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SandBoxCommutativeCategory

Edit detail for SandBoxCommutativeCategory revision 5 of 11

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Editor: Bill Page Time: 2008/07/26 05:59:52 GMT-7
Note: avoid implicit conversion of string to symbol

changed:
-Commutative(n:Symbol):Category == with nil
Commutative(n:String):Category == with nil

changed:
-CommutativeDomain(): Commutative(_*) with
CommutativeDomain(): Commutative("*") with

Can the attribute commutative("*") be replaced with a category definition like

spad)abbrev category COM Commutative
Commutative(n:String):Category == with nil

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/4589802368271964260-25px001.spad using 
      old system compiler.
   COM abbreviates category Commutative 
------------------------------------------------------------------------
   initializing NRLIB COM for Commutative 
   compiling into NRLIB COM 

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

   finalizing NRLIB COM 
   Processing Commutative for Browser database:
--->-->Commutative(constructor): Not documented!!!!
--->-->Commutative(): Missing Description
------------------------------------------------------------------------
   Commutative is now explicitly exposed in frame initial 
   Commutative will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/COM.NRLIB/code

spad)abbrev domain COMD CommutativeDomain
CommutativeDomain(): Commutative("*") with
    coerce:%->OutputForm
  == add
    coerce(x)== x pretend OutputForm

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/5314528024349234223-25px002.spad using 
      old system compiler.
   COMD abbreviates domain CommutativeDomain 
------------------------------------------------------------------------
   initializing NRLIB COMD for CommutativeDomain 
   compiling into NRLIB COMD 
   compiling exported coerce : $ -> OutputForm
      COMD;coerce;$Of;1 is replaced by x 
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |CommutativeDomain| REDEFINED

;;;     ***       |CommutativeDomain| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor CommutativeDomain
      Time: 0 seconds

   finalizing NRLIB COMD 
   Processing CommutativeDomain for Browser database:
--->-->CommutativeDomain((coerce ((OutputForm) %))): Not documented!!!!
--->-->CommutativeDomain(constructor): Not documented!!!!
--->-->CommutativeDomain(): Missing Description
------------------------------------------------------------------------
   CommutativeDomain is now explicitly exposed in frame initial 
   CommutativeDomain will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/COMD.NRLIB/code

axiom
CommutativeDomain has Commutative("*")

(1)

Type: Boolean

axiom
CommutativeDomain has Commutative("+")

(2)

Type: Boolean

That is amazing. As demonstrated above, CommutativeDomain is just declared to be Commutative("*") even though there is no exported operation *.

In fact, what is demonstrated here has nothing to do with the actual names of operations exported by a domain, but just with the declaration that CommutativeDomain is of category Commutative("*").

Since above the definition says Commutative(n:Symbol) there should be double quotes around the *.

Is this the really problem? --yixin.cao, Sat, 26 Jul 2008 00:20:36 -0700 reply

Even such a category is possible, so we can define domain D:Join(Commutative(*),Commutative(+),Commutative(max),....). But when I need to write a algorithm package to do some computations on that domain, in which I have several new functions(supposed all (D,D)->D), say, f1, f2, f3, how do I say f1 and f3 are commutative, while f2 is not?

One choice is adding properties inference with static analysis into the compiler(is there a possibility this inference algorithm be designed perfect?). Another is to define the property commutativity directly on the function *, instead of the domain. Or both.