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Edit detail for SandBoxMaybe revision 26 of 46

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Editor: Bill Page
Time: 2008/05/27 13:41:04 GMT-7
Note: Maybe(T:Type)==

changed:
- == Integer add
-    subtractIfCan(x,y) ==
-      x > y => x-y
-      "failed"
   == Integer add
     subtractIfCan(x,y) ==
       x > y => x-y
       "failed"

spad
)abbrev domain MAYBE Maybe Maybe(T: Type) == Union(T,"failed")
spad
   Compiling OpenAxiom source code from file 
      /var/zope2/var/LatexWiki/3867167196268790065-25px001.spad using 
      Spad compiler.
   MAYBE abbreviates domain Maybe 
------------------------------------------------------------------------
   initializing NRLIB MAYBE for Maybe 
   compiling into NRLIB MAYBE 
(time taken in buildFunctor:  0)
;;;     ***       |Maybe| REDEFINED
;;;     ***       |Maybe| REDEFINED
Time: 0 SEC.
   Cumulative Statistics for Constructor Maybe
      Time: 0 seconds
   >> System error:
   PROG2 is not of type NUMBER.

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/zope2/var/LatexWiki/6798525157762352212-25px002.spad using 
      Spad compiler.
   MAYBE abbreviates domain Maybe 
------------------------------------------------------------------------
   initializing NRLIB MAYBE for Maybe 
   compiling into NRLIB MAYBE 
(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 cat 
(|Type|)   has no 
(|UnionCategory| |#1| "failed")    finalizing NRLIB MAYBE 
   Processing Maybe for Browser database:
--->-->Maybe(): Missing Description
------------------------------------------------------------------------
   Maybe is now explicitly exposed in frame initial 
   Maybe will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MAYBE.NRLIB/code.o

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/zope2/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/zope2/var/LatexWiki/2205496008028295448-25px004.spad using 
      Spad compiler.
   MYFIELD abbreviates domain MyField 
------------------------------------------------------------------------
   initializing NRLIB MYFIELD for MyField 
   compiling into NRLIB MYFIELD 
****** Domain: $ already in scope
augmenting $: (CharacteristicNonZero)
augmenting (Integer): (PolynomialFactorizationExplicit)
****** Domain: $ already in scope
augmenting $: (CharacteristicNonZero)
augmenting (Integer): (PolynomialFactorizationExplicit)
augmenting (Integer): (ConvertibleTo (Pattern (Float)))
augmenting (Integer): (Eltable (Integer) (Integer))
augmenting (Integer): (Evalable (Integer))
augmenting (Integer): (InnerEvalable (Symbol) (Integer))
augmenting (Integer): (PartialDifferentialRing (Symbol))
augmenting (Integer): (PatternMatchable (Float))
augmenting (Integer): (PolynomialFactorizationExplicit)
augmenting (Integer): (RetractableTo (Symbol))
(time taken in buildFunctor:  43)
;;;     ***       |MyField| REDEFINED
;;;     ***       |MyField| REDEFINED
Time: 0.85 SEC.
   Cumulative Statistics for Constructor MyField
      Time: 0.85 seconds
   finalizing NRLIB MYFIELD 
   Processing MyField for Browser database:
--->-->MyField(): Missing Description
------------------------------------------------------------------------
   MyField is now explicitly exposed in frame initial 
   MyField will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MYFIELD.NRLIB/code.o

axiom
)sh MyField MyField is a domain constructor Abbreviation for MyField is MYFIELD This constructor is exposed in this frame. Issue )edit /var/zope2/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 : () -> % ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % 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 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 : (%,(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 : (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 ?^? : (%,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 % init : () -> % if Integer has STEP 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 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 ?~=? : (%,%) -> Boolean

axiom
x:Maybe(Integer)
Type: Void
axiom
x:=-3
LatexWiki Image(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/zope2/var/LatexWiki/7945389118523770429-25px008.spad using 
      Spad 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((= ((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
------------------------------------------------------------------------
   Maybe2 is now explicitly exposed in frame initial 
   Maybe2 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MAYBE2.NRLIB/code.o

axiom
)show Maybe2 Maybe2 T$: Type is a domain constructor Abbreviation for Maybe2 is MAYBE2 This constructor is exposed in this frame. Issue )edit /var/zope2/var/LatexWiki/7945389118523770429-25px008.spad to see algebra source code for MAYBE2 ------------------------------- Operations -------------------------------- ?=? : (%,%) -> Boolean autoCoerce : % -> failed autoCoerce : % -> T$ 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)

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/zope2/var/LatexWiki/1259072050906152969-25px011.spad using 
      Spad compiler.
   MYPAIR abbreviates domain MyPair 
------------------------------------------------------------------------
   initializing NRLIB MYPAIR for MyPair 
   compiling into NRLIB MYPAIR 
(time taken in buildFunctor:  0)
;;;     ***       |MyPair| REDEFINED
;;;     ***       |MyPair| REDEFINED
Time: 0 SEC.
   Cumulative Statistics for Constructor MyPair
      Time: 0 seconds
   >> System error:
   SETRECORDELT is not of type NUMBER.

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/zope2/var/LatexWiki/5737796087530002187-25px013.spad using 
      Spad compiler.
   MYPAIR2 abbreviates domain MyPair2 
------------------------------------------------------------------------
   initializing NRLIB MYPAIR2 for MyPair2 
   compiling into NRLIB MYPAIR2 
(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 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|))    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
------------------------------------------------------------------------
   MyPair2 is now explicitly exposed in frame initial 
   MyPair2 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MYPAIR2.NRLIB/code.o

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/zope2/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)

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?