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	SandBoxSpecies
SandBoxSpeciesAldor ←	↑	→ SandBoxSpeciesCategory

SandBoxSpeciesBayreuth

Edit detail for SandBoxSpeciesBayreuth revision 2 of 12

	1 2 3 4 5 6 7 8 9 10 11 12
Editor: Thomas Feulner Time: 2008/06/16 05:30:20 GMT-7
Note:

changed:
-A(L: LabelType): CombinatorialSpecies L == (E + X*A*A)(L) add;
-Subsets(L: LabelType): CombinatorialSpecies L == (SetSpecies*SetSpecies)(L) add;
BTree(L: LabelType): CombinatorialSpecies L == (E + X*BTree*BTree)(L) add;
MySubset(L: LabelType): CombinatorialSpecies L == (SetSpecies*SetSpecies)(L) add;

changed:
-X := A(Z)
-
-labels: SetSpecies Z := set [7::Z,8::Z,15::Z]
X := BTree(Z)

labels: SetSpecies Z := set [1::Z,2::Z,4::Z]

changed:
-X:=EmptySetSpecies(Z)
[structures(labels)$EmptySetSpecies(Z)]$ACLIST(EmptySetSpecies(Z))
[structures(labels)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))
[structures(labels2)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))
[structures(labels)$SetSpecies(Z)]$ACLIST(SetSpecies(Z))
subs:=[(structures(labels)$MySubset(Z))]$ACLIST(MySubset(Z))
subs.2
[structures(labels)$Subset(Z)]$ACLIST(Subset(Z))
[structures(labels)$Partition(Z)]$ACLIST(Partition(Z))
\end{axiom}

Two ways to construct LinearOrder:
\begin{aldor}
#includeDir "/var/lib/zope/combinat/include"
#libraryDir "/var/lib/zope/combinat/lib"
#include "combinat"

macro {
        E == EmptySetSpecies;
        X == SingletonSpecies;
        + == Plus;
        * == Times;
}
MyLinearOrder(L:LabelType):CombinatorialSpecies L == (E + X*MyLinearOrder)(L) add;
\end{aldor}
\begin{axiom}
X:=MyLinearOrder(Z)

changed:
-X:=SingletonSpecies(Z)
MyLinearOrder2 := Interpret([parse "Plus(EmptySetSpecies,Times(SingletonSpecies,Self))"], ACInteger);
X:=MyLinearOrder2(Z)

removed:
-X:=SingletonSpecies(Z)
-[structures(labels2)$X]$ACLIST(X)
-X:=SetSpecies(Z)
-[structures(labels)$X]$ACLIST(X)
-X:=Subsets(Z)
-subs:=[(structures(labels)$X)]$ACLIST(X)
-subs.2

changed:
-I can't use the following species in Axiom. 
-
I can't use the following species because of the Mathaction specific build. But they are implemented in Combinat!

changed:
-
-The last error occurs, because we are using the Permutation Category (?) of Axiom? 
-
-
-
-
-
Permutation does already exist within Axiom, use another name.

Now with other labels:
\begin{axiom}
labels3 : SetSpecies ACString := set ["abc"::ACString,"def"::ACString,"xyz"::ACString]
[structures(labels)$Subset(ACString)]$ACLIST(Subset(ACString))

\end{axiom}

axiom)cd ~/combinat/src
   The current FriCAS default directory is /var/lib/zope/combinat/src

axiom)re ../lib/combinat.input

axiom
)lib cscombinatversion.ao

axiom

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

axiom
)lib csaxcompat.ao

axiom

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

axiom
)lib csaxcompat2.ao

axiom

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
   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
   Partial is now explicitly exposed in frame initial 
   Partial will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
Won't parse: (Type)->NIL

axiom
)lib csistruc.ao

axiom

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

axiom
)lib csdistpoly.ao

axiom

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

axiom
)lib csstream.ao

axiom

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

axiom
)lib csseries.ao

axiom

Reading /var/lib/zope/combinat/src/csseries.asy
   SeriesOrder is now explicitly exposed in frame initial 
   SeriesOrder will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csseries
   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

axiom
)lib csidxpp.ao

axiom

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

axiom
)lib cssiprimes.ao

axiom

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

axiom
)lib cssitools.ao

axiom

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

axiom
)lib csgseries.ao

axiom

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

axiom
)lib csmultinom.ao

axiom

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

axiom
)lib csspexpr.ao

axiom

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

axiom
)lib csspecies.ao

axiom

Reading /var/lib/zope/combinat/src/csspecies.asy
   SetSpecies is now explicitly exposed in frame initial 
   SetSpecies 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
   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
   CombinatorialSpecies is now explicitly exposed in frame initial 
   CombinatorialSpecies 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
   NonEmpty is now explicitly exposed in frame initial 
   NonEmpty 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
   Partition is now explicitly exposed in frame initial 
   Partition 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

axiom
)lib csexamples.ao

axiom

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
   SetSpecies is already explicitly exposed in frame initial 
   SetSpecies 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
Won't parse: (ACLabelType)->NIL
Won't parse: (Type)->NIL

axiom
)lib csinterp.ao

axiom

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

axiom
)lib csparse.ao

axiom

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

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

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/7896689979910980793-25px002.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 
      ./7896689979910980793-25px002.lsp
   Issuing )library command for 7896689979910980793-25px002
   Reading /var/lib/zope/combinat/src/7896689979910980793-25px002.asy
   BTree is now explicitly exposed in frame initial 
   BTree will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/7896689979910980793-25px002
   MySubset is now explicitly exposed in frame initial 
   MySubset will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/7896689979910980793-25px002

axiom
Z := ACInteger

(1)

Type: Domain

axiom
X := BTree(Z)

(2)

Type: Domain

axiom
labels: SetSpecies Z := set [1::Z,2::Z,4::Z]

(3)

Type: SetSpecies? ACInteger?

axiom
labels2 : SetSpecies Z := set[5005::Z]

(4)

Type: SetSpecies? ACInteger?

axiom)set output tex off

axiom)set output algebra on
[structures(labels)$X]$ACLIST(X)
   (5)
   [((1, "nil"), ((2, "nil"), ((4, "nil"), "nil"))),
    ((1, "nil"), ((4, "nil"), ((2, "nil"), "nil"))),
    ((1, "nil"), ((2, ((4, "nil"), "nil")), "nil")),
    ((1, "nil"), ((4, ((2, "nil"), "nil")), "nil")),
    ((2, "nil"), ((1, "nil"), ((4, "nil"), "nil"))),
    ((2, "nil"), ((4, "nil"), ((1, "nil"), "nil"))),
    ((2, "nil"), ((1, ((4, "nil"), "nil")), "nil")),
    ((2, "nil"), ((4, ((1, "nil"), "nil")), "nil")),
    ((1, ((2, "nil"), "nil")), ((4, "nil"), "nil")),
    ((2, ((1, "nil"), "nil")), ((4, "nil"), "nil")),
    ((4, "nil"), ((1, "nil"), ((2, "nil"), "nil"))),
    ((4, "nil"), ((2, "nil"), ((1, "nil"), "nil"))),
    ((4, "nil"), ((1, ((2, "nil"), "nil")), "nil")),
    ((4, "nil"), ((2, ((1, "nil"), "nil")), "nil")),
    ((1, ((4, "nil"), "nil")), ((2, "nil"), "nil")),
    ((4, ((1, "nil"), "nil")), ((2, "nil"), "nil")),
    ((2, ((4, "nil"), "nil")), ((1, "nil"), "nil")),
    ((4, ((2, "nil"), "nil")), ((1, "nil"), "nil")),
    ((1, ((2, "nil"), ((4, "nil"), "nil"))), "nil"),
    ((1, ((4, "nil"), ((2, "nil"), "nil"))), "nil"),
    ((1, ((2, ((4, "nil"), "nil")), "nil")), "nil"),
    ((1, ((4, ((2, "nil"), "nil")), "nil")), "nil"),
    ((2, ((1, "nil"), ((4, "nil"), "nil"))), "nil"),
    ((2, ((4, "nil"), ((1, "nil"), "nil"))), "nil"),
    ((2, ((1, ((4, "nil"), "nil")), "nil")), "nil"),
    ((2, ((4, ((1, "nil"), "nil")), "nil")), "nil"),
    ((4, ((1, "nil"), ((2, "nil"), "nil"))), "nil"),
    ((4, ((2, "nil"), ((1, "nil"), "nil"))), "nil"),
    ((4, ((1, ((2, "nil"), "nil")), "nil")), "nil"),
    ((4, ((2, ((1, "nil"), "nil")), "nil")), "nil")]

Type: ACList? BTree? ACInteger?

axiom)set output tex on

axiom)set output algebra off
[structures(labels)$EmptySetSpecies(Z)]$ACLIST(EmptySetSpecies(Z))

(5)

Type: ACList? EmptySetSpecies? ACInteger?

axiom
[structures(labels)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))

(6)

Type: ACList? SingletonSpecies? ACInteger?

axiom
[structures(labels2)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))

(7)

Type: ACList? SingletonSpecies? ACInteger?

axiom
[structures(labels)$SetSpecies(Z)]$ACLIST(SetSpecies(Z))

(8)

Type: ACList? SetSpecies? ACInteger?

axiom
subs:=[(structures(labels)$MySubset(Z))]$ACLIST(MySubset(Z))

(9)

Type: ACList? MySubset? ACInteger?

axiom
subs.2

(10)

Type: MySubset? ACInteger?

axiom
[structures(labels)$Subset(Z)]$ACLIST(Subset(Z))

(11)

Type: ACList? Subset ACInteger?

axiom
[structures(labels)$Partition(Z)]$ACLIST(Partition(Z))

(12)

Type: ACList? Partition ACInteger?

Two ways to construct LinearOrder?:

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

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/7566739481302953094-25px004.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 
      ./7566739481302953094-25px004.lsp
   Issuing )library command for 7566739481302953094-25px004
   Reading /var/lib/zope/combinat/src/7566739481302953094-25px004.asy
   MyLinearOrder is now explicitly exposed in frame initial 
   MyLinearOrder will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/7566739481302953094-25px004

axiom
X:=MyLinearOrder(Z)

(13)

Type: Domain

axiom
[structures(labels)$X]$ACLIST(X)

(14)

Type: ACList? MyLinearOrder? ACInteger?

axiomMyLinearOrder2 := Interpret([parse "Plus(EmptySetSpecies,Times(SingletonSpecies,Self))"],
ACInteger);

Type: Domain

axiom
X:=MyLinearOrder2(Z)

(15)

Type: Domain

axiom
[structures(labels)$X]$ACLIST(X)

(16)

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

I can't use the following species because of the Mathaction specific build. But they are implemented in Combinat!

axiomX:=LinearOrder(Z)
   There are no library operations named LinearOrder
      Use HyperDoc Browse or issue
                            )what op LinearOrder
      to learn if there is any operation containing " LinearOrder " in
      its name.
   Cannot find a definition or applicable library operation named
      LinearOrder with argument type(s)
                                   Domain
      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
X:=Cycle(Z)
   There are no library operations named Cycle
      Use HyperDoc Browse or issue
                               )what op Cycle
      to learn if there is any operation containing " Cycle " in its
      name.
   Cannot find a definition or applicable library operation named Cycle
      with argument type(s)
                                   Domain
      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
X:=Permutation(Z)

(17)

Type: Domain

axiom[structures(labels2)$X]$ACLIST(X)
   The function structures is not implemented in Permutation ACInteger
      .

Permutation does already exist within Axiom, use another name.

Now with other labels:

axiom
labels3 : SetSpecies ACString := set [abc,def,xyz]

(18)

Type: SetSpecies? ACString?

axiom[structures(labels)$Subset(ACString)]$ACLIST(Subset(ACString))
   There are 1 exposed and 0 unexposed library operations named
      structures having 1 argument(s) but none was determined to be
      applicable. Use HyperDoc Browse, or issue
                           )display op structures
      to learn more about the available operations. Perhaps
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named
      structures with argument type(s)
                            SetSpecies ACInteger
      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.