):Rep == x :: Rep
        per(r:Rep):% == r :: %

        part2expr:Partition -> SExpression -- should go to Partition

        part2sexpr(p:Partition):SExpression ==
           pl:List Integer := coerce(p)
           convert( [convert(k)@SExpression for k in pl])@SExpression

        apply(f:%,p:Partition):A ==
            repf:Rep := rep f
            import Rep
            ps:SExpression := part2sexpr(p)
            res:= search(ps,rep f)$Rep
            res case "failed" => 
                output("F called")$OutputPackage
                res1:A :=F(p)
--                repf(ps) := res1 -- method 1 
                HPUT(rep f,ps,res1)$Lisp -- method 2 (faster?)
                res1
            res pretend A</spad>

fricas

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7804888174701501931-25px001.spad
      using old system compiler.
   FWC abbreviates domain FunctionWithCache 
------------------------------------------------------------------------
   initializing NRLIB FWC for FunctionWithCache 
   compiling into NRLIB FWC 
   compiling local rep : % -> Rep
      FWC;rep is replaced by x 
Time: 0 SEC.

   compiling local per : Rep -> %
      FWC;per is replaced by r 
Time: 0 SEC.

   compiling local part2sexpr : Partition -> SExpression
Time: 0 SEC.

   compiling exported apply : (%,Partition) -> A
Time: 0 SEC.

****** Domain: (Record (: key (SExpression)) (: entry A)) already in scope
augmenting (Record (: key (SExpression)) (: entry A)): (Evalable (Record (: key (SExpression)) (: entry A)))
****** Domain: % already in scope
augmenting %: (finiteAggregate)
****** Domain: % already in scope
augmenting %: (finiteAggregate)
****** Domain: (Record (: key (SExpression)) (: entry A)) already in scope
augmenting (Record (: key (SExpression)) (: entry A)): (OrderedSet)
****** Domain: % already in scope
augmenting %: (finiteAggregate)
****** Domain: % already in scope
augmenting %: (finiteAggregate)
****** Domain: A already in scope
augmenting A: (OrderedSet)
****** Domain: A already in scope
augmenting A: (Evalable A)
****** Domain: (Record (: key (SExpression)) (: entry A)) already in scope
augmenting (Record (: key (SExpression)) (: entry A)): (ConvertibleTo (InputForm))
****** Domain: (SExpression) already in scope
augmenting (SExpression): (OrderedSet)
****** Domain: % already in scope
augmenting %: (finiteAggregate)
(time taken in buildFunctor:  4336)

;;;     ***       |FunctionWithCache| REDEFINED

;;;     ***       |FunctionWithCache| REDEFINED
Time: 0.01 SEC.

   Warnings: 
      [1] apply: pretendA -- should replace by @

   Cumulative Statistics for Constructor FunctionWithCache
      Time: 0.03 seconds

--------------non extending category----------------------
.. FunctionWithCache(#1,#2) of cat 
(|Join| (|TableAggregate| (|SExpression|) |#1|)
        (CATEGORY |domain| (SIGNATURE |apply| (|#1| % (|Partition|)))))   has no 
(|finiteAggregate|)    finalizing NRLIB FWC 
   Processing FunctionWithCache for Browser database:
--->-->FunctionWithCache(constructor): Not documented!!!!
--------(apply (A % (Partition)))---------
--->-->FunctionWithCache(): Missing Description
; compiling file "/var/aw/var/LatexWiki/FWC.NRLIB/FWC.lsp" (written 01 NOV 2024 12:49:18 AM):

; wrote /var/aw/var/LatexWiki/FWC.NRLIB/FWC.fasl
; compilation finished in 0:00:00.020
------------------------------------------------------------------------
   FunctionWithCache is now explicitly exposed in frame initial 
   FunctionWithCache will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/FWC.NRLIB/FWC

How to use:

fricas

f:FunctionWithCache(Integer,pdct):=empty()

$\label{eq1} \mbox{\rm table} \left({}\right)$

(1)

Type: FunctionWithCache?(Integer,theMap(PRTITION;pdct;%I;18,655))

fricas

p:Partition := partition [1,1]

$\label{eq2}\left({1}^{2}\right)$

(2)

Type: Partition

fricas

f(p)

   F called

$\label{eq3}2$

(3)

Type: PositiveInteger?

fricas

f(p)

$\label{eq4}2$

(4)

Type: PositiveInteger?

Subject: Be Bold !!

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