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SandBoxSpecies

Edit detail for SandBoxSpecies revision 1 of 8

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Editor: kratt6 Time: 2008/06/12 08:07:40 GMT-7
Note:

changed:
-
Test species in axiom/FriCAS.

The species project is written in Aldor.  Thus we need to load the libraries explicitly:
\begin{axiom}
)cd ~/combinat/src
)re ../lib/combinat.input
\end{axiom}

We took the decision not to rely on the Axiom algebra.  Unfortunately, this means that integration in Axiom is a little unsatisfactory.  Eg., instead of 'Integer' and 'List', we need to use 'ACInteger' and 'ACList'.  Often explicit coercions are necessary. 

This should give the set partitions of {1,2,3,4}
\begin{axiom}
l: SetSpecies ACINT := set [i::ACINT for i in 1..4]
[structures(l)$Partition ACINT]$ACLIST(Partition ACINT)
\end{axiom}

\begin{aldor}
#includeDir "/var/lib/zope/combinat/include"
#libraryDir "/var/lib/zope/combinat/lib"
#include "combinat"

macro {
        E == EmptySetSpecies;
        X == SingletonSpecies;
        + == Plus;
        * == Times;
}

A(L: LabelType): CombinatorialSpecies L == (E + X*A*A)(L) add;
\end{aldor}

Due to types not being first class objects in the Axiom interpreter, we had to write a little interpreter to allow for user specified species: 

\begin{axiom}
T := Interpret([parse "Plus(SingletonSpecies, Times(Self, Self))"], ACInteger);
)sh T
l := set [i::ACINT for i in 1..3]
[structures(l)$T]$ACLIST(T)
\end{axiom}

We are still not 100% sure how to represent isomorphism types.  So far, we had two ideas: in the 'iso-experiment' branch, we have separate (but tightly connected) representation:

\begin{axiom}
IsoT := ACIsomorphismType(ACINT, T)
)sh IsoT
m: MultiSet ACINT := multiset([1$ACINT for i in 1..3]::ACList ACINT)
[isomorphismTypes(m)$IsoT]$ACList(IsoT)
\end{axiom}

debugging needed here...

Test species in axiom/FriCAS?.

The species project is written in Aldor. Thus we need to load the libraries explicitly:

axiom)cd ~/combinat/src
   The current FriCAS default directory is /var/lib/zope/combinat/src
)re ../lib/combinat.input
)lib cscombinatversion.ao
   Reading /var/lib/zope/combinat/src/cscombinatversion.asy
   LibraryInformationCombinat is now explicitly exposed in frame
      initial
   LibraryInformationCombinat will be automatically loaded when needed
      from /var/lib/zope/combinat/src/cscombinatversion
)lib csaxcompat.ao
   Reading /var/lib/zope/combinat/src/csaxcompat.asy
   ACCharacter is now explicitly exposed in frame initial
   ACCharacter will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACFraction is now explicitly exposed in frame initial
   ACFraction will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACIntegerTools is now explicitly exposed in frame initial
   ACIntegerTools will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACInteger is now explicitly exposed in frame initial
   ACInteger will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACList is now explicitly exposed in frame initial
   ACList will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACMachineInteger is now explicitly exposed in frame initial
   ACMachineInteger will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACPrimitiveArray is now explicitly exposed in frame initial
   ACPrimitiveArray will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACString is now explicitly exposed in frame initial
   ACString will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACSymbol is now explicitly exposed in frame initial
   ACSymbol will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   Array is now explicitly exposed in frame initial
   Array will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   ACLabelType is now explicitly exposed in frame initial
   ACLabelType will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   OutputType is now explicitly exposed in frame initial
   OutputType will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
   TotallyOrderedType is now explicitly exposed in frame initial
   TotallyOrderedType will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat
)lib csaxcompat2.ao
   Reading /var/lib/zope/combinat/src/csaxcompat2.asy
   ExpressionTreeExpt is now explicitly exposed in frame initial
   ExpressionTreeExpt will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreeLeaf is now explicitly exposed in frame initial
   ExpressionTreeLeaf will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreePlus is now explicitly exposed in frame initial
   ExpressionTreePlus will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreePrefix is now explicitly exposed in frame initial
   ExpressionTreePrefix will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreeTimes is now explicitly exposed in frame initial
   ExpressionTreeTimes will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTree is now explicitly exposed in frame initial
   ExpressionTree will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   GeneratorException is now explicitly exposed in frame initial
   GeneratorException will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   Generator is now explicitly exposed in frame initial
   Generator will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreeOperator is now explicitly exposed in frame initial
   ExpressionTreeOperator will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   Partial is now explicitly exposed in frame initial
   Partial will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionType is now explicitly exposed in frame initial
   ExpressionType will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   GeneratorExceptionType is now explicitly exposed in frame initial
   GeneratorExceptionType will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
Won't parse: (Type)->NIL
)lib csistruc.ao
   Reading /var/lib/zope/combinat/src/csistruc.asy
   SparseAdditiveArray is now explicitly exposed in frame initial
   SparseAdditiveArray will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csistruc
   SparseFiniteMonoidRing is now explicitly exposed in frame initial
   SparseFiniteMonoidRing will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csistruc
   IndexedFreeAdditiveCombinationType is now explicitly exposed in
      frame initial
   IndexedFreeAdditiveCombinationType will be automatically loaded when
      needed from /var/lib/zope/combinat/src/csistruc
   IndexedFreeArithmeticType is now explicitly exposed in frame initial
   IndexedFreeArithmeticType will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csistruc
)lib csdistpoly.ao
   Reading /var/lib/zope/combinat/src/csdistpoly.asy
   SparseDistributedPolynomial is now explicitly exposed in frame
      initial
   SparseDistributedPolynomial will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csdistpoly
)lib csstream.ao
   Reading /var/lib/zope/combinat/src/csstream.asy
   DataStream is now explicitly exposed in frame initial
   DataStream will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csstream
)lib csseries.ao
   Reading /var/lib/zope/combinat/src/csseries.asy
   FormalPowerSeries is now explicitly exposed in frame initial
   FormalPowerSeries will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csseries
   FormalPowerSeriesCategory is now explicitly exposed in frame initial
   FormalPowerSeriesCategory will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csseries
   SeriesOrder is now explicitly exposed in frame initial
   SeriesOrder will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csseries
)lib csidxpp.ao
   Reading /var/lib/zope/combinat/src/csidxpp.asy
   SparseIndexedPowerProduct is now explicitly exposed in frame initial
   SparseIndexedPowerProduct will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csidxpp
)lib cssiprimes.ao
   Reading /var/lib/zope/combinat/src/cssiprimes.asy
   SmallIntegerPrimes is now explicitly exposed in frame initial
   SmallIntegerPrimes will be automatically loaded when needed from
      /var/lib/zope/combinat/src/cssiprimes
)lib cssitools.ao
   Reading /var/lib/zope/combinat/src/cssitools.asy
   SmallIntegerTools is now explicitly exposed in frame initial
   SmallIntegerTools will be automatically loaded when needed from
      /var/lib/zope/combinat/src/cssitools
)lib csgseries.ao
   Reading /var/lib/zope/combinat/src/csgseries.asy
   CycleIndexSeries is now explicitly exposed in frame initial
   CycleIndexSeries will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csgseries
   CycleIndexVariable is now explicitly exposed in frame initial
   CycleIndexVariable will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csgseries
   ExponentialGeneratingSeries is now explicitly exposed in frame
      initial
   ExponentialGeneratingSeries will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csgseries
   OrdinaryGeneratingSeries is now explicitly exposed in frame initial
   OrdinaryGeneratingSeries will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csgseries
)lib csmultinom.ao
   Reading /var/lib/zope/combinat/src/csmultinom.asy
   MultinomialTools is now explicitly exposed in frame initial
   MultinomialTools will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csmultinom
)lib csspexpr.ao
   Reading /var/lib/zope/combinat/src/csspexpr.asy
   SpeciesExpression is now explicitly exposed in frame initial
   SpeciesExpression will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspexpr
)lib csspecies.ao
   Reading /var/lib/zope/combinat/src/csspecies.asy
   ACIsomorphismType is now explicitly exposed in frame initial
   ACIsomorphismType will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Subset is now explicitly exposed in frame initial
   Subset will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Times is now explicitly exposed in frame initial
   Times will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Augment is now explicitly exposed in frame initial
   Augment will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   CharacteristicSpecies is now explicitly exposed in frame initial
   CharacteristicSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Combination is now explicitly exposed in frame initial
   Combination will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Compose is now explicitly exposed in frame initial
   Compose will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Derivative is now explicitly exposed in frame initial
   Derivative will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   DropEmpty is now explicitly exposed in frame initial
   DropEmpty will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   EmptySetSpecies is now explicitly exposed in frame initial
   EmptySetSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   FunctorialCompose is now explicitly exposed in frame initial
   FunctorialCompose will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiCompose is now explicitly exposed in frame initial
   MultiCompose will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiDerivative is now explicitly exposed in frame initial
   MultiDerivative will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiPlus is now explicitly exposed in frame initial
   MultiPlus will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiSetCombination is now explicitly exposed in frame initial
   MultiSetCombination will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiSetPartition is now explicitly exposed in frame initial
   MultiSetPartition will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiSet is now explicitly exposed in frame initial
   MultiSet will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiSubset is now explicitly exposed in frame initial
   MultiSubset will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   MultiTimes is now explicitly exposed in frame initial
   MultiTimes will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Multiple is now explicitly exposed in frame initial
   Multiple will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   CombinatorialSpecies is now explicitly exposed in frame initial
   CombinatorialSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   NonEmpty is now explicitly exposed in frame initial
   NonEmpty will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Plus is now explicitly exposed in frame initial
   Plus will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   RestrictedSpecies is now explicitly exposed in frame initial
   RestrictedSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   SetSpecies is now explicitly exposed in frame initial
   SetSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   IsomorphismTypeCategory is now explicitly exposed in frame initial
   IsomorphismTypeCategory will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csspecies
   SingletonSpecies is now explicitly exposed in frame initial
   SingletonSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
   Partition is now explicitly exposed in frame initial
   Partition will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csspecies
)lib csexamples.ao
   Reading /var/lib/zope/combinat/src/csexamples.asy
   ACBinaryTree is now explicitly exposed in frame initial
   ACBinaryTree will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csexamples
   Combination is already explicitly exposed in frame initial
   Combination will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csexamples
   Generator is already explicitly exposed in frame initial
   Generator will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csexamples
   SetSpecies is already explicitly exposed in frame initial
   SetSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csexamples
Won't parse: (Type)->NIL
Won't parse: (ACLabelType)->NIL
)lib csinterp.ao
   Reading /var/lib/zope/combinat/src/csinterp.asy
   Interpret is now explicitly exposed in frame initial
   Interpret will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csinterp
   InterpretingTools is now explicitly exposed in frame initial
   InterpretingTools will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csinterp
   LabelSpecies is now explicitly exposed in frame initial
   LabelSpecies will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csinterp
)lib csparse.ao
   Reading /var/lib/zope/combinat/src/csparse.asy
   MyParser is now explicitly exposed in frame initial
   MyParser will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csparse

We took the decision not to rely on the Axiom algebra. Unfortunately, this means that integration in Axiom is a little unsatisfactory. Eg., instead of Integer and List, we need to use ACInteger and ACList. Often explicit coercions are necessary.

This should give the set partitions of {1,2,3,4}

axiom
l: SetSpecies ACINT := set [i::ACINT for i in 1..4]

(1)

Type: SetSpecies? ACInteger?

axiom
[structures(l)$Partition ACINT]$ACLIST(Partition ACINT)

(2)

Type: ACList? Partition ACInteger?

aldor#includeDir "/var/lib/zope/combinat/include"
#libraryDir "/var/lib/zope/combinat/lib"
#include "combinat"
macro {
        E == EmptySetSpecies;
        X == SingletonSpecies;
        + == Plus;
        * == Times;
}
A(L: LabelType): CombinatorialSpecies L == (E + X*A*A)(L) add;

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/5200085684951427974-25px003.as using 
      AXIOM-XL compiler and options 
-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
#1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
   Compiling Lisp source code from file 
      ./5200085684951427974-25px003.lsp
   Issuing )library command for 5200085684951427974-25px003
   Reading /var/lib/zope/combinat/src/5200085684951427974-25px003.asy
   A is now explicitly exposed in frame initial 
   A will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/5200085684951427974-25px003

Due to types not being first class objects in the Axiom interpreter, we had to write a little interpreter to allow for user specified species:

axiom
T := Interpret([parse "Plus(SingletonSpecies, Times(Self, Self))"], ACInteger);

Type: Domain

axiom)sh T
 Interpret([CONCATPlus(PAREN (AGGLST (CONCAT (NOTHING) SingletonSpecies) (CONCAT
Times (PAREN (AGGLST (CONCAT (NOTHING) Self) (CONCAT (NOTHING)
Self))))))],ACInteger) is a domain constructor.
 Abbreviation for Interpret is INTERPR
 This constructor is exposed in this frame.
 Issue )edit csinterp.as to see algebra source code for INTERPR
------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                coerce : % -> OutputForm
 hash : % -> SingleInteger             latex : % -> String
 ?~=? : (%,%) -> Boolean
 ?<<? : (OutputForm,%) -> OutputForm
 IsomorphismType : () -> IsomorphismTypeCategory ACInteger
 cycleIndexSeries : () -> CycleIndexSeries
 expression : () -> SpeciesExpression
 generatingSeries : () -> ExponentialGeneratingSeries
 isomorphismTypeGeneratingSeries : () -> OrdinaryGeneratingSeries
 structures : SetSpecies ACInteger -> Generator %
l := set [i::ACINT for i in 1..3]

(3)

Type: SetSpecies? ACInteger?

axiom
[structures(l)$T]$ACLIST(T)

(4)

Type: ACList? Interpret([CONCATPlus(PAREN (AGGLST (CONCAT (NOTHING) SingletonSpecies) (CONCAT Times (PAREN (AGGLST (CONCAT (NOTHING) Self) (CONCAT (NOTHING) Self))))))]?,ACInteger?)

We are still not 100% sure how to represent isomorphism types. So far, we had two ideas: in the iso-experiment branch, we have separate (but tightly connected) representation:

axiom
IsoT := ACIsomorphismType(ACINT, T)

(5)

Type: Domain

axiom)sh IsoT
 ACIsomorphismType(ACInteger,Interpret([CONCATPlus(PAREN (AGGLST (CONCAT
(NOTHING) SingletonSpecies) (CONCAT Times (PAREN (AGGLST (CONCAT (NOTHING) Self)
(CONCAT (NOTHING) Self))))))],ACInteger)) is a domain constructor.
 Abbreviation for ACIsomorphismType is ACISOMO
 This constructor is exposed in this frame.
 Issue )edit csspecies.as to see algebra source code for ACISOMO
------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                coerce : % -> OutputForm
 hash : % -> SingleInteger             latex : % -> String
 ?~=? : (%,%) -> Boolean
 ?<<? : (OutputForm,%) -> OutputForm
 isomorphismTypes : MultiSet ACInteger -> Generator %
m: MultiSet ACINT := multiset([1$ACINT for i in 1..3]::ACList ACINT)

(6)

Type: MultiSet? ACInteger?

axiom[isomorphismTypes(m)$IsoT]$ACList(IsoT)
   >> System error:
   Caught fatal error [memory may be damaged]

debugging needed here...