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SandBoxMaybe

last edited 11 years ago by Bill Page

Edit detail for SandBoxMaybe revision 46 of 46

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

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

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 04 APR 2022 05:52:28 PM):

; /var/aw/var/LatexWiki/MAYBE.NRLIB/MAYBE.fasl written
; compilation finished in 0:00:00.005
------------------------------------------------------------------------
   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 --------------------------------

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): (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): (RetractableTo (Symbol))
(time taken in buildFunctor:  90)

;;;     ***       |MyField| REDEFINED

;;;     ***       |MyField| REDEFINED
Time: 0.19 SEC.

   Cumulative Statistics for Constructor MyField
      Time: 0.19 seconds

   finalizing NRLIB MYFIELD 
   Processing MyField for Browser database:
--->-->MyField(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYFIELD.NRLIB/MYFIELD.lsp" (written 04 APR 2022 05:52:28 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.
 86 Names for 119 Operations in this Domain.
------------------------------- Operations --------------------------------

 ?*? : (Integer, %) -> %               ?*? : (PositiveInteger, %) -> %
 ?*? : (%, Integer) -> %               ?*? : (%, %) -> %
 ?+? : (%, %) -> %                     ?-? : (%, %) -> %
 -? : % -> %                           ?/? : (Integer, Integer) -> %
 ?/? : (%, %) -> %                     ?<? : (%, %) -> Boolean
 ?<=? : (%, %) -> Boolean              ?=? : (%, %) -> Boolean
 ?>? : (%, %) -> Boolean               ?>=? : (%, %) -> Boolean
 D : (%, NonNegativeInteger) -> %      D : % -> %
 OMwrite : (%, Boolean) -> String      OMwrite : % -> String
 1 : () -> %                           0 : () -> %
 ?^? : (%, Integer) -> %               ?^? : (%, PositiveInteger) -> %
 abs : % -> %                          annihilate? : (%, %) -> Boolean
 antiCommutator : (%, %) -> %          associates? : (%, %) -> Boolean
 associator : (%, %, %) -> %           ceiling : % -> Integer
 coerce : % -> OutputForm              coerce : Fraction(Integer) -> %
 coerce : Integer -> %                 coerce : % -> %
 commutator : (%, %) -> %              convert : % -> DoubleFloat
 convert : % -> Float                  convert : % -> InputForm
 convert : % -> Pattern(Integer)       denom : % -> Integer
 denominator : % -> %                  differentiate : % -> %
 factor : % -> Factored(%)             floor : % -> Integer
 fractionPart : % -> %                 gcd : List(%) -> %
 gcd : (%, %) -> %                     hash : % -> SingleInteger
 init : () -> %                        inv : % -> %
 latex : % -> String                   lcm : List(%) -> %
 lcm : (%, %) -> %                     max : (%, %) -> %
 min : (%, %) -> %                     negative? : % -> Boolean
 numer : % -> Integer                  numerator : % -> %
 one? : % -> Boolean                   opposite? : (%, %) -> Boolean
 positive? : % -> Boolean              prime? : % -> Boolean
 ?quo? : (%, %) -> %                   recip : % -> Union(%,"failed")
 ?rem? : (%, %) -> %                   retract : % -> Fraction(Integer)
 retract : % -> Integer                sample : () -> %
 sign : % -> Integer                   sizeLess? : (%, %) -> Boolean
 smaller? : (%, %) -> Boolean          squareFree : % -> Factored(%)
 squareFreePart : % -> %               unit? : % -> Boolean
 unitCanonical : % -> %                wholePart : % -> Integer
 zero? : % -> Boolean                  ?~=? : (%, %) -> Boolean
 ?*? : (Fraction(Integer), %) -> %
 ?*? : (NonNegativeInteger, %) -> %
 ?*? : (%, Fraction(Integer)) -> %
 D : (%, (Integer -> Integer), NonNegativeInteger) -> %
 D : (%, (Integer -> Integer)) -> %
 OMwrite : (OpenMathDevice, %, Boolean) -> Void
 OMwrite : (OpenMathDevice, %) -> Void
 ?^? : (%, NonNegativeInteger) -> %
 characteristic : () -> NonNegativeInteger
 differentiate : (%, (Integer -> Integer), NonNegativeInteger) -> %
 differentiate : (%, (Integer -> Integer)) -> %
 differentiate : (%, NonNegativeInteger) -> %
 divide : (%, %) -> Record(quotient: %,remainder: %)
 euclideanSize : % -> NonNegativeInteger
 expressIdealMember : (List(%), %) -> Union(List(%),"failed")
 exquo : (%, %) -> Union(%,"failed")
 extendedEuclidean : (%, %) -> Record(coef1: %,coef2: %,generator: %)
 extendedEuclidean : (%, %, %) -> Union(Record(coef1: %,coef2: %),"failed")
 factorFraction : % -> Fraction(Factored(Integer))
 factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))
 factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))
 gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
 hashUpdate! : (HashState, %) -> HashState
 lcmCoef : (%, %) -> Record(llcm_res: %,coeff1: %,coeff2: %)
 leftPower : (%, NonNegativeInteger) -> %
 leftPower : (%, PositiveInteger) -> %
 leftRecip : % -> Union(%,"failed")
 map : ((Integer -> Integer), %) -> %
 multiEuclidean : (List(%), %) -> Union(List(%),"failed")
 nextItem : % -> Union(%,"failed")
 patternMatch : (%, Pattern(Integer), PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%)
 principalIdeal : List(%) -> Record(coef: List(%),generator: %)
 reducedSystem : Matrix(%) -> Matrix(Integer)
 reducedSystem : (Matrix(%), Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer))
 retractIfCan : % -> Union(Fraction(Integer),"failed")
 retractIfCan : % -> Union(Integer,"failed")
 rightPower : (%, NonNegativeInteger) -> %
 rightPower : (%, PositiveInteger) -> %
 rightRecip : % -> Union(%,"failed")
 solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)), SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed")
 squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))
 subtractIfCan : (%, %) -> Union(%,"failed")
 unitNormal : % -> Record(unit: %,canonical: %,associate: %)

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

Macro versus domain

fricas

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

Type: Void

fricas

)sh Maybe(Integer)

 Union(Integer,"failed") is a domain constructor.
 5 Names for 11 Operations in this Domain.
------------------------------- 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 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 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 04 APR 2022 05:52:28 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)

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 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 
****** comp fails at level 1 with expression: ******
((|RecordCategory| (|:| X T$) (|:| Y T$)))
****** level 1  ******
$x:= (RecordCategory (: X T$) (: Y 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 SEC.

   Cumulative Statistics for Constructor MyNonNegativeInteger
      Time: 0 seconds

--------------non extending category----------------------
.. MyNonNegativeInteger of cat 
(|Join| (|IntegerNumberSystem|)
        (CATEGORY |domain|
         (SIGNATURE |subtractIfCan| ((|Union| $ "failed") $ $))))   has no 
(|LinearlyExplicitOver| (|Integer|))    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 04 APR 2022 05:52:28 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

... --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:

fricas

)version

Value = "FriCAS 1.3.7 compiled at Wed Jun 30 16:44:06 UTC 2021"

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:

fricas

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

   Domain is not a valid type.

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 1.3.7 compiled at Wed Jun 30 16:44:06 UTC 2021"

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?

... --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.