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SandBoxMaybe

last edited 13 years ago by Bill Page

Edit detail for SandBoxMaybe revision 18 of 46

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Editor: Bill Page Time: 2008/05/27 12:46:05 GMT-7
Note:

added:

From BillPage Tue May 27 12:46:05 -0700 2008
From: Bill Page
Date: Tue, 27 May 2008 12:46:05 -0700
Subject: 
Message-ID: <20080527124605-0700@axiom-wiki.newsynthesis.org>

Yes, I understand the meaning of 'Type', but "earlier":http://axiom-wiki.newsynthesis.org/SandBoxMaybe#msg20080526202503-0700@axiom-wiki.newsynthesis.org in this thread shows the error message::

   System error:
   The variable T$ is unbound.

This page is running OpenAxiom:
\begin{axiom}
)version
\end{axiom}

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

fricas

(1) -> <spad>

fricas

)abbrev domain MAYBE Maybe
Maybe(T: Type) == Union(T,"failed")</spad>

fricas

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 
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 15 SEP 2026 05:10:50 AM):

; wrote /var/aw/var/LatexWiki/MAYBE.NRLIB/MAYBE.fasl
; compilation finished in 0:00:00.000
------------------------------------------------------------------------
   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:  30722)
Time: 0.07 SEC.

   Cumulative Statistics for Constructor MyField
      Time: 0.07 seconds

   finalizing NRLIB MYFIELD 
   Processing MyField for Browser database:
--->-->MyField(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYFIELD.NRLIB/MYFIELD.lsp" (written 15 SEP 2026 05:10:50 AM):

; wrote /var/aw/var/LatexWiki/MYFIELD.NRLIB/MYFIELD.fasl
; compilation finished in 0:00:00.004
------------------------------------------------------------------------
   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.
 87 names for 120 operations in this domain.
------------------------------- Operations --------------------------------

 0 : () -> %                           1 : () -> %
 ?*? : (%, %) -> %                     ?*? : (%, Integer) -> %
 ?*? : (Integer, %) -> %               ?*? : (PositiveInteger, %) -> %
 ?+? : (%, %) -> %                     -? : % -> %
 ?-? : (%, %) -> %                     ?/? : (%, %) -> %
 ?/? : (Integer, Integer) -> %         ?<? : (%, %) -> Boolean
 ?<=? : (%, %) -> Boolean              ?=? : (%, %) -> Boolean
 ?>? : (%, %) -> Boolean               ?>=? : (%, %) -> Boolean
 D : % -> %                            D : (%, NonNegativeInteger) -> %
 OMwrite : % -> String                 OMwrite : (%, Boolean) -> String
 ?^? : (%, Integer) -> %               ?^? : (%, PositiveInteger) -> %
 abs : % -> %                          annihilate? : (%, %) -> Boolean
 antiCommutator : (%, %) -> %          associates? : (%, %) -> Boolean
 associator : (%, %, %) -> %           ceiling : % -> Integer
 coerce : % -> %                       coerce : Fraction(Integer) -> %
 coerce : Integer -> %                 coerce : % -> OutputForm
 commutator : (%, %) -> %              convert : % -> DoubleFloat
 convert : % -> Float                  convert : % -> InputForm
 convert : % -> Pattern(Integer)       denom : % -> Integer
 denominator : % -> %                  differentiate : % -> %
 factor : % -> Factored(%)             floor : % -> Integer
 fractionPart : % -> %                 gcd : (%, %) -> %
 gcd : List(%) -> %                    hash : % -> SingleInteger
 init : () -> %                        inv : % -> %
 latex : % -> String                   lcm : (%, %) -> %
 lcm : List(%) -> %                    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)) -> %
 ?*? : (Fraction(Integer), %) -> %
 ?*? : (NonNegativeInteger, %) -> %
 D : (%, (Integer -> Integer)) -> %
 D : (%, (Integer -> Integer), NonNegativeInteger) -> %
 OMwrite : (OpenMathDevice, %) -> Void
 OMwrite : (OpenMathDevice, %, Boolean) -> Void
 ?^? : (%, NonNegativeInteger) -> %
 characteristic : () -> NonNegativeInteger
 differentiate : (%, (Integer -> Integer)) -> %
 differentiate : (%, (Integer -> Integer), NonNegativeInteger) -> %
 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,%)
 plenaryPower : (%, PositiveInteger) -> %
 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)
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 15 SEP 2026 05:10:50 AM):

; wrote /var/aw/var/LatexWiki/MAYBE2.NRLIB/MAYBE2.fasl
; compilation finished in 0:00:00.004
------------------------------------------------------------------------
   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.

... --Bill Page, Tue, 27 May 2008 12:46:05 -0700 reply

Yes, I understand the meaning of Type, but earlier in this thread shows the error message:

   System error:
   The variable T$ is unbound.

This page is running OpenAxiom?:

fricas

)version

"FriCAS 1.3.12 compiled at Sat  7 Jun 23:54:49 CEST 2025"