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spad
)abbrev domain MAYBE Maybe
Maybe(T: Type) == Union(T,"failed")
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3867167196268790065-25px001.spad
      using old system compiler.
   MAYBE abbreviates domain Maybe 
------------------------------------------------------------------------
   initializing NRLIB MAYBE for Maybe 
   compiling into NRLIB MAYBE 
****** comp fails at level 1 with expression: ******
((|UnionCategory| T$ "failed"))
****** level 1  ******
$x:= (UnionCategory T$ failed)
$m:= $EmptyMode
$f:=
((((T$ # #) (|$DomainsInScope| # #))))
>> Apparent user error: cannot compile (UnionCategory T$ failed)

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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6798525157762352212-25px002.spad
      using old system compiler.
   MAYBE abbreviates domain Maybe 
------------------------------------------------------------------------
   initializing NRLIB MAYBE for Maybe 
   compiling into NRLIB MAYBE 
;;; *** |Maybe| REDEFINED
;;; *** |Maybe| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor Maybe Time: 0 seconds
--------------non extending category---------------------- .. Maybe(#1) of cat (|Type|) has no (|UnionCategory| |#1| "failed") finalizing NRLIB MAYBE Processing Maybe for Browser database: --->-->Maybe(): Missing Description ; compiling file "/var/aw/var/LatexWiki/MAYBE.NRLIB/MAYBE.lsp" (written 31 JUL 2013 05:08:18 PM):
; /var/aw/var/LatexWiki/MAYBE.NRLIB/MAYBE.fasl written ; compilation finished in 0:00:00.006 ------------------------------------------------------------------------ Maybe is now explicitly exposed in frame initial Maybe will be automatically loaded when needed from /var/aw/var/LatexWiki/MAYBE.NRLIB/MAYBE

fricas
)show Maybe
Maybe(T$: Type) is a domain constructor Abbreviation for Maybe is MAYBE This constructor is exposed in this frame. ------------------------------- Operations --------------------------------
>> System error: The variable T$ is unbound.

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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2205496008028295448-25px004.spad
      using old system compiler.
   MYFIELD abbreviates domain MyField 
------------------------------------------------------------------------
   initializing NRLIB MYFIELD for MyField 
   compiling into NRLIB MYFIELD 
****** Domain: $ already in scope
augmenting $: (CharacteristicNonZero)
****** Domain: (Integer) already in scope
augmenting (Integer): (PolynomialFactorizationExplicit)
****** Domain: (Integer) already in scope
augmenting (Integer): (ConvertibleTo (Pattern (Float)))
****** Domain: (Integer) already in scope
augmenting (Integer): (Eltable (Integer) (Integer))
****** Domain: (Integer) already in scope
augmenting (Integer): (Evalable (Integer))
****** Domain: (Integer) already in scope
augmenting (Integer): (InnerEvalable (Symbol) (Integer))
****** Domain: (Integer) already in scope
augmenting (Integer): (PartialDifferentialRing (Symbol))
****** Domain: (Integer) already in scope
augmenting (Integer): (PatternMatchable (Float))
****** Domain: (Integer) already in scope
augmenting (Integer): (PolynomialFactorizationExplicit)
****** Domain: (Integer) already in scope
augmenting (Integer): (RetractableTo (Symbol))
(time taken in buildFunctor:  100)
;;; *** |MyField| REDEFINED
;;; *** |MyField| REDEFINED Time: 0.15 SEC.
Cumulative Statistics for Constructor MyField Time: 0.15 seconds
finalizing NRLIB MYFIELD Processing MyField for Browser database: --->-->MyField(): Missing Description ; compiling file "/var/aw/var/LatexWiki/MYFIELD.NRLIB/MYFIELD.lsp" (written 31 JUL 2013 05:08:18 PM):
; /var/aw/var/LatexWiki/MYFIELD.NRLIB/MYFIELD.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/MYFIELD

fricas
)sh MyField
MyField is a domain constructor Abbreviation for MyField is MYFIELD This constructor is exposed in this frame. ------------------------------- Operations -------------------------------- ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % ?*? : (%,%) -> % ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ?-? : (%,%) -> % -? : % -> % ?/? : (Integer,Integer) -> % ?/? : (%,%) -> % ?=? : (%,%) -> Boolean 1 : () -> % 0 : () -> % ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % annihilate? : (%,%) -> Boolean associates? : (%,%) -> 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 opposite? : (%,%) -> Boolean prime? : % -> Boolean ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ?rem? : (%,%) -> % retract : % -> Integer sample : () -> % sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) squareFreePart : % -> % unit? : % -> Boolean unitCanonical : % -> % zero? : % -> Boolean ?~=? : (%,%) -> Boolean ?*? : (NonNegativeInteger,%) -> % ?<? : (%,%) -> Boolean if Integer has ORDSET ?<=? : (%,%) -> Boolean if Integer has ORDSET ?>? : (%,%) -> Boolean if Integer has ORDSET ?>=? : (%,%) -> Boolean if Integer has ORDSET D : (%,(Integer -> Integer)) -> % D : (%,(Integer -> Integer),NonNegativeInteger) -> % D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) D : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) D : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) D : (%,Symbol) -> % if Integer has PDRING(SYMBOL) D : (%,NonNegativeInteger) -> % if Integer has DIFRING D : % -> % if Integer has DIFRING OMwrite : % -> String if Integer has INS and Integer has OM OMwrite : (%,Boolean) -> String if Integer has INS and Integer has OM OMwrite : (OpenMathDevice,%) -> Void if Integer has INS and Integer has OM OMwrite : (OpenMathDevice,%,Boolean) -> Void if Integer has INS and Integer has OM ?^? : (%,NonNegativeInteger) -> % 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 : (%,(Integer -> Integer)) -> % differentiate : (%,(Integer -> Integer),NonNegativeInteger) -> % differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) differentiate : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) differentiate : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) differentiate : (%,Symbol) -> % if Integer has PDRING(SYMBOL) differentiate : (%,NonNegativeInteger) -> % if Integer has DIFRING differentiate : % -> % if Integer has DIFRING 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(%) hashUpdate! : (HashState,%) -> HashState init : () -> % if Integer has STEP lcmCoef : (%,%) -> Record(llcm_res: %,coeff1: %,coeff2: %) 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 smaller? : (%,%) -> Boolean if Integer has COMPAR 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 versus domain
fricas
macro Maybe(T) == Union(T,"failed")
Type: Void
fricas
)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 ?~=? : (%,%) -> Boolean

fricas
x:Maybe(Integer)
Type: Void
fricas
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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7945389118523770429-25px008.spad
      using old system compiler.
   MAYBE2 abbreviates domain Maybe2 
------------------------------------------------------------------------
   initializing NRLIB MAYBE2 for Maybe2 
   compiling into NRLIB MAYBE2 
   compiling exported coerce : T$ -> $
Time: 0.01 SEC.
(time taken in buildFunctor: 0)
;;; *** |Maybe2| REDEFINED
;;; *** |Maybe2| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor Maybe2 Time: 0.01 seconds
--------------non extending category---------------------- .. Maybe2(#1) of cat (CATEGORY |domain| (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE |autoCoerce| (|failed| $)) (SIGNATURE |autoCoerce| (|#1| $)) (SIGNATURE |autoCoerce| ($ |failed|)) (SIGNATURE |autoCoerce| ($ |#1|)) (SIGNATURE |case| ((|Boolean|) $ |failed|)) (SIGNATURE |case| ((|Boolean|) $ |#1|)) (SIGNATURE |coerce| (|failed| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |coerce| ($ |#1|))) has no (|UnionCategory| |#1| "failed") finalizing NRLIB MAYBE2 Processing Maybe2 for Browser database: --->-->Maybe2(constructor): Not documented!!!! --->-->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(): Missing Description ; compiling file "/var/aw/var/LatexWiki/MAYBE2.NRLIB/MAYBE2.lsp" (written 31 JUL 2013 05:08:18 PM):
; /var/aw/var/LatexWiki/MAYBE2.NRLIB/MAYBE2.fasl written ; compilation finished in 0:00:00.009 ------------------------------------------------------------------------ Maybe2 is now explicitly exposed in frame initial Maybe2 will be automatically loaded when needed from /var/aw/var/LatexWiki/MAYBE2.NRLIB/MAYBE2

fricas
)show Maybe2
Maybe2(T$: Type) is a domain constructor Abbreviation for Maybe2 is MAYBE2 This constructor is exposed in this frame. ------------------------------- Operations -------------------------------- ?=? : (%,%) -> Boolean autoCoerce : % -> failed autoCoerce : % -> T$ autoCoerce : failed -> % autoCoerce : T$ -> % ?case? : (%,failed) -> Boolean ?case? : (%,T$) -> Boolean coerce : % -> failed coerce : % -> T$ coerce : % -> OutputForm coerce : T$ -> %

fricas
y:Maybe2(Integer)
Type: Void
fricas
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)

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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1259072050906152969-25px011.spad
      using old system compiler.
   MYPAIR abbreviates domain MyPair 
------------------------------------------------------------------------
   initializing NRLIB MYPAIR for MyPair 
   compiling into NRLIB MYPAIR 
   Semantic Errors: 
      [1] compColonInside: colon inside expressions is unsupported
Warnings: [1] RecordCategory has no value
****** comp fails at level 2 with expression: ****** (|RecordCategory| | << | (|:| X T$) | >> | (|:| Y T$)) ****** level 2 ****** $x:= (: X T$) $m:= $EmptyMode $f:= ((((T$ # #) (|$DomainsInScope| # #))))
>> Apparent user error: cannot compile (RecordCategory (: X T$) (: Y T$))

fricas
)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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5737796087530002187-25px013.spad
      using old system compiler.
   MYPAIR2 abbreviates domain MyPair2 
------------------------------------------------------------------------
   initializing NRLIB MYPAIR2 for MyPair2 
   compiling into NRLIB MYPAIR2 
;;; *** |MyPair2| REDEFINED
;;; *** |MyPair2| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor MyPair2 Time: 0 seconds
--------------non extending category---------------------- .. MyPair2(#1) of cat (CATEGORY |domain| (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |.| ((|Integer|) $ X)) (SIGNATURE |.| ((|Integer|) $ Y)) (SIGNATURE |setelt| ((|Integer|) $ X (|Integer|))) (SIGNATURE |setelt| ((|Integer|) $ Y (|Integer|))) (SIGNATURE ~= ((|Boolean|) $ $)) (SIGNATURE |construct| ($ (|Integer|) (|Integer|)))) has no (|RecordCategory| (|:| X |#1|) (|:| Y |#1|)) >> System error: code vector slot is (Boolean) ; must be number

fricas
)show MyPair2(Integer)
MyPair2 is an unknown constructor and so is unavailable. Did you mean to use -> but type something different instead?

fricas
x2:MyPair2(INT):=[-1,-2]
MyPair2 is an unknown constructor and so is unavailable. Did you mean to use -> but type something different instead?

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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5893753003779373514-25px016.spad
      using old system compiler.
   MYNNI abbreviates domain MyNonNegativeInteger 
------------------------------------------------------------------------
   initializing NRLIB MYNNI for MyNonNegativeInteger 
   compiling into NRLIB MYNNI 
   compiling exported subtractIfCan : ($,$) -> Union($,failed)
Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |MyNonNegativeInteger| REDEFINED
;;; *** |MyNonNegativeInteger| REDEFINED Time: 0.01 SEC.
Cumulative Statistics for Constructor MyNonNegativeInteger Time: 0.01 seconds
(|RealConstant|) extends (|ConvertibleTo| (|DoubleFloat|)) but not (|ConvertibleTo| (|String|)) --------------non extending category---------------------- .. MyNonNegativeInteger of cat (|Join| (|IntegerNumberSystem|) (CATEGORY |domain| (SIGNATURE |subtractIfCan| ((|Union| $ "failed") $ $)))) has no (|ConvertibleTo| (|String|)) finalizing NRLIB MYNNI Processing MyNonNegativeInteger for Browser database: --->-->MyNonNegativeInteger(constructor): Not documented!!!! --->-->MyNonNegativeInteger((subtractIfCan ((Union % failed) % %))): Not documented!!!! --->-->MyNonNegativeInteger(): Missing Description ; compiling file "/var/aw/var/LatexWiki/MYNNI.NRLIB/MYNNI.lsp" (written 31 JUL 2013 05:08:18 PM):
; /var/aw/var/LatexWiki/MYNNI.NRLIB/MYNNI.fasl written ; compilation finished in 0:00:00.009 ------------------------------------------------------------------------ MyNonNegativeInteger is now explicitly exposed in frame initial MyNonNegativeInteger will be automatically loaded when needed from /var/aw/var/LatexWiki/MYNNI.NRLIB/MYNNI

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

Do we have a `without' construct?

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.

The version of OpenAxiom being used for this page was build from svn on May 27, 2008:
fricas
)version
Value = "FriCAS 1.2.1 compiled at Friday July 26, 2013 at 15:08:49 "

Re: without construct --page, Tue, 27 May 2008 15:46:58 -0700 reply
No, it's only in my imagination.

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.

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:
fricas
Maybe3(T: Domain):Domain == Union(T,"failed")
Function declaration Maybe3 : NIL -> NIL has been added to workspace.
Type: Void
fricas
x:Maybe3(Integer):=-2
fricas
Compiling function Maybe3 with type NIL -> NIL 
Cannot generate conversion for argument #1 in Maybe3 from type Type to NIL . x:="failed"

\label{eq2}\mbox{\tt "failed"}(2)
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:

fricas
)version
Value = "FriCAS 1.2.1 compiled at Friday July 26, 2013 at 15:08:49 "

This example still fails:

fricas
xy:MyPair2(INT):=[-1,2]
MyPair2 is an unknown constructor and so is unavailable. Did you mean to use -> but type something different instead?

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.



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