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SandBoxMaybe

last edited 12 years ago by Bill Page

Edit detail for SandBoxMaybe revision 45 of 46

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Editor: Bill Page Time: 2013/03/15 20:45:05 GMT+0
Note: newer version of OpenAxiom

removed:
-

... --gdr, Mon, 26 May 2008 14:24:29 -0700 reply

spad

)abbrev domain MAYBE Maybe
Maybe(T: Type) == Union(T,"failed")

spad

   Compiling OpenAxiom source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3867167196268790065-25px001.spad
      using Spad compiler.
   MAYBE abbreviates domain Maybe 
------------------------------------------------------------------------
   initializing NRLIB MAYBE for Maybe 
   compiling into NRLIB MAYBE 
   Adding $ modemaps
   Adding T$ modemaps
(time taken in buildFunctor:  0)

;;;     ***       |Maybe| REDEFINED

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

   Cumulative Statistics for Constructor Maybe
      Time: 0 seconds

   >> System error:
   The value |%bind| is not of type REAL.

need result type --Bill Page, Mon, 26 May 2008 20:25:03 -0700 reply

spad

)abbrev domain MAYBE Maybe
Maybe(T: Type):Type == Union(T,"failed")

spad

   Compiling OpenAxiom source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6798525157762352212-25px002.spad
      using Spad compiler.
   MAYBE abbreviates domain Maybe 
------------------------------------------------------------------------
   initializing NRLIB MAYBE for Maybe 
   compiling into NRLIB MAYBE 
   Adding $ modemaps
   Adding T$ modemaps
(time taken in buildFunctor:  0)

;;;     ***       |Maybe| REDEFINED

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

   Cumulative Statistics for Constructor Maybe
      Time: 0 seconds

--------------non extending category----------------------
   Maybe #1 of category Type
    has no UnionCategory(#1,"failed")
----------------------------------------------------------
   finalizing NRLIB MAYBE 
   Processing Maybe for Browser database:
--->/usr/local/lib/open-axiom/x86_64-unknown-linux-gnu/1.4.0-2011-02-20/src/algebra/MAYBE.spad-->Maybe: Missing Description

; compiling file "/var/aw/var/LatexWiki/MAYBE.NRLIB/code.lsp" (written 25 MAR 2013 03:45:29 PM):
; compiling (/VERSIONCHECK 2)
; compiling (DEFUN |Maybe| ...)
; compiling (DEFUN |Maybe;| ...)
; compiling (MAKEPROP (QUOTE |Maybe|) ...)

; /var/aw/var/LatexWiki/MAYBE.NRLIB/code.fasl written
; compilation finished in 0:00:00.011
------------------------------------------------------------------------
   Maybe is now explicitly exposed in frame initial 
   Maybe will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MAYBE.NRLIB/code.fasl

axiom

)show Maybe

 Maybe T$: Type  is a domain constructor
 Abbreviation for Maybe is MAYBE 
 This constructor is exposed in this frame.
 Issue )edit /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6798525157762352212-25px002.spad to see algebra source code for MAYBE 

------------------------------- Operations --------------------------------
                          No exported operations

need result type --gdr, Mon, 26 May 2008 22:03:52 -0700 reply

No, there should not be a need for specifying result type. In fact, if you specify "Type" as result type, you explicitly ask for not having any exported operation. That wasn't the intent. The intent was to get whatever the right hand side exported as exports. Such as in

spad

)abbrev domain MYFIELD MyField
MyField() == Fraction Integer

spad

   Compiling OpenAxiom source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2205496008028295448-25px004.spad
      using Spad compiler.
   MYFIELD abbreviates domain MyField 
------------------------------------------------------------------------
   initializing NRLIB MYFIELD for MyField 
   compiling into NRLIB MYFIELD 
   Adding $ modemaps
   Adding $ modemaps
 Note: Domain $ already in scope
   augmenting $: CharacteristicNonZero
   Adding Integer modemaps
   augmenting Integer: PolynomialFactorizationExplicit
   Adding $ modemaps
 Note: Domain $ already in scope
   augmenting $: CharacteristicNonZero
   Adding Integer modemaps
   augmenting Integer: PolynomialFactorizationExplicit
   Adding Integer modemaps
   augmenting Integer: ConvertibleTo Pattern Float
   Adding Integer modemaps
   augmenting Integer: Eltable(Integer,Integer)
   Adding Integer modemaps
   augmenting Integer: Evalable Integer
   Adding Integer modemaps
   augmenting Integer: InnerEvalable(Symbol,Integer)
   Adding Integer modemaps
   augmenting Integer: PartialDifferentialSpace Symbol
   Adding Integer modemaps
   augmenting Integer: PatternMatchable Float
   Adding Integer modemaps
   augmenting Integer: PolynomialFactorizationExplicit
   Adding Integer modemaps
   augmenting Integer: RetractableTo Symbol
(time taken in buildFunctor:  340)

;;;     ***       |MyField| REDEFINED

;;;     ***       |MyField| REDEFINED
Time: 0.56 SEC.

   Cumulative Statistics for Constructor MyField
      Time: 0.56 seconds

   finalizing NRLIB MYFIELD 
   Processing MyField for Browser database:
--->-->MyField: Missing Description
; compiling file "/var/aw/var/LatexWiki/MYFIELD.NRLIB/code.lsp" (written 25 MAR 2013 03:45:30 PM):
; compiling (/VERSIONCHECK 2)
; compiling (DEFUN |MyField| ...)
; compiling (DEFUN |MyField;| ...)
; compiling (MAKEPROP (QUOTE |MyField|) ...)
; compiling (MAKEPROP (QUOTE |MyField|) ...)

; /var/aw/var/LatexWiki/MYFIELD.NRLIB/code.fasl written
; compilation finished in 0:00:00.013
------------------------------------------------------------------------
   MyField is now explicitly exposed in frame initial 
   MyField will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYFIELD.NRLIB/code.fasl

axiom

)sh MyField

 MyField  is a domain constructor
 Abbreviation for MyField is MYFIELD 
 This constructor is exposed in this frame.
 Issue )edit /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2205496008028295448-25px004.spad to see algebra source code for MYFIELD 

------------------------------- Operations --------------------------------
 ?*? : (%,Integer) -> %                ?*? : (Integer,%) -> %
 ?*? : (Fraction Integer,%) -> %       ?*? : (%,Fraction Integer) -> %
 ?*? : (%,%) -> %                      ?*? : (Integer,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?**? : (%,Integer) -> %
 ?**? : (%,PositiveInteger) -> %       ?+? : (%,%) -> %
 ?-? : (%,%) -> %                      -? : % -> %
 ?/? : (Integer,Integer) -> %          ?/? : (%,%) -> %
 ?=? : (%,%) -> Boolean                1 : () -> %
 0 : () -> %                           associates? : (%,%) -> Boolean
 before? : (%,%) -> Boolean            coerce : Integer -> %
 coerce : Fraction Integer -> %        coerce : % -> %
 coerce : Integer -> %                 coerce : % -> OutputForm
 denom : % -> Integer                  denominator : % -> %
 factor : % -> Factored %              gcd : List % -> %
 gcd : (%,%) -> %                      hash : % -> SingleInteger
 inv : % -> %                          latex : % -> String
 lcm : List % -> %                     lcm : (%,%) -> %
 numer : % -> Integer                  numerator : % -> %
 one? : % -> Boolean                   prime? : % -> Boolean
 ?quo? : (%,%) -> %                    recip : % -> Union(%,"failed")
 ?rem? : (%,%) -> %                    retract : % -> Integer
 sample : () -> %                      sizeLess? : (%,%) -> Boolean
 squareFree : % -> Factored %          squareFreePart : % -> %
 unit? : % -> Boolean                  unitCanonical : % -> %
 zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,NonNegativeInteger) -> %
 ?<? : (%,%) -> Boolean if Integer has ORDSET
 ?<=? : (%,%) -> Boolean if Integer has ORDSET
 ?>? : (%,%) -> Boolean if Integer has ORDSET
 ?>=? : (%,%) -> Boolean if Integer has ORDSET
 D : (%,NonNegativeInteger) -> % if Integer has DIFFSPC
 D : % -> % if Integer has DIFFSPC
 D : (%,List Symbol,List NonNegativeInteger) -> % if Integer has PDSPC SYMBOL
 D : (%,Symbol,NonNegativeInteger) -> % if Integer has PDSPC SYMBOL
 D : (%,List Symbol) -> % if Integer has PDSPC SYMBOL
 D : (%,Symbol) -> % if Integer has PDSPC SYMBOL
 D : (%,(Integer -> Integer),NonNegativeInteger) -> %
 D : (%,(Integer -> Integer)) -> %
 OMwrite : (OpenMathDevice,%,Boolean) -> Void if Integer has INS and Integer has OM
 OMwrite : (OpenMathDevice,%) -> Void if Integer has INS and Integer has OM
 OMwrite : (%,Boolean) -> String if Integer has INS and Integer has OM
 OMwrite : % -> String if Integer has INS and Integer has OM
 abs : % -> % if Integer has OINTDOM
 ceiling : % -> Integer if Integer has INS
 characteristic : () -> NonNegativeInteger
 charthRoot : % -> Union(%,"failed") if $ has CHARNZ and Integer has PFECAT or Integer has CHARNZ
 coerce : Symbol -> % if Integer has RETRACT SYMBOL
 conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and Integer has PFECAT
 convert : % -> DoubleFloat if Integer has REAL
 convert : % -> Float if Integer has REAL
 convert : % -> InputForm if Integer has KONVERT INFORM
 convert : % -> Pattern Float if Integer has KONVERT PATTERN FLOAT
 convert : % -> Pattern Integer if Integer has KONVERT PATTERN INT
 differentiate : (%,NonNegativeInteger) -> % if Integer has DIFFSPC
 differentiate : % -> % if Integer has DIFFSPC
 differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Integer has PDSPC SYMBOL
 differentiate : (%,Symbol,NonNegativeInteger) -> % if Integer has PDSPC SYMBOL
 differentiate : (%,List Symbol) -> % if Integer has PDSPC SYMBOL
 differentiate : (%,Symbol) -> % if Integer has PDSPC SYMBOL
 differentiate : (%,(Integer -> Integer),NonNegativeInteger) -> %
 differentiate : (%,(Integer -> Integer)) -> %
 divide : (%,%) -> Record(quotient: %,remainder: %)
 ?.? : (%,Integer) -> % if Integer has ELTAB(INT,INT)
 euclideanSize : % -> NonNegativeInteger
 eval : (%,Symbol,Integer) -> % if Integer has IEVALAB(SYMBOL,INT)
 eval : (%,List Symbol,List Integer) -> % if Integer has IEVALAB(SYMBOL,INT)
 eval : (%,List Equation Integer) -> % if Integer has EVALAB INT
 eval : (%,Equation Integer) -> % if Integer has EVALAB INT
 eval : (%,Integer,Integer) -> % if Integer has EVALAB INT
 eval : (%,List Integer,List Integer) -> % if Integer has EVALAB INT
 expressIdealMember : (List %,%) -> Union(List %,"failed")
 exquo : (%,%) -> Union(%,"failed")
 extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
 extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
 factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if Integer has PFECAT
 factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if Integer has PFECAT
 floor : % -> Integer if Integer has INS
 fractionPart : % -> % if Integer has EUCDOM
 gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
 init : () -> % if Integer has STEP
 leftReducedSystem : Vector % -> Matrix Integer
 leftReducedSystem : (Vector %,%) -> Record(mat: Matrix Integer,vec: Vector Integer)
 leftReducedSystem : (Vector %,%) -> Record(mat: Matrix Integer,vec: Vector Integer) if Integer has LINEXP INT
 leftReducedSystem : Vector % -> Matrix Integer if Integer has LINEXP INT
 map : ((Integer -> Integer),%) -> %
 max : (%,%) -> % if Integer has ORDSET
 min : (%,%) -> % if Integer has ORDSET
 multiEuclidean : (List %,%) -> Union(List %,"failed")
 negative? : % -> Boolean if Integer has OINTDOM
 nextItem : % -> Union(%,"failed") if Integer has STEP
 patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if Integer has PATMAB FLOAT
 patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if Integer has PATMAB INT
 positive? : % -> Boolean if Integer has OINTDOM
 principalIdeal : List % -> Record(coef: List %,generator: %)
 random : () -> % if Integer has INS
 reducedSystem : Matrix % -> Matrix Integer
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer)
 reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if Integer has LINEXP INT
 reducedSystem : Matrix % -> Matrix Integer if Integer has LINEXP INT
 retract : % -> Integer if Integer has RETRACT INT
 retract : % -> Fraction Integer if Integer has RETRACT INT
 retract : % -> Symbol if Integer has RETRACT SYMBOL
 retractIfCan : % -> Union(Integer,"failed") if Integer has RETRACT INT
 retractIfCan : % -> Union(Fraction Integer,"failed") if Integer has RETRACT INT
 retractIfCan : % -> Union(Symbol,"failed") if Integer has RETRACT SYMBOL
 retractIfCan : % -> Union(Integer,"failed")
 sign : % -> Integer if Integer has OINTDOM
 solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if Integer has PFECAT
 squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if Integer has PFECAT
 subtractIfCan : (%,%) -> Union(%,"failed")
 unitNormal : % -> Record(unit: %,canonical: %,associate: %)
 wholePart : % -> Integer if Integer has EUCDOM

macro --Bill Page, Tue, 27 May 2008 07:30:43 -0700 reply

Macro versus domain

axiom

macro Maybe(T) == Union(T,"failed")

Type: Void

axiom

)sh Maybe(Integer)

 Union(Integer,"failed") is a domain constructor.
------------------------------- Operations --------------------------------

 ?=? : (%,%) -> Boolean                autoCoerce : % -> "failed"
 autoCoerce : % -> Integer             autoCoerce : "failed" -> %
 autoCoerce : Integer -> %             ?case? : (%,"failed") -> Boolean
 ?case? : (%,Integer) -> Boolean       coerce : % -> "failed"
 coerce : % -> Integer                 coerce : % -> OutputForm
 hash : % -> SingleInteger             ?~=? : (%,%) -> Boolean

axiom

x:Maybe(Integer)

Type: Void

axiom

x:=-3

$\label{eq1}- 3$

(1)

Type: Union(Integer,...)

explicit exports --Bill Page, Tue, 27 May 2008 07:46:20 -0700 reply

spad

)abbrev domain MAYBE2 Maybe2
Maybe2(T: Type):with
    _= : (%,%) -> Boolean
    autoCoerce : % -> failed
    autoCoerce : % -> T
    autoCoerce : failed -> %
    autoCoerce : T -> %
    _case: (%,failed) -> Boolean
    _case: (%,T) -> Boolean
    coerce : % -> failed
    coerce : % -> T
    coerce : % -> OutputForm
    coerce : T -> %
  == Union(T,"failed") add
    coerce(x:T):% == autoCoerce(x)

spad

   Compiling OpenAxiom source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7945389118523770429-25px008.spad
      using Spad compiler.
   MAYBE2 abbreviates domain Maybe2 
------------------------------------------------------------------------
   initializing NRLIB MAYBE2 for Maybe2 
   compiling into NRLIB MAYBE2 
   Adding $ modemaps
   Adding T$ modemaps
   compiling exported coerce : T -> %
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Maybe2| REDEFINED

;;;     ***       |Maybe2| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor Maybe2
      Time: 0 seconds

--------------non extending category----------------------
   Maybe2 #1 of category CATEGORY(domain,=: (%,%) -> Boolean,
      autoCoerce: % -> failed,autoCoerce: % -> #1,autoCoerce: failed
       -> %,autoCoerce: #1 -> %,case: (%,failed) -> Boolean,case: (
      %,#1) -> Boolean,coerce: % -> failed,coerce: % -> #1,coerce: 
      % -> OutputForm,coerce: #1 -> %)
    has no UnionCategory(#1,"failed")
----------------------------------------------------------
   finalizing NRLIB MAYBE2 
   Processing Maybe2 for Browser database:
--->-->Maybe2((= ((Boolean) % %))): Not documented!!!!
--->-->Maybe2((autoCoerce (failed %))): Not documented!!!!
--->-->Maybe2((autoCoerce (T$ %))): Not documented!!!!
--->-->Maybe2((autoCoerce (% failed))): Not documented!!!!
--->-->Maybe2((autoCoerce (% T$))): Not documented!!!!
--->-->Maybe2((case ((Boolean) % failed))): Not documented!!!!
--->-->Maybe2((case ((Boolean) % T$))): Not documented!!!!
--->-->Maybe2((coerce (failed %))): Not documented!!!!
--->-->Maybe2((coerce (T$ %))): Not documented!!!!
--->-->Maybe2((coerce ((OutputForm) %))): Not documented!!!!
--->-->Maybe2((coerce (% T$))): Not documented!!!!
--->-->Maybe2(constructor): Not documented!!!!
--->-->Maybe2: Missing Description
; compiling file "/var/aw/var/LatexWiki/MAYBE2.NRLIB/code.lsp" (written 25 MAR 2013 03:45:30 PM):
; compiling (/VERSIONCHECK 2)
; compiling (DEFUN |MAYBE2;coerce;T$$;1| ...)
; compiling (DEFUN |Maybe2| ...)
; compiling (DEFUN |Maybe2;| ...)
; compiling (MAKEPROP (QUOTE |Maybe2|) ...)

; /var/aw/var/LatexWiki/MAYBE2.NRLIB/code.fasl written
; compilation finished in 0:00:00.010
------------------------------------------------------------------------
   Maybe2 is now explicitly exposed in frame initial 
   Maybe2 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MAYBE2.NRLIB/code.fasl

axiom

)show Maybe2

 Maybe2 T$: Type  is a domain constructor
 Abbreviation for Maybe2 is MAYBE2 
 This constructor is exposed in this frame.
 Issue )edit /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7945389118523770429-25px008.spad to see algebra source code for MAYBE2 

------------------------------- Operations --------------------------------
 ?=? : (%,%) -> Boolean                autoCoerce : % -> failed
 autoCoerce : % -> T                   autoCoerce : failed -> %
 autoCoerce : T -> %                   ?case? : (%,failed) -> Boolean
 ?case? : (%,T) -> Boolean             coerce : % -> failed
 coerce : % -> T                       coerce : % -> OutputForm
 coerce : T -> %

axiom

y:Maybe2(Integer)

Type: Void

axiom

y:=-3

Function:  autoCoerce : Integer -> % is missing from domain: Maybe2 Integer
   Internal Error
   The function autoCoerce with signature $(Integer) is missing from 
      domain Maybe2(Integer) 

   Continuing to read the file...

y:=autoCoerce(-3::Integer)

   Internal Error
   The function autoCoerce with signature Integer -> % is missing from
      domain Maybe2(Integer) 

   Continuing to read the file...

macro --gdr, Tue, 27 May 2008 08:01:39 -0700 reply

But, the use of macro is a workaround a fundamental problem in the compiler -- which I'm desperately trying to convey.

explicit exports --gdr, Tue, 27 May 2008 08:03:19 -0700 reply

This and the original bug comes from the same source in the compiler.

Re: problem in the compiler --Bill Page, Tue, 27 May 2008 08:06:29 -0700 reply

I agree. I am just trying to understand it.

Why does:

  Maybe(T: Type) == Union(T,"failed")

and:

  Maybe(T: Type):Type == Union(T,"failed")

have such different semantics? Is this a good thing? Maybe there is a need for something that stands for the type of the rhs:

  Maybe(T: Type):rhs == Union(T,"failed")

Re: problem in the compiler --gdr, Tue, 27 May 2008 09:20:19 -0700 reply

Remember that Type is a category that exports no operation. so when you say Maybe(T: Type): Type, you are exlicitly saying that Maybe(T: Type) is a domain constructor that exports no operation. Indeed, if you try )show with OpenAxiom?, you will see that it say, Maybe has no exported operations. Which is right.

However, when one says Maybe(T: Type) == Union(T, "failed"), one is saying that Maybe(T) is exactly like Union(T,"failed"), except for the name. Consequently, Maybe has the exports inferred from the right hand side. This works for all domains, except the `builtin' domains. If you try Record or Enumeration, you should hit a bug in the compiler at some point.

exports inferred from RHS --Bill Page, Tue, 27 May 2008 12:58:47 -0700 reply

spad

)abbrev domain MYPAIR MyPair
MyPair(T:Type) == Record(X:T,Y:T)

spad

   Compiling OpenAxiom source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1259072050906152969-25px011.spad
      using Spad compiler.
   MYPAIR abbreviates domain MyPair 
------------------------------------------------------------------------
   initializing NRLIB MYPAIR for MyPair 
   compiling into NRLIB MYPAIR 
   Adding $ modemaps
   Adding T$ modemaps
(time taken in buildFunctor:  0)

;;;     ***       |MyPair| REDEFINED

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

   Cumulative Statistics for Constructor MyPair
      Time: 0.01 seconds

   >> System error:
   The value SETRECORDELT is not of type REAL.

axiom

)show MyPair(Integer)

   MyPair is an unknown constructor and so is unavailable. Did you mean
      to use -> but type something different instead?

spad

)abbrev domain MYPAIR2 MyPair2
MyPair2(T:Type): with
    _= : (%,%) -> Boolean
    coerce : % -> OutputForm
    copy : % -> %
    _. : (%,X) -> Integer
    _. : (%,Y) -> Integer
    setelt : (%,X,Integer) -> Integer
    setelt : (%,Y,Integer) -> Integer
    _~_= : (%,%) -> Boolean
    construct : (Integer,Integer) -> %
  == Record(X:T,Y:T)

spad

   Compiling OpenAxiom source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5737796087530002187-25px013.spad
      using Spad compiler.
   MYPAIR2 abbreviates domain MyPair2 
------------------------------------------------------------------------
   initializing NRLIB MYPAIR2 for MyPair2 
   compiling into NRLIB MYPAIR2 
   Adding $ modemaps
   Adding T$ modemaps
(time taken in buildFunctor:  0)

;;;     ***       |MyPair2| REDEFINED

;;;     ***       |MyPair2| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MyPair2
      Time: 0 seconds

--------------non extending category----------------------
   MyPair2 #1 of category CATEGORY(domain,=: (%,%) -> Boolean,coerce
      : % -> OutputForm,copy: % -> %,.: (%,X) -> Integer,.: (%,Y)
       -> Integer,setelt: (%,X,Integer) -> Integer,setelt: (%,Y,
      Integer) -> Integer,~=: (%,%) -> Boolean,construct: (Integer,
      Integer) -> %)
    has no RecordCategory(X: #1,Y: #1)
----------------------------------------------------------
   finalizing NRLIB MYPAIR2 
   Processing MyPair2 for Browser database:
--->-->MyPair2((= ((Boolean) % %))): Not documented!!!!
--->-->MyPair2((coerce ((OutputForm) %))): Not documented!!!!
--->-->MyPair2((copy (% %))): Not documented!!!!
--->-->MyPair2((. ((Integer) % X))): Not documented!!!!
--->-->MyPair2((. ((Integer) % Y))): Not documented!!!!
--->-->MyPair2((setelt ((Integer) % X (Integer)))): Not documented!!!!
--->-->MyPair2((setelt ((Integer) % Y (Integer)))): Not documented!!!!
--->-->MyPair2((~= ((Boolean) % %))): Not documented!!!!
--->-->MyPair2((construct (% (Integer) (Integer)))): Not documented!!!!
--->-->MyPair2(constructor): Not documented!!!!
--->-->MyPair2: Missing Description
; compiling file "/var/aw/var/LatexWiki/MYPAIR2.NRLIB/code.lsp" (written 25 MAR 2013 03:45:30 PM):
; compiling (/VERSIONCHECK 2)
; compiling (DEFUN |MyPair2| ...)
; compiling (DEFUN |MyPair2;| ...)
; compiling (MAKEPROP (QUOTE |MyPair2|) ...)

; /var/aw/var/LatexWiki/MYPAIR2.NRLIB/code.fasl written
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   MyPair2 is now explicitly exposed in frame initial 
   MyPair2 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYPAIR2.NRLIB/code.fasl

axiom

)show MyPair2(Integer)

 MyPair2 Integer is a domain constructor.
 Abbreviation for MyPair2 is MYPAIR2 
 This constructor is exposed in this frame.
 Issue )edit /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5737796087530002187-25px013.spad to see algebra source code for MYPAIR2 

------------------------------- Operations --------------------------------

 ?.? : (%,X) -> Integer                ?.? : (%,Y) -> Integer
 ?=? : (%,%) -> Boolean                coerce : % -> OutputForm
 copy : % -> %                         setelt : (%,X,Integer) -> Integer
 setelt : (%,Y,Integer) -> Integer     ?~=? : (%,%) -> Boolean
 construct : (Integer,Integer) -> %

axiom

x2:MyPair2(INT):=[-1,-2]

   Internal Error
   The function construct with signature (Integer,Integer) -> % is 
      missing from domain MyPair2(Integer) 

   Continuing to read the file...

Maybe(T:Type)== --Bill Page, Tue, 27 May 2008 13:37:18 -0700 reply

gdr wrote:

one is saying that Maybe(T) is exactly like Union(T,"failed")

What is the advantage of this notation over the use of a macro?

Besides domain composition, constant substitution and passing of parameters, like:

  Maybe(T: Type) == Union(Fraction T,"failed")

what other useful expressions are allowed on the rhs?

Persumably add would not make sense because we cannot specify new exports - at least not without explicitly specifying all exports.

This is a common problem for possible re-use of code (subject of another thread). For example:

   NonNegativeInteger():rhs
     without
       _-:(%,%) -> %
     with
       subtractIfCan:(%,%)->Union(%,"failed")
   == Integer add
     subtractIfCan(x,y) ==
       x > y => x-y
       "failed"

What should I put instead of rhs? Should I be able to explicitly "forget" (or replace) some exports?

spad

)abbrev domain MYNNI MyNonNegativeInteger
MyNonNegativeInteger():IntegerNumberSystem with
    subtractIfCan:(%,%)->Union(%,"failed")
  == Integer add
    subtractIfCan(x:%,y:%):Union(%,"failed") ==
      x > y => x-y
      "failed"

spad

   Compiling OpenAxiom source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5893753003779373514-25px016.spad
      using Spad compiler.
   MYNNI abbreviates domain MyNonNegativeInteger 
------------------------------------------------------------------------
   initializing NRLIB MYNNI for MyNonNegativeInteger 
   compiling into NRLIB MYNNI 
   Adding $ modemaps
   compiling exported subtractIfCan : (%,%) -> Union(%,failed)
   Adding Boolean modemaps
Time: 0.01 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MyNonNegativeInteger| REDEFINED

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

   Cumulative Statistics for Constructor MyNonNegativeInteger
      Time: 0.01 seconds

(|RealConstant|)    extends 
(|ConvertibleTo| (|DoubleFloat|))    but not 
(|ConvertibleTo| (|String|)) --------------non extending category----------------------
   MyNonNegativeInteger of category IntegerNumberSystem with 
         subtractIfCan : (%,%) -> Union(%,"failed")
    has no ConvertibleTo String
----------------------------------------------------------
   finalizing NRLIB MYNNI 
   Processing MyNonNegativeInteger for Browser database:
--->-->MyNonNegativeInteger((subtractIfCan ((Union % failed) % %))): Not documented!!!!
--->-->MyNonNegativeInteger(constructor): Not documented!!!!
--->-->MyNonNegativeInteger: Missing Description
; compiling file "/var/aw/var/LatexWiki/MYNNI.NRLIB/code.lsp" (written 25 MAR 2013 03:45:30 PM):
; compiling (/VERSIONCHECK 2)
; compiling (DEFUN |MYNNI;subtractIfCan;2$U;1| ...)
; compiling (DEFUN |MyNonNegativeInteger| ...)
; compiling (DEFUN |MyNonNegativeInteger;| ...)
; compiling (MAKEPROP (QUOTE |MyNonNegativeInteger|) ...)
; compiling (MAKEPROP (QUOTE |MyNonNegativeInteger|) ...)

; /var/aw/var/LatexWiki/MYNNI.NRLIB/code.fasl written
; compilation finished in 0:00:00.012
------------------------------------------------------------------------
   MyNonNegativeInteger is now explicitly exposed in frame initial 
   MyNonNegativeInteger will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYNNI.NRLIB/code.fasl

... --gdr, Tue, 27 May 2008 15:28:30 -0700 reply

A macro name is not a constructor name, so that makes a fundamental difference.

... --gdr, Tue, 27 May 2008 15:29:31 -0700 reply

Do we have a `without' construct?

... --gdr, Tue, 27 May 2008 15:39:25 -0700 reply

With an OpenAxiom? built on May 16, 2008 I have a different behaviour: The assignment is rejected because there is no conversion from [-1,2] to MyPair2(INT). Which is right. The output of the compiler indicates to me that the website is running a very old OpenAxiom?.

not so old --page, Tue, 27 May 2008 15:45:24 -0700 reply

The version of OpenAxiom? being used for this page was build from svn on May 27, 2008:

axiom

)version

Value = "Monday March 7, 2011 at 19:18:42 "

Re: without construct --page, Tue, 27 May 2008 15:46:58 -0700 reply

No, it's only in my imagination.

Re: macro --page, Tue, 27 May 2008 16:52:11 -0700 reply

Previously Bill Page wrote:

  Macro versus domain

    macro Maybe(T) == Union(T,"failed")

gdr wrote:

  But, the use of macro is a workaround a fundamental problem
  in the compiler ...

Bill Page wrote:

  Agreed, but what is the advantage of this notation:

    Maybe(T:Type) == Union(T,"failed")

  over the use of a macro?

gdr wrote:

  A macro name is not a constructor name, so that makes
  a fundamental difference.

Of course there is a difference to the compiler but is there a "fundamental difference" to the programmer? Does the language benefit from being able to compile domains with an identical list exports as some other domain?

I suppose here's one possible advantage:

To provide standard simplified interfaces to more complex domains defined in the library.
Macros are not stored as part of the Axiom library.

macro --gdr, Tue, 27 May 2008 16:58:18 -0700 reply

Well, as you said, macros are not stored in the databases. In OpenAxiom?, one can use constructor names as arguments to functions. That does not work with macro names -- they don't really define a new category or domain or package.

Something you can only do in OpenAxiom?! --page, Tue, 27 May 2008 17:42:52 -0700 reply

Because you can pass domains as arguments to functions:

axiom

Maybe3(T: Domain):Domain == Union(T,"failed")

   Function declaration Maybe3 : Domain -> Domain has been added to 
      workspace.

Type: Void

axiom

x:Maybe3(Integer):=-2

axiom

Compiling function Maybe3 with type Domain -> Domain

$\label{eq2}- 2$

(2)

Type: Union(Integer,...)

axiom

x:="failed"

$\label{eq3}\mbox{\tt "failed"}$

(3)

Type: Union("failed",...)

Internal Error --page, Tue, 27 May 2008 20:49:00 -0700 reply

gdr wrote:

  With an OpenAxiom built on May 16, 2008 I have a different behaviour:
  The assignment is rejected because there is no conversion from
  [-1,2] to MyPair2(INT).

After upgrading this page to OpenAxiom? built with current (May 27, 2008 Rev: 614) source:

axiom

)version

Value = "Monday March 7, 2011 at 19:18:42 "

This example still fails:

axiom

xy:MyPair2(INT):=[-1,2]

   Internal Error
   The function construct with signature (Integer,Integer) -> % is 
      missing from domain MyPair2(Integer) 

   Continuing to read the file...

... --gdr, Tue, 27 May 2008 23:34:12 -0700 reply

this is weird: I cannot reproduce the failure.

I can reproduce the failure --gdr, Wed, 28 May 2008 00:05:03 -0700 reply
Now, I can: I failed to copy and paste properly. And on reflection, the fact the interpreter rejected the code should have alerted me to close closer. And yes, the failure is related to the same bug.